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and one tail? 4. Two dice are rolled simultaneously. Each die may land with any one of the six numbers faceup. a. Use the counting principle to determine the number of outcomes in this sample space. b. Display the sample space by drawing a graph of the set of ordered pairs. 5. A sack contains four marbles: one red, on... |
that it lands: a. (7, 7) e. (2, 8) b. not (7, 7) f. not (2, 8) c. (not 7, not 7) g. (not 2, not 8) d. (7, not 7) or (not 7, 7) h. (2, not 8) or (not 2, 8) 12. A fair coin is tossed 50 times and lands heads up each time. What is the probability that it will land heads up on the next toss? Explain your answer. Applying ... |
four choices. Tell how many possible ways there are to answer the questions on the test if the test consists of the following number of questions: a. 1 question b. 3 questions c. 5 questions d. n questions 20. Options on a bicycle include two types of handlebars, two types of seats, and a choice of 15 colors. The bike... |
. Both lights are red. b. Both lights are green. c. The first light is red, and the second is green. d. The first light is green, and the second is red. e. At least one light is red, that is, not both lights are green. f. Both lights are the same color. 26. A manufacturer of radios knows that the probability of a defec... |
P(second king) 3 51 By the counting principle for probabilities: P(both kings) P(first king) P(second king) 52 3 3 4 51 5 1 13 3 1 17 5 1 221 This result could also have been obtained using the counting principle. The number of elements in the sample space is 52 51. The number of elements in the event (two kings) is. ... |
of cards in the deck and the number of kings in the deck remain constant. In this case, P(B given that A has occurred) P(B). In general, if A and B are two independent events, P(A and B) P(A) P(B) Rolling two dice is similar to drawing two cards with replacement because the number of faces on each die remains constant... |
a yellow marble, R and Y are depen1 dent events. We need the probability of Y given that R has occurred, which is 3 since once the red marble has been drawn, only 3 marbles remain, one of which is yellow. 1 4 1 4 P(R followed by Y) P(R and Y) P(R) P(Y | R) 1 3 1 4 1 12 This result can be shown by displaying the sample... |
. Find the probability that: a. both marbles are white b. both marbles are blue c. both marbles are the same color Probabilities with Two or More Activities 621 Solution These are dependent events. a. On the first draw: P(white) 4 6 Since the white marble drawn is not replaced, five marbles, of which three are white, a... |
the outcome is 1. Therefore, P(1 and less than 5) P(1). P(1 less than 5) P(1 and less than 5) P(less than 5) 5 P(1) P(less than 5) 5 1 6 5 6 5 1 5 Answer Fred has two quarters and one nickel in his pocket. The pocket has a hole in it, and a coin drops out. Fred picks up the coin and puts it back into his pocket. A few... |
the Honor Roll. What is the probability that a randomly chosen student who plays a sport is also in the Honor Roll? Solution Let A the event that the student is an athlete, and B the event that the student is in the Honor Roll. Then, A and B the event that a student is an athlete and is in the Honor Roll. Therefore, t... |
ordered pairs. b. Find the probability of spinning the digits 2 and 3 in that order. c. Find the probability that the same digit is spun both times. d. What is the probability that the first digit spun is larger than the second? 7. A jar contains nine orange disks and three blue disks. A girl chooses one at random and... |
be late, find the probability of each outcome below. (1) Both children who were late were girls. (2) Both children who were late were boys. (3) The same child was late both times. (4) At least one of the children who was late was a boy. c. What is the probability that the child who was late for dinner was a boy given ... |
. Tillie is approaching the toll booth on an expressway. She has three quarters and four dimes in her purse. She takes out two coins at random from her purse. Find the probability of each outcome. a. Both coins are quarters. b. Both coins are dimes. c. The coins are a dime and a quarter, in any order. d. The value of t... |
. If the first player puts an X in a corner square, what is the probability that the second player will put an O in a corner square? c. In a game of Tic-Tac-Toe, the first player puts an X in the center square and the second player puts an O in a corner square. What is the probability that the first player will put her... |
we see that there are 3 2 1 or 6 possible orders. Consider another situation. A chef is preparing a recipe with 10 ingredients. He puts all of one ingredient in a bowl, followed by all of another ingredient, and so on. How many possible orders are there for placing the 10 ingredients in a bowl? Using the counting prin... |
There are 24 permutations, that is, 24 different orders or arrangements, of these four people, in which all four of them get on the bus. We may also represent this number of permutations by the symbol 4P4. The symbol 4P4 is read as: “the number of permutations of four objects taken four at a time.” Here, the letter P ... |
. Permutations That Use Some of the Elements At times, we deal with situations involving permutations in which we are given n objects, but we use fewer than n objects in each arrangement. For example, a teacher has announced that he will call students from the first row to explain homework problems at the board. The st... |
3 1 4. Permutations and the Calculator There are many ways to use a calculator to evaluate a permutation. In the three solutions presented here, we will evaluate the permutation 8P3, the order in which, from a set of 8 elements, 3 can be selected. 632 Probability METHOD 1. Use the Multiplication Key,. The number permu... |
use. 6P2 6 5 30 6P2 4 30 Calculator Solution ENTER: 6 MATH 2 2 ENTER DISPLAY: 6 n P r 2 3 0 Answer 6P2 = 30 EXAMPLE 4 How many three-letter “words” (arrangements of letters) can be formed from the letters L, O, G, I, C if each letter is used only once in a word? Solution Forming three-letter arrangements from a set of... |
, 19P7. Permutations 635 Applying Skills 23. Using the letters E, M, I, T: a. How many arrangements of four letters can be found if each letter is used only once in the “word”? b. List these “words.” 24. In how many different ways can five students be arranged in a row? 25. In a game of cards, Gary held exactly one clu... |
English alphabet? 34. Twenty-five people are waiting for a bus. When the bus arrives, there is room for 18 people to board. In how many ways could 18 of the people who are waiting board the bus? 35. Forty people attend a party at which eight door prizes are to be awarded. In how many orders can the names of the winner... |
fifth column is the same as a word in the sixth column. 24 Therefore, only the first, third, and fifth columns are different and there are 2 or 12 arrangements of four letters when two of them are the same. This is the number of arrangements of four letters divided by the number of arrangements of two letters. Now con... |
-digit numerals EXAMPLE 2 Three children, Rita, Ann, and Marie, take turns doing the dishes each night of the week. At the beginning of each week they make a schedule. If Rita does the dishes three times, and Ann and Marie each do them twice, how many different schedules are possible? Solution We can think of this as a... |
eral formed from the given digits is chosen at random, what is the probability that it is greater than 12,000 and less than 13,000? 23. 1, 2, 3, 4, 5 24. 1, 2, 2, 2, 2 25. 1, 1, 2, 2, 2 26. 2, 2, 2, 2, 3 In 27–31, when written without using exponents, a2x can be written as aax, axa, or xaa. How many different arrangeme... |
treasurer. Thus there are 4 3 or 12 possible outcomes. Using the initials to represent the students involved, we can write these 12 arrangements: (A, B) (B, A) (B, C) (C, B) (A, C) (C, A) (B, D) (D, B) (A, D) (D, A) (C, D) (D, C) These are the permutations. We could have found that there are 12 permutations by using t... |
can they choose a three-member committee to work on the club’s next project? Is order important to this answer? If 3 officers were to be elected, such as a president, a treasurer, and a secretary, then order would be important and the number of permutations would be needed. However, a committee is a set of people. In ... |
the sequence of keys needed to find nCr is similar to that for nPr. The combination symbol is entry 3 in the PRB menu. ENTER: 4 MATH 3 3 ENTER DISPLAY: 4 n C r 3 4 Note: The notation also represents the number of combinations of n things taken r at a time. Thus: n r A B n r B A nCr or n r A B P n r r! Some Relationshi... |
1. Order is not important. Think of ordered elements such as ordered pairs and ordered triples. 2. An arrangement or a slate of officers indicates a permutation. Think of sets. 2. A committee, or a selection of a group, indicates a combination. EXAMPLE 1 Evaluate: 10C3 Solution This is the number of combinations of 10... |
this is a combination of 30 students, taken 3 at a time. 30 30C3 P 3! 5 30 3 29 3 28 3 b. This is a compound event. To find the number of ways to select 1 boy out of 10 boys for a team, use 10C1. To find the number of ways to select 2 girls out of 20 for the team, use 20C2. Then, by the counting principle, multiply th... |
number of non-collinear points in a plane, how many straight lines can be drawn? a. 3 b. 4 c. 5 d. 7 e. 8 f. n 19. Consider the following formulas: n! (n 2 r)! r! P n r r! (2) nCr (3) nCr (1) nCr a. Evaluate 8C3 using each of the three formulas. b. Evaluate 11C7 using each of the three formulas. c. Can all three formu... |
2 are mystery books d. all are car-repair manuals 25. Cards are drawn at random from a 52-card deck. Find the number of different 5-card poker hands possible consisting of: a. any 5 cards from the deck c. 4 queens and any other card e. 2 aces and 3 picture cards b. 3 aces and 2 kings d. 5 spades f. 5 jacks 26. How man... |
compound event of choosing 2 girls and 2 boys, or 6. 3 6 18. n(E. 3C2 4C2 (3) Thus P(E) C 2 4 C 2 3 3 7C4 5 18 35. Answer P(2 girls, 2 boys) 18 35 EXAMPLE 3 The students chosen are Callie, Jessica, Carlos, and Sanjit. In how many orders can these 4 students be called upon in the spelling bee? Solution The number of wa... |
answer. Applying Skills 3. The Art Club consists of 4 girls (Jennifer, Anna, Gloria, Teresa) and 2 boys (Mark and Dan). a. In how many ways can the club elect a president and a treasurer? b. Find the probability that the 2 officers elected are both girls. c. How many 2-person teams can be selected to work on a project... |
in either order c. 2 jacks either order d. 2 clubs e. an ace and a jack in either order f. an ace and a jack in that order g. a heart given that the king of hearts h. a king given that a queen was was drawn drawn 8. Mrs. Carberry has 4 quarters and 3 nickels in her purse. If she takes 3 coins out of her purse without ... |
) Find the probability that Tim is in the crowd scene. 13. There are 8 candidates for 3 seats in the student government. The candidates include 3 boys (Alberto, Peter, Thomas) and 5 girls (Elizabeth, Maria, Joanna, Rosa, Danielle). If all candidates have an equal chance of winning, find the probability that the winners... |
the number of ways that the event can occur, divided by the total number of possibilities in the sample space. If P(E) represents the probability of event E, n(E) represents the number of outcomes in event E and n(S) represents the number of outcomes in the sample space S. The formula, which applies to fair and unbias... |
The num- ber of permutations of n objects taken n at a time, nPn, is equal to n factorial: nPn = n! n (n 1) (n 2) 3 2 1 The number of permutations of n objects taken r at a time, where r n, is equal to: nPr 5 n(n 2 1)(n 2 2) h r factors or nPr n! (n 2 r)! A permutation of n objects taken n at a time in which r are ide... |
or why not.. Can 654 Probability 3. The numerical value of nPr is the product of r factors. Express the smallest of those factors in terms of n and r. 4. If P(A).4, P(B).3, and P(A B).2, find P(A B). 5. If P(A).5, P(B).2, and P(A B).5, find P(A B). In 6–11, evaluate each expression: 6. 8! 7. 5P5 8. 12P2 9. 5C5 10. 12C... |
2) 1 girl and 3 boys (3) 4 boys c. What is the probability that the fourth member chosen is a girl if the first three are 2 boys and a girl? d. What is the probability that a boy is on the committee? Review Exercises 655 20. From a 52-card deck, 2 cards are drawn at random without replacement. Find the probability of s... |
(S) the number of five-letter words that can be formed using the letters in the word RADIO. Find n(S). b. Let n(E) the number of five-letter words that can be formed using the letters in the word RADIO, in which the first letter is a vowel Find n(E). 656 Probability c. If the letters in RADIO are rearranged at random, ... |
next patient of the doctor described in the chapter opener on page 575 will need either a flu shot or a pneumonia shot. Exploration Rachael had a box of disks, all the same size and shape. She removed 20 disks from the box, marked them, and then returned them to the box. After mixing the marked disks with the others i... |
3(x 1) 7x, the value of x is (1) 1.5 (2) 4.5 (3) 0.9 (4) 3.75 7. The product of 4x–2 and 5x3 is (1) 20x–6 (2) 20x (3) 9x–6 (4) 9x 8. There are 12 members of the basketball team. At each game, the coach selects a group of five team members to start the game. For how many games could the coach make different selections?... |
45 speak English and Spanish, 10 speak English and Cumulative Review 659 Japanese, 13 speak Spanish and Japanese, and 5 speak all three languages. How many students do not speak English? 14. Abe, Brian, and Carmela share the responsibility of caring for the family pets. During a seven-day week, Abe and Brian each take... |
Data 661 In our daily lives, we often deal with problems that involve many related items of numerical information called data. For example, in the daily newspaper we can find data dealing with sports, with business, with politics, or with the weather. Statistics is the study of numerical data. There are three typical ... |
team wants to know the expected life span of flashlight batteries made by its company. 3. A company advertising on television wants to know the most frequently watched TV shows so that its ads will be seen by the greatest number of people. When a statistical study is conducted, it is not always possible to obtain info... |
group, representative of the entire population of items being studied. From the study of the small group, reasonable conclusions can be drawn about the entire group. EXAMPLE 1 To determine which television programs are the most popular in a large city, a poll is conducted by selecting people at random at a street corn... |
. To avoid such problems, the researchers working directly with the test subjects are not told which group a subject belongs to. Interpreting Graphs of Data Oftentimes embellishments to graphs distort the perception of the data, and so you must exercise care when interpreting graphs of data. 1. Two- and three-dimension... |
who responded. Do you think that the questionnaires that were returned represent a fair sample of all of the persons who tried the soap? Explain why or why not. Developing Skills In 3–10, determine if each variable is quantitative or qualitative. 3. Political affiliation 4. Opinions of students on a new music album 5.... |
necessary to conduct a statistical study. 27. Explain why the graph below is misleading. SUMMER OLYMPIC GAMES CHAMPIONS 100-METER RACE 1988 Carl Lewis (USA) 9.92 sec 1992 Linford Christie (GBR) 9.96 sec 1996 Donovan Bailey (CAN) 9.84 sec 2000 Maurice Green (USA) 9.87 sec 2004 Justin Gatlin (USA) 9.85 sec Organizing Da... |
, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 7 We can immediately observe certain facts from this ordered list: more students were absent 0 days than any other number of days, the same number of students were absent 5 and 7 days. However, for more a quantitative analysis, it is useful to make a table. ... |
50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75 Organizing Data 669 Because of the large number of different scores, it is convenient to organize these data into groups or intervals, which must be equal in size. Here we will use six intervals: 41–50, 51–60, 61–70, 71–80, 81–90, 91–100. Each interval has a length of 10,... |
69–76 61–68 53–60 45–52 6 4 9 7 3 0 3 Constructing a Stem-and-Leaf Diagram Another method of displaying data is called a stem-and-leaf diagram. The stemand-leaf diagram groups the data without losing the individual data values. A group of 30 students were asked to record the length of time, in minutes, spent on math h... |
. Based on the grouped data, which interval contains the greatest number of students? c. How many students weigh less than 70 kilograms? Solution a. Interval Tally Frequency (number) 80–89 70–79 60–69 50–59 40–49 5 7 6 8 4 b. The interval 50–59 contains the greatest number of students, 8. Answer c. The three lowest int... |
the data? e. How many students are taller than 175 centimeters? 4. a. Copy and complete the table to group the data, which gives the lifespan, in hours, of 50 flashlight batteries: 73, 81, 92, 80, 108, 76, 84, 102, 58, 72, 82, 100, 70, 72, 95, 105, 75, 84, 101, 62, 63, 104, 97, 85, 106, 72, 57, 85, 82, 90, 54, 75, 80,... |
The following data show test scores for 30 students: 90, 83, 87, 71, 62, 46, 67, 72, 75, 100, 93, 81, 74, 75, 82, 83, 83, 84, 92, 58, 95, 98, 81, 88, 72, 59, 95, 50, 73, 93 674 Statistics a. Construct a table, using intervals of length 10 starting with 91–100. b. Construct a table, using intervals of length 12 startin... |
RAM In Section 16-2 we organized data by grouping them into intervals of equal length. After the data have been organized, a graph can be used to visualize the intervals and their frequencies. The table below shows the distribution of test scores for 32 students in a class. The data have been organized into six interva... |
) Repeat the process to enter the frequencies that correspond to each inter- val in L2. (4) Clear any functions in the Y= menu. (5) Turn on Plot1 from the STAT PLOT menu, and configure it to graph a histogram. Make sure to also set Xlist to L1 and Freq to L2. ENTER: STAT PLOT ENTER 2nd 1 L1 ENTER 2nd 2nd L2 (6) In the ... |
ENTER to select On and the histogram. Type 2nd L1 into Xlist and 2nd L2 into Freq. (3) Set the Window. Each interval has length 4, so set Xmin to 12 (4 less than the smallest interval value), Xmax to 44 (4 more than the largest interval value), and Xscl to 4. Make Ymin 0 and Ymax 12 to be greater than the largest freq... |
4–6 7–9 10–12 13–15 16–18 24 30 28 41 19 8 6. For the table of grouped data given in Exercise 5, answer the following questions: a. What is the total frequency in the table? b. What interval contains the greatest frequency? c. The number of data values reported for the interval 4–6 is what percent of the total number ... |
.0–40.9 33.0–36.9 29.0–32.9 25.0–28.9 21.0–24.9 Hands-On-Activity Construct a histogram to display the data that you collected and organized in the Hands-On Activities for Sections 16-1 and 16-2. 1. Draw the histogram on graph paper. 2. Follow the steps in this section to display the histogram on a graphing calculator.... |
85. The mean (arithmetic average) is 85. Let us consider another example. In a car wash, there are seven employees whose ages are 17, 19, 20, 17, 46, 17, and 18. What is the mean of the ages of these employees? Here, we add the seven ages to get a sum of 154. Then, 154 7 22. While the mean age of 22 is the correct ans... |
so there is no middle value. What is now the median age? STEP 1. Arrange the ages in numerical order: STEP 2. There is no single middle number. 17, 17, 18, 18, 19, 20, 21, 46 17, 17, 18, 18, 19, 20, 21, 46 ↑ ↑ 2 5 181 2 18 1 19 Find the two middle numbers: STEP 3. Find the mean (arithmetic average) of the two middle n... |
’s test scores in science are 72, 80, 86, 93, and 94. Here, every number appears the same number of times, once. Since no number appears more often than the others, we define such data as having no mode. Procedure To find the mode for a set of data, find the number or numbers that occur most often. 1. If one number app... |
will use in later sections in this chapter and in more advanced courses. EXAMPLE 2 Renaldo has marks of 75, 82, and 90 on three mathematics tests. What mark must he obtain on the next test to have an average of exactly 85 for the four math tests? The Mean, the Median, and the Mode 685 Solution The word average, by its... |
example of a linear transformation of a set of data. Let us start by examining additive transformations. For instance, consider the data 2, 2, 3, 4, 5. If 10 is added to each data value, the data set becomes: 12, 12, 13, 14, 15 Notice that every measure of central tendency has been shifted to the right by 10 units old... |
2 41 2 4. Find the median for each set of data., b. 22, 38, 18, 14, 22, 30 d. 1.00, 0.01, 1.10, 0.12, 1.00, 1.03 a. 1, 2, 5, 3, 4 c. 3, 8, 12, 7, 1, 0, 4 e. 3.2, 8.7, 1.4 b. 2, 9, 2, 9, 7 d. 80, 83, 97, 79, 25 f. 2.00, 0.20, 2.20, 0.02, 2.02 g. 21, 24, 23, 22, 20, 24, 23, 21, 22, 23 h. 5, 7, 9, 3, 8, 7, 5, 6 5. What i... |
mean median (4) mean median 11. For the set of data 8, 8, 9, 10, 15, which statement is true? (1) mean median (2) mean mode (3) median mode (4) mean median 688 Statistics 12. When the data consists of 3, 4, 5, 4, 3, 4, 5, which statement is true? (1) mean median (2) mean mode (3) median mode (4) mean median 13. For wh... |
data value is multiplied by 2 and increased by 5, what is the mean of the transformed data set? 19. Three consecutive integers can be represented by x, x 1, and x 2. The average of these consecutive integers is 32. What are the three integers? 20. Three consecutive even integers can be represented by x, x 2, and x 4. ... |
the week? 30. If the heights, in centimeters, of a group of students are 180, 180, 173, 170, and 167, what is the mean height of these students? 31. What is the median age of a family whose members are 42, 38, 14, 13, 10, and 8 years old? 32. What is the median age of a class in which 14 students are 14 years old and ... |
in., 3 3 4 in., 3 1 in., 1 in., 2 in., 2 in. b. Describe the average-size nail used by the carpenter, using at least one of these mea- sures of central tendency. Explain your answer. Hands-On Activity Find the mean, the median, and the mode for the data that you collected in the Hands-On Activity for Section 16-1. It ... |
grouped in the table shown earlier, a simple counting procedure can be used to find the median, the 13th number. When we add the frequencies of the first four intervals, starting at the top, we find that these intervals include data for: 4 0 2 6 12 students Therefore, the next lower interval (with frequency greater th... |
2. Then use the 1-Var Stats from the STAT CALC menu to display information about the data. ENTER: STAT ENTER 2nd L1, 2nd L2 ENTER DISPLAY< n = 2 5 Measures of Central Tendency and Grouped Data 693 The display shows that the mean, x–, is 4.4, the sum of the number of books read is 110, and the number of students, the to... |
of greatest frequency. For the mode, we look for a single number that has the greatest frequency. For the modal interval, we look for the interval that has the greatest frequency. 694 Statistics Interval Containing the Median To find the interval containing the median, we follow the procedure described earlier in this... |
up, we have 1 2 4 7. Again, the frequency of the next interval is 3, and the 8th, 9th, and 10th heights are in this interval. The 9th height, the median, is 74. 71 72 2 1 4 Measures of Central Tendency and Grouped Data 695 c. (1) Multiply each height by its corresponding frequency: 75 5 375 76 0 0 71 1 71 72 2 144 77 ... |
9 12 15 10 126–150 101–125 76–100 51–75 26–50 1–25 4 6 6 3 7 2 Applying Skills 9. On a test consisting of 20 questions, 15 students received the following scores: 17, 14, 16, 18, 17, 19, 15, 15, 16, 13, 17, 12, 18, 16, 17 a. Make a frequency table for these students listing scores from 12 to 20. b. Find the median sco... |
. In what interval is the median for these grouped data? d. What is the modal interval? 698 Statistics 16-6 QUARTILES, PERCENTILES, AND CUMULATIVE FREQUENCY Quartiles When the values in a set of data are listed in numerical order, the median separates the values into two equal parts. The numbers that separate the set i... |
5 inches, 69.5 is the upper quartile, or third quartile. Note: The quartiles are sometimes denoted Q1, Q2, and Q3. Quartiles, Percentiles, and Cumulative Frequency 699 Procedure To find the quartile values for a set of data: 1. Arrange the data in ascending order from left to right. 2. Find the median for the set of da... |
. The long whisker at the left shows us that the data are more scattered at the lower than at the higher end. A graphing calculator can display a boxand-whisker plot. Enter the data in L1, then go to the STAT PLOT menu to select the type of graph to draw. ENTER: 2nd STAT PLOT 1 ENTER ENTER 2nd L1 ALPHA = Ty Now display... |
, |_____| |________| 7, 8, 8, 9, 10, 11, ↑ 8.5 |_________| 14, 14, 17 12, The first and third quartile values, 6 and 12, are data values. If we think of each of these as a half data value in the groups that they separate, each group contains 3 data values, which is 25% of the total. 1 2 Percentiles A percentile is a nu... |
, 87, 87, 87, 88, 90, 92, 93, 95, 98 Solution (1) Find the sum of the number of marks less than 87 and half of the number of 87’s: Number of marks less than 87 21 Half of the number of 87’s (0.5 3) 1.5 22.5 (2) Divide the sum by the total number of marks: (3) Change the decimal value to a percent: 0.75 75%. 22.5 30 5 0... |
students scored 90 or less. 5. How many students scored 100 or less on the test? By adding the five lowest frequencies, 20 40 75 60 45, we see that 240 students scored 100 or less. This result makes sense because 240 students took the test and all of them scored 100 or less. Constructing a Cumulative Frequency Histogr... |
“What percent of the students scored 70 or below on the test?” The height of each bar represents both the number of students and the percent of the students who had scores at or below the largest number in the interval represented by that bar. Since 25%, or a quarter, of the scores were 70 or below, we say that 70 is ... |
. The first two digits in each price will be the stem. The lowest price is $2.25 and the highest price is $3.00. b. Since there are 15 prices, the median is the 8th from the top or from the bottom. The median is $2.57. c. The middle value of the set of numbers below the median is the first quartile. That price is $2.48... |
. Diagram e. Diagram f. 63rd percentile Note: A cumulative frequency histogram can be drawn on a calculator just like a regular histogram. In list L2, where we previously entered the frequencies for each individual interval, we now enter each cumulative frequency. EXERCISES Writing About Mathematics 1. a. Is it possibl... |
- togram. b. In what interval is the median? c. The value 10 occurs twice in the data. What is the percentile rank of 10? 11. For the data given in the table: a. Construct a cumulative frequency his- togram. b. In what interval is the median? c. In what interval is the upper quartile? d. What percent of scores are 17 o... |
have averages that are less than Cecilia’s? 710 Statistics 15. In the table at the right, data are given for the heights, in inches, of 22 football players. a. Copy and complete the table. b. Draw a cumulative frequency histogram. c. Find the height that is the lower quartile. d. Find the height that is the upper quar... |
the variables based on their scatter plots. CASE 1 approximate a straight line that has a positive slope. The data has positive linear correlation. The points in the scatter plot A driver recorded the number of gallons of gasoline used and the number of miles driven each time she filled the tank. In this example, ther... |
P Bivariate Statistics 713 CASE 3 The data has no correlation. Before giving a test, a teacher asked each student how many minutes each had spent the night before preparing for the test. After correcting the test, she prepared the table below which compares the number of minutes of study to the number of correct answe... |
fixed distance to decrease. This example indicates both negative correlation and causation. It is important to note that correlation is not the same as causation. Correlation is an indication of the strength of the linear relationship or association between the variables, but it does not mean that changes in one varia... |
) b 194.75 188.37 b 6.38 b Round the values to three significant digits. A possible equation for a line of best fit is y 32.2x 6.38. The calculator can also be used to find a line called the regression line to fit a bivariate set of data. Use the LinReg(ax+b) function in the STAT CALC menu. 716 Statistics ENTER: STAT 4... |
of a town shown below. The population grew at a constant rate during the years in which the data was gathered. However, we do not expect the population to continue to grow forever, and thus, it may not be possible to extrapolate far into the future. 280 270 260 250 240 230 220 210 200 190 180 170 160 ) 1960 1965 1970 ... |
regression line using LinReg(ax+b) from the STAT CALC menu. 5. Enter the equation of the regression line in the Y= menu and use to show the relationship between the data and the regression line. GRAPH 6. Use the equation of the line to predict related outcomes. In this course, we have found a line of best fit by findi... |
7 2 4 5 36.5 7.7 < 4.74 y 5 mx 1 b 20 5 36.5 7.7 (4) 1 b An equation of a best fit line is y 4.74x 1.05. 1.05 < b d. The data are in L1 and L2. ENTER: STAT 4 ENTER DISPLAY The equation of the regression line is y = 4.89x 0.660. e. Let x 20. Use the equation from c. y 4.74x 1.05 y 4.74(20) 1.05 y 95.85 Use the equation ... |
and length of each of the 14 long-distance telephone calls that she made in the past month. Her record is given below. Minutes 3.7 1.0 19.6 0.8 4.3 34.8 2.9 Cost $0.35 $0.11 $2.12 $0.09 $0.47 $3.78 $0.24 Minutes 2.5 7.1 10.9 5.8 1.5 1.4 8.0 Cost $0.27 $0.79 $1.21 $0.65 $0.20 $0.17 $0.89 a. Draw a scatter plot of the d... |
last 24 persons who enrolled in a health club. Height Weight Height Weight Height Weight Height Weight 69 67 63 73 71 79 160 160 135 185 215 225 75 76 70 73 68 74 180 155 175 170 190 190 66 66 68 68 72 77 145 130 160 140 170 195 71 66 67 78 72 69 165 155 140 210 160 145 a. Draw a scatter plot on graph paper to display... |
17 59 7 59 24 50 18 55 4 56 7 54 3 57 13 45 31 49 6 43 23 49 12 56 5 62 1 a. Draw a scatter plot on graph paper to display the data. b. Does the data have positive, negative, or no linear correlation? c. Is there a causal relationship? d. Draw and find an equation of a line of best fit. e. Use a calculator to find the... |
tendency. The mean is the sum of the data values divided by the total frequency. The median is the middle value when the data values are placed in numerical order. The mode is the data value that has the largest frequency. Quartile values separate the data into four equal parts. A box-and-whisker plot displays a set o... |
. Do you agree with Courtney? Explain why or why not. 2. A set of data contains N numbers arranged in numerical order. a. When is the median one of the numbers in the set of data? b. When is the median not one of the numbers in the set of data? 3. For each of the following sets of data, find: a. the mean b. the median ... |
interval. b. Draw a frequency histogram of the data. c. In what interval does the median lie? d. Which interval contains the lower quartile? Score Frequency Cumulative Frequency 10. The table shows the scores of 25 test papers. a. Is the data univariate or bivariate? b. Find the mean score. c. Find the median score. d... |
ics and 30% of former alcoholics, versus only 15% of the non-alcoholics developed a more dangerous form of pneumonia. The researchers concluded that alcoholism raises the risk for developing pneumonia. Discuss possible problems with this study. 728 Statistics 15. Aurora buys oranges every week. The accompanying table l... |
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