context
stringlengths 545
71.9k
| questionsrc
stringlengths 16
10.2k
| question
stringlengths 11
563
|
|---|---|---|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example .
|
how do you use a cumulative z-table to calculate the percentage between two numbers using their z-scores ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
what is a z-score used for ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example .
|
in what videos does sal teach how to determine z-scores more rigorously ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 .
|
why is the z table ( based on a normal distribution having mean 0 and sd 1 ) usable for any other normal distribution ( having different mean and different sd ) ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete .
|
what if its and interval , such as what is the probability of getting a score between two numbers ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
how do i find absolute value using z score ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 .
|
what is the median , lower quartile and upper quartile of 74 ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean .
|
how can there be two types of standard deviation ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean .
|
hiw do i explain the relationship between z scores and standard deviation ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 .
|
1 ) if 80 % of students are to be promoted , what should be the marks for promotion ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
what is the purpose of calculating z-score ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing .
|
how do you know what problems to draw or not to draw a bell curve ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing .
|
how can i specify my bell curve equation so that the maximum and minimum are defined ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
let 's see . we have a mean of 81 . that 's our mean .
|
so we can indicate the mean with both that little upside down 'h ' symbol by 81 and a greek letter 'm ' ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
what if z-score value is way bigger than the values provided in the table ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
let 's say z=8 , how do you find its probability if 8 does not match with any value of z from the table ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
what if z-score value is way bigger than the values provided in the table ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
let 's say z=8 , how do you find its probability if 8 does not match with any value of z from the table ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing .
|
what is a bell curve ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean .
|
why do you divide by the standard deviation ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it .
|
for a normal distribution with mean -11 and standard deviation 0.2 , what values leaves probability 0.291 in both tails ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it .
|
a study of 55 white mice showed that their average was 3.2 ounces.the standard deviation of the population is 0.9 ounces.which of the following is the 90 % confidence interval for the mean weight per white mouse ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ?
|
why is z-score so important ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 .
|
approximately what percentage of the observations should have a value greater than 35 but less than 55 ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 .
|
would you have to use a standard normal table ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean .
|
if you are working with a z-score , like in the activity set `` z-scores 3 '' ; how do you decide when to subtract the z-score from 1 or just use the given value ?
|
here 's the second problem from ck12.org 's ap statistics flexbook . it 's an open source textbook , essentially . i 'm using it essentially to get some practice on some statistics problems . so here , number 2 . the grades on a statistics midterm for a high school are normally distributed with a mean of 81 and a standard deviation of 6.3 . all right . calculate the z-scores for each of the following exam grades . draw and label a sketch for each example . we can probably do it all on the same example . but the first thing we 'd have to do is just remember what is a z-score . what is a z-score ? a z-score is literally just measuring how many standard deviations away from the mean ? just like that . so we literally just have to calculate how many standard deviations each of these guys are from the mean , and that 's their z-scores . so let me do part a . so we have 65 . so first we can just figure out how far is 65 from the mean . let me just draw one chart here that we can use the entire time . so it 's just our distribution . let 's see . we have a mean of 81 . that 's our mean . and then a standard deviation of 6.3 . so our distribution , they 're telling us that it 's normally distributed . so i can draw a nice bell curve here . they 're saying it 's normally distributed , so that 's as good of a bell curve as i 'm capable of drawing . this is the mean right there at 81 . and the standard deviation is 6.3 . so one standard deviation above and below is going to be 6.3 away from that mean . so if we go 6.3 in the positive direction , that value right there is going to be 87.3 . if we go 6.3 in the negative direction , where does that get us ? what , 74.7 ? right , if we add 6 , it 'll get us to 80.7 , and then 0.3 will get us to 81 . so that 's one standard deviation below and above the mean , and then you 'd add another 6.3 to go 2 standard deviations , so on and so forth . so that 's a drawing of the distribution itself . so let 's figure out the z-scores for each of these grades . 65 is how far ? 65 is maybe going to be here someplace . so we first want to say , well how far is it just from our mean ? so the distance is , you just want to positive number here . well actually , you want a negative number . because you want your z-score to be positive or negative . negative would mean to the left of the mean and positive would mean to the right of the mean . so we say 65 minus 81 . so that 's literally how far away we are . but we want that in terms of standard deviations . so we divide that by the length or the magnitude of our standard deviation . so 65 minus 81 . let 's see , 81 minus 65 is what ? it is 5 plus 11 . it 's 16 . so this is going to be minus 16 over 6.3 . we 'll take our calculator out . and let 's see , if we have minus 16 divided by 6.3 , you get minus 2 point -- oh , it 's like 54 . approximately equal to minus 2.54 . that 's the z-score for a grade of 65 . pretty straightforward . let 's do a couple more . let 's do all of them . 83 . so how is it away from the mean ? well , it 's 83 minus 81 . it 's two grades above the mean . but we want it in terms of standard deviations . how many standard deviations . so this was part a . a was right here . we were 2.5 standard deviations below the mean . so this is part a . 1 , 2 , and then 0.5 . so this was a right there , 65 . and then part b , 83 , 83 is going to be right here . a little bit higher , but right here . and the z-score here , 83 minus 81 divided by 6.3 will get us -- let 's see , clear the calculator . so we have 83 minus 81 is 2 divided by 6.3 . it 's 0.32 , roughly . so here we get 0.32 . so 83 is 0.32 standard deviations above the mean . and so it would be roughly 1/3 third of the standard deviation along the way , right ? because this as one whole standard deviation . so we 're 0.3 of a standard deviation above the mean . choice number c. or not choice , part c , i guess i should call it . 93 . well , we do the same exercise . 93 is how much above the mean ? well , it 's 93 minus 81 is 12 . but we want it in terms of standard deviations . so 12 is how many standard deviations above the mean ? well , it 's going to be almost 2 . let 's take the calculator out . so we get 12 divided by 6.3 . it 's 1.9 standard deviations . its z-score is 1.9 . which means it 's 1.9 standard deviations above the mean . so the mean is 81 , we go one whole standard deviation , and then 0.9 standard deviations , and that 's where a score of 93 would lie , right there . its z-score is 1.9 . and all that means is 1.9 standard deviations above the mean . let 's do the last one . i 'll do it in magenta . d , part d. a score of 100 . we do n't even need the problem anymore . a score of 100 . well , same thing . we figure out how far is 100 above the mean -- remember , the mean was 81 -- and we divide that by the length or the size or the magnitude of our standard deviation . so 100 minus 81 is equal to 19 over 6.3 . so it 's going to be a little over 3 standard deviations . and in the next problem we 'll see what does that imply in terms of the probability of that actually occurring . but if we just want to figure out the z-score , 19 divided by 6.3 is equal to 3.01 . so it 's very close . 3.02 , really , if i were to round . so it 's very close to 3.02 . its z-score is 3.02 , or a grade of 100 is 3.02 standard deviations above the mean . so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart . a little bit above that , 3.02 standard deviations above the mean , that 's where a score of 100 will be . and you can see the probability , the height of this -- that 's what the chart tells us -- it 's actually a very low probability . actually , not just a very low probability of getting something higher than that . because as we learned before , in a probably density function , if this is a continuous , not a discreet , the probability of getting exactly that is 0 , if this was n't discrete . but since this is scores on a test , we know that it 's actually a discrete probability function . but the probability is low of getting higher than that , because you can see where we sit on the bell curve . well anyway , hopefully this at least clarified how to solve for z-scores , which is pretty straightforward mathematically . and in the next video , we 'll interpret z-scores and probabilities a little bit more .
|
so remember , this was the mean right here at 81 . we go 1 standard deviation above the mean , 2 standard deviations above the mean , the third standard deviation above the mean is right there . so we 're sitting right there on our chart .
|
x value is greater than 108 , mean 100 , standard deviation 8 , in the population and sampling distribution excel worksheet , can anybody help to find it ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term .
|
what is the difference between the `` market revolution '' and the `` industrial revolution '' ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ?
|
did booms and busts not happen under mercantilism ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important .
|
which revolution was more impactful in the united states : the american or market ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life .
|
did americans view having bosses as a threat to democracy ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them .
|
are there any other particularly bad economic `` busts '' worth noting ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust .
|
i am sure we are all familiar with the panic of 1819 , the great depression , and the recession of 2008 , but were there any other really bad ones ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ?
|
can someone give me a short summary of what an `` entry-market system '' is ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that .
|
was the labor of men and women treated differently or were they treated equally ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods .
|
had a similar system of employment under a boss for a designated wage existed somewhere else before this time period ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
did the british have better technology in 1820 's ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home .
|
why were children allowed to work in factories ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term .
|
how is the industrial revolution different from the market revolution , are they similar ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling .
|
how would these people find satisfaction in their work when consigned to the ranks of permanent wage laborers ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals .
|
were younger children also working in the mills or factories ?
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term . in this video , i want to talk about three major effects of the market revolution , and those were changes in labor , entry into a national and international market system and the second great awakening . all right , so what effect did the market revolution have on labor ? well , we 've already talked about this a little bit in the earlier videos , but here is a view of a textile factory floor . now this is from a slightly later period , but i think it gives you a good sense of what it was like to work in a textile factory . with the market revolution really comes the emergence of factory labor in the united states . and there are a couple of ways that , that 's important . one is that people start working for wages . it 's a move away from subsistence farming and a barter economy , which also means that people are n't necessarily in charge of themselves anymore . and there 's a lot that goes along with that , which means that people stop being their own bosses . instead , they report to other bosses . and that can be problematic because it means that you have a lot less control over your daily life . so imagine that you 're a farmer and you 're really sick . oh well , you know maybe you do n't plant some seed that day and you do it the next day . imagine that you work at a textile mill and you get really sick , you do n't report to work and you get fired . so people are no longer able to set the pace of their own lives by and large . and with things like interchangeable parts , for example , fewer and fewer artisans , so masters of a craft , are making goods from start to finish . so it used to be perhaps you would be a master shoemaker , a master cobbler , and you would make every part of that shoe from tanning the leather to nailing in the sole . the system of interchangeable parts , which will later become even more codified as the assembly-line system , means that most people are only doing one part of a task . so instead of doing all of making a shoe and saying at the end of it , `` i made this shoe , `` i am a master maker of shoes , '' now your entire job might just be to hammer in one nail and then hand off the shoe to the next person . so there 's never anything that you can point to and say , `` i made that . '' so a lot of people say that this is a period when people stop being able to take pride in their own work or at least not as much pride . but what 's even more important about this process of interchangeable parts , assembly-line labor , is that it leads to an overall , what they call , deskilling . so removing the skill from labor . and what 's important about that is that if you 've broken down a task into enough small parts that you 've got people literally hammering in the same nail on a different shoe 12 hours a day , then you do n't necessarily need highly trained artisans to do that . and what happens if you are not highly trained , we 'll call this unskilled labor , and you decide you want to strike for higher pay ? well , your boss does n't need to train anyone to hammer in that nail so you 'll just get fired . so it makes the labor force in general a little bit more precarious because you do n't need an exceptional skill to have a factory job , but you are easily replaced . all right , let 's talk about entry into a market system . now what do i mean by this ? in this time period , the united states develops what 's called a market economy . and that 's different from what most people had been doing up until that point because people in the united states had mainly shipped raw materials over to europe , england particularly , to be processed and made into finished goods . and this is similar to the system of mercantilism that you might be familiar with from the colonial era . well , the war of 1812 and some of the conflict leading up to it , led the united states to embargo england , which was a manufacturing center . so people could n't send their raw materials there . they responded by investing in their own factories . so the war of 1812 is actually a pretty important moment for the development of domestic industrialization at home . and so now , instead of this kind of import/export or barter economy , people are making deals with other investors all over the united states , all over the world . so this gives people an opportunity to invest and to speculate . and that means that as they 're a part of an international market of investment speculation , they 're prone to the kinds of booms and busts that characterize capitalism , right ? now we often think of the great depression as having been the first major american depression . but really , it was the largest and most recent up until that point , because after the war of 1812 , the united states kinda goes through approximately a 20-year cycle of boom and bust . so boom is when things are getting better , things are looking up , the economy is going really well , and then a bubble of some kind bursts . and in 1819 , they had the very first of these bubbles burst , it 's called the panic of 1819 in land speculation . and this is the first time that the united states had actually experienced any kind of economic depression . so imagine how frightening that would have been to them . one of the hardest things about market-based capitalism is that individuals do n't really have control over the larger market . it 's not one person that made the great depression happen . it was an overall loss in consumer confidence or perhaps overproduction , right ? if too many people are supplying the same commodity , the price is dropping through the laws of supply and demand . so now , the laws of supply and demand and the pressures of an international market are really changing the nature of american commerce because they 're enmeshed in that market . and that has all kinds of political and social ramifications for the united states . understanding the volatility of belonging to an international market kind of helps explain why andrew jackson was so obsessed with the national bank at this time period , right ? because it represents this confusing matrix of international supply and demand and people getting credit or not getting credit . and being part of this international market is something that 's going to have a major effect on the american south , and particularly the enslaved population that lives in the american south because they 're going to be supplying cotton to the world 's textile mills . and those are textile mills in new england and textile mills in england . and as the world demands cotton for processing , the south is going to supply that cotton , which is picked by enslaved individuals . and one of the reasons that the confederacy believes that it can succeed as an independent nation is because they 're supplying cotton to england . and when england managed to find its own supply of cotton from egypt and india , the economic chances of the confederacy were sunk . and the last thing that i think is related to this market revolution is the second great awakening . now i do n't wan na go into too much detail about this because of a whole separate series of videos about the second great awakening , but this second great awakening was kind of an explosion of religious fervor , which was happening at almost exactly the same time as the market revolution . and many american historians actually think that it 's these confusing and confounding and anxious forces that lead a lot of people to take up religion . because as the world is changing around them , as people now have to relate in different ways to their neighbors as bosses and employees rather than bartering partners , and as they 're swept up in international markets that are outside their control , people look for new explanations and comfort in an increasingly confusing world . so that 's one explanation for the second great awakening . so i started out this series of videos by saying that some historians have argued that the market revolution was actually more revolutionary than the american revolution . now that 's a difficult question to answer because we 're talking about a revolution in politics as opposed to kind of a revolution of economics . but i will say that though the american revolution dissolved the political bonds between the united states and great britain , its social and economic impact were relatively limited . most people kind of ended up in the same place socially after the american revolution as they were before it . but the market revolution changes an awful lot in american society in terms of how they participate internationally and how people organize their daily lives . so i think there is a strong argument to be made that this revolution of economics , technology , even religion , is considerably farther reaching than the american revolution .
|
so why do we care about the market revolution ? the industrial revolution and the transportation and the communication revolutions of the early 19th century had a major impact on american society , both in the short term and in the long term .
|
what is the difference between the `` market revolution '' and the `` industrial revolution '' ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
what 's the difference between a 'subset ' and a 'strict subset ' ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
is a null set also a subset of itself ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 .
|
when would you use sets in real life ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
so , is n't every set a subset and a `` strict '' subset of the universal set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
if a set contains 2 ( as a example ) elements , what will be the number of sets of it 's proper subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
why ca n't we write that `` a '' is a strict subset of `` a '' ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
how can b be a subset of a if b does n't have all of the elements that are in a ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set .
|
one very simple question , what does `` notion '' mean ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
what is the differents between subsets and supersets ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 .
|
a set has 3 elements , how many subsets does it have ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
what is the difference between a subset and a proper subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
could a subset be partially `` contained '' and still be called a subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
for example , a = { 2,4,6 } b = { 1,2,3 } is b a subset of a ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
how to symbolize `` not a subset of '' ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
can we write that a is a subset of b ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 .
|
so does the order of the elements in the sets matter while saying this is a subset of that , that is , etc.. example : a = { 1,3,2 } , b = { 1 , 2 , 3 } can we say that a is also a subset of b ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
is c a subset of b ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
why is a null set a subset of every set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
what is the uses of an empty set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
does a null set have any strict subsets ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset .
|
why would someone want to use the superset notation in place of the subset notation ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
why would someone use a is a superset of b instead of just saying b is a subset of a ( other than just wanting to have the letters in alphabetical order ) ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
so if a `` strict '' subset only rules out `` the exact same set '' ... why would you ever need to make a notation for `` strict '' subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
does a `` non '' strict subset realy come up that often ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
do you have the proof for finding the total number of subsets of a finite set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
is b also a strict subset of c ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
and what is the power set and how do we solve it ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
is null set/void set a 'strict ' subset or a 'not strict ' subset or any other set say a= { 1,2 } ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 .
|
should n't the numbers in set c be in numerical order ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
can a null set be a strict subset of itself or is nothing in the set considered something ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set .
|
do you have to have the curly brackets around each number were were you could say that { 2 } is a subset of a or can you just say 2 ( without curly brackets ) is a subset of a. i know without the curly brackets is just a regular member but was n't sure if we 're checking subsets only or can we check just members too against subsets ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
is an empty set a subset of any set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
why is it false to say a is a strict subset of itself ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so let me write this . this is b . b is a strict or proper subset .
|
how to solve this a= { x^2+y^2=16 } and b= { 9x^2 + 25y^2=225 } , then n ( a intersection b ) = ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
so do all of the members of a subset have to be in the original set , or just some ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
is census of human a finite set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
what is the point of having a subset because if a set is equal to a different set , well would n't you write equal not subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ?
|
i realized that does the `` c '' ( as in c_ ) have to face the superset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
how will you know when to you the normal subset and when to use the strict subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 .
|
why sets are denoted by capital letters ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
if a set contains 2 ( as a example ) elements , what will be the number of sets of it 's proper subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
is every subset of a set either a strict subset or a subset that contains every member of the original set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a .
|
so ... .could be set `` a '' a superset of itself as well ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so are all sets subsets of the universal set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
then whats the difference between a subset and a strict subset ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 .
|
if a= [ 1,2 ] and b= [ 3,2,1 ] ; is it right to say that a is superset or `` equal '' to b ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b .
|
if yes , how can the '' equal to '' sign be verified ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 .
|
what are equal and equivalent sets ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 .
|
if a= { 1,2,3,4 } and b = { 1,2,2,3,3,3,4,4 } then , can we say a and b are equal ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
also can we say b is equivalent to a if we say a is equal to b in the first case ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
what subsets do 47 belongs to ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
how does the formula for computing the number of subsets for a certain set work ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
example : a { 1 , 2 , 3 , 4 , } b { 1 , 2 } b is a subset of a , b is a strict subset of a , a is a super set of b. is there such a thing as a strict super set ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
why we can not write a is strict subset of a ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 .
|
what if you have a = { 1 , 2 , 3 , { 6 , 7 } , 5 } do you say { 6 } is an element of a ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 .
|
do the curly braces make any difference ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down .
|
what if a is a subset of b ?
|
let 's define ourselves some sets . so let 's say the set a is composed of the numbers 1 . 3 . 5 , 7 , and 18 . let 's say that the set b -- let me do this in a different color -- let 's say that the set b is composed of 1 , 7 , and 18 . and let 's say that the set c is composed of 18 , 7 , 1 , and 19 . now what i want to start thinking about in this video is the notion of a subset . so the first question is , is b a subset of a ? and there you might say , well , what does subset mean ? well , you 're a subset if every member of your set is also a member of the other set . so we actually can write that b is a subset -- and this is a notation right over here , this is a subset -- b is a subset of a . b is a subset . so let me write that down . b is subset of a . every element in b is a member of a . now we can go even further . we can say that b is a strict subset of a , because b is a subset of a , but it does not equal a , which means that there are things in a that are not in b . so we could even go further and we could say that b is a strict or sometimes said a proper subset of a . and the way you do that is , you could almost imagine that this is kind of a less than or equal sign , and then you kind of cross out this equal part of the less than or equal sign . so this means a strict subset , which means everything that is in b is a member a , but everything that 's in a is not a member of b . so let me write this . this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a . in fact , every set is a subset of itself , because every one of its members is a member of a . we can not write that a is a strict subset of a . this right over here is false . so let 's give ourselves a little bit more practice . can we write that b is a subset of c ? well , let 's see . c contains a 1 , it contains a 7 , it contains an 18 . so every member of b is indeed a member c. so this right over here is true . now , can we write that c is a subset ? can we write that c is a subset of a ? can we write c is a subset of a ? let 's see . every element of c needs to be in a . so a has an 18 , it has a 7 , it has a 1 . but it does not have a 19 . so once again , this right over here is false . now we could have also added -- we could write b is a subset of c. or we could even write that b is a strict subset of c. now , we could also reverse the way we write this . and then we 're really just talking about supersets . so we could reverse this notation , and we could say that a is a superset of b , and this is just another way of saying that b is a subset of a . but the way you could think about this is , a contains every element that is in b . and it might contain more . it might contain exactly every element . so you can kind of view this as you kind of have the equals symbol there . if you were to view this as greater than or equal . they 're note quite exactly the same thing . but we know already that we could also write that a is a strict superset of b , which means that a contains everything b has and then some . a is not equivalent to b . so hopefully this familiarizes you with the notions of subsets and supersets and strict subsets .
|
this is b . b is a strict or proper subset . so , for example , we can write that a is a subset of a .
|
whats the difference between a subset and a strict subset ?
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.