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relative frequency of direct hits that were AT MOST a category 3 storm? a. 0.3480 b. 0.9231 c. 0.2601 d. 0.3370 1.4 Experimental Design and Ethics 87. How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental se... |
live at least 16 miles from campus? c. If the same survey were done at Great Basin College in Elko, Nevada, do you think the percentages would be the same? Why? 91. Several online textbook retailers advertise that they have lower prices than on-campus bookstores. However, an important factor is whether the Internet re... |
hips-Society/Articles/A0374-How-George-Gallup-Picked-the-President Dominic Lusinchi, “’President’ Landon and the 1936 Literary Digest Poll: Were Automobile and Telephone Owners to Blame?” Social Science History 36, no. 1: 23-54 (2012), http://ssh.dukejournals.org/content/36/1/23.abstract (accessed May 1, 2013). “The Li... |
, “Levels of Measurement,” http://infinity.cos.edu/faculty/woodbury/stats/tutorial/Data_Levels.htm (accessed May 1, 2013). Courtney Taylor, “Levels of Measurement,” about.com, http://statistics.about.com/od/HelpandTutorials/a/Levels-OfMeasurement.htm (accessed May 1, 2013). David Lane. “Levels of Measurement,” Connexio... |
nhtsa.dot.gov/Main/index.aspx (accessed May 1, 2013). Data from www.businessweek.com (accessed May 1, 2013). Data from www.forbes.com (accessed May 1, 2013). “America’s Best Small Companies,” http://www.forbes.com/best-small-companies/list/ (accessed May 1, 2013). U.S. Department of Health and Human Services, Code of F... |
to reflect a population of one school. 27 Even though the specific data support each researcher’s conclusions, the different results suggest that more data need to be collected before the researchers can reach a conclusion. 29 There is not enough information given to judge if either one is correct or incorrect. 31 The... |
the mean health costs of the clients the mean health costs of the sample e. X = the health costs of one client f. values for X, such as 34, 9, 82, and so on 47 a. all the clients of this counselor b. a group of clients of this marriage counselor c. d. the proportion of all her clients who stay married the proportion o... |
levels. Because we cannot isolate these variables of interest, we cannot draw valid conclusions about the connection between education and crime. Possible lurking variables include police expenditures, unemployment levels, region, average age, and size. 79 a. Possible reasons: increased use of caller id, decreased use... |
he only sampled seven subjects and he only investigated one textbook in each subject. There are several possible sources of bias in the study. The seven subjects that he investigated are all in mathematics and the sciences; there are many subjects in the humanities, social sciences, and other subject areas, (for examp... |
you have collected data, what will you do with it? Data can be described and presented in many different formats. For example, suppose you are interested in buying a house in a particular area. You may have no clue about the house prices, so you might ask your real estate agent to give you a sample data set of prices.... |
choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two. Likewise, the number 5,432 has stem 543 and leaf two. The decimal 9.3 ha... |
due to mistakes (for example, writing down 50 instead of 500) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later. Example 2.2 The data are the distances (in kilometers) from a home to local supermarkets. Cr... |
Age President Age President Age Washington J. Adams Jefferson Madison Monroe J. Q. Adams Jackson Van Buren 57 61 57 57 58 57 61 54 Lincoln A. Johnson Grant Hayes Garfield Arthur Cleveland B. Harrison W. H. Harrison 68 Cleveland McKinley 52 56 46 54 49 51 47 55 55 54 Hoover 54 F. Roosevelt 51 Truman Eisenhower Kennedy ... |
33 35 28 13 26 30 37 47 53 1989–1990 1990–1991 1991–1992 1992–1993 1993–1994 1994–1995 1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006 2006–2007 2007–2008 2008–2009 2009–2010 Another type of graph that is useful for specific data values is a line graph. In ... |
3 This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 75 2.5 The population in Park City is made up of children, working-age adults, and retirees. Table 2.10 shows the three age groups, the number of people... |
book, you will use a histogram to display the data. One advantage of a histogram is that it can readily display large data sets. A rule of thumb is to use a histogram when the data set consists of 100 values or more. A histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axi... |
1.495 (1.5 – 0.005 = 1.495). If the value with the most decimal places is 3.234 and the lowest value is 1.0, a convenient starting point is 0.9995 (1.0 – 0.0005 = 0.9995). If all the data happen to be integers and the smallest value is two, then a convenient starting point is 1.5 (2 – 0.5 = 1.5). Also, when the starti... |
0.05, 0.005, etc. are convenient numbers, use 0.05 and subtract it from 60, the smallest value, for the convenient starting point. 60 – 0.05 = 59.95 which is more precise than, say, 61.5 by one decimal place. The starting point is, then, 59.95. The largest value is 74, so 74 + 0.05 = 74.05 is the ending value. Next, c... |
in the interval 71.95–73.95. The height 74 is in the interval 73.95–75.95. The following histogram displays the heights on the x-axis and relative frequency on the y-axis. Figure 2.5 2.7 The following data are the shoe sizes of 50 male students. The sizes are continuous data since shoe size is measured. Construct a hi... |
width of each bar or class interval. If the data are discrete and there are not too many different values, a width that places the data values in the middle of the bar or class interval is the most convenient. Since the data consist of the numbers 1, 2, 3, 4, 5, 6, and the starting point is 0.5, a width of one places ... |
). Arrow down to Freq. Enter L2 (2nd 2). • Press GRAPH. • Use the TRACE key and the arrow keys to examine the histogram. 2.8 The following data are the number of sports played by 50 student athletes. The number of sports is discrete data since sports are counted. 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1; 1;... |
; 35; 15; 26; 40; 28; 18; 20; 25; 34; 39; 42; 24; 22; 19; 27; 22; 34; 40; 20; 38; and 28 Use 10–19 as the first interval. Count the money (bills and change) in your pocket or purse. Your instructor will record the amounts. As a class, construct a histogram displaying the data. Discuss how many intervals you think is ap... |
.S. Presidents’ ages at inauguration shown in Table 2.15. Age at Inauguration Frequency 41.5–46.5 46.5–51.5 51.5–56.5 56.5–61.5 61.5–66.5 66.5–71.5 Table 2.15 4 11 14 9 4 2 Frequency polygons are useful for comparing distributions. This is achieved by overlaying the frequency polygons drawn for different data sets. Exa... |
we make each point on the graph correspond to a date and a measured quantity. The points on the graph are typically connected by straight lines in the order in which they occur. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 Example 2.... |
218.312 218.439 218.711 218.803 219.179 218.056 2011 226.545 226.889 226.421 226.230 225.672 224.939 2012 230.379 231.407 231.317 230.221 229.601 229.594 Table 2.19 Solution 2.12 Figure 2.10 86 CHAPTER 2 | DESCRIPTIVE STATISTICS 2.12 The following table is a portion of a data set from www.worldbank.org. Use the table ... |
used to determine a minimum testing score that will be used as an acceptance factor. For example, suppose Duke accepts SAT scores at or above the 75th percentile. That translates into a score of at least 1220. Percentiles are mostly used with very large populations. Therefore, if you were to say that 90% of the test s... |
5 The median or second quartile is seven. The lower half of the data are 1, 1, 2, 2, 4, 6, 6.8. The middle value of the lower half is two. 1; 1; 2; 2; 4; 6; 6.8 The number two, which is part of the data, is the first quartile. One-fourth of the entire sets of values are the same as or less than two and three-fourths of... |
59,000; 1,095,000; 5,500,000 M = 488,800 Q1 = 230,500 + 387,000 2 = 308,750 Q3 = 639,000 + 659,000 2 = 649,250 IQR = 649,000 – 308,750 = 340,250 (1.5)(IQR) = (1.5)(340,250) = 510,375 Q1 – (1.5)(IQR) = 308,750 – 510,375 = –201,625 Q3 + (1.5)(IQR) = 649,000 + 510,375 = 1,159,375 No house price is less than –201,625. Howe... |
.5(1.5) = 122.25 Since the minimum and maximum values for the day class are greater than 16.25 and less than 122.25, there are no outliers. Night class outliers are calculated as: Q1 – IQR (1.5) = 78 – 11(1.5) = 61.5 Q3 + IQR(1.5) = 89 + 11(1.5) = 105.5 For this class, any test score less than 61.5 is an outlier. There... |
n the table (between the 40th and 41st values). Therefore, we need to take the mean of the 40th an 41st values. The 80th percentile = 8 + 9 2 = 8.5 b. The 90th percentile will be the 45th data value (location is 0.90(50) = 45) and the 45th data value is nine. c. Q1 is also the 25th percentile. The 25th percentile locat... |
smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. Find the 70th percentile. b. Find the 83rd percentile. Solution 2.17 a. b. k = 70 i = the index n = 29 i = k 100 (n + 1) = ( 70 100 )(29 + 1) = 21. Twenty-one is an integer, and th... |
; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. Find the percentile for 58. b. Find the percentile for 25. Solution 2.18 a. Counting from the bottom of the list, there are 18 data values less than 58. There is one value of 58. x = 18 and y = 1. x + 0.5y n (100) = 18 + 0.5(1) 29 (100) = 63.80. 58... |
contain the following information. • • • • information about the context of the situation being considered the data value (value of the variable) that represents the percentile the percent of individuals or items with data values below the percentile the percent of individuals or items with data values above the perce... |
eight. Interpret the 40th percentile in the context of this situation. 94 CHAPTER 2 | DESCRIPTIVE STATISTICS Example 2.22 Sharpe Middle School is applying for a grant that will be used to add fitness equipment to the gym. The principal surveyed 15 anonymous students to determine how many minutes a day the students spe... |
end of the box and the third quartile marks the other end of the box. Approximately the middle 50 percent of the data fall inside the box. The "whiskers" extend from the ends of the box to the smallest and largest data values. The median or second quartile can be between the first and third quartiles, or it can be one... |
quartile = 64.5 • Q2: Second quartile or median= 66 • Q3: Third quartile = 70 Figure 2.12 a. Each quarter has approximately 25% of the data. b. The spreads of the four quarters are 64.5 – 59 = 5.5 (first quarter), 66 – 64.5 = 1.5 (second quarter), 70 – 66 = 4 (third quarter), and 77 – 70 = 7 (fourth quarter). So, the ... |
255; 270; 275; 290; 301; 303; 315; 317; 318; 326; 333; 343; 349; 360; 369; 377; 388; 391; 392; 398; 400; 402; 405; 408; 422; 429; 450; 475; 512 For some sets of data, some of the largest value, smallest value, first quartile, median, and third quartile may be the same. For instance, you might have a data set in which ... |
ile and the largest value? What percentage of the data is between the first quartile and the largest value? d. Create a box plot for each set of data. Use one number line for both box plots. e. Which box plot has the widest spread for the middle 50% of the data (the data between the first and third quartiles)? What doe... |
box-and-whisker plot are: Min: 10 Q1: 15 Med: 95 Q3: 490 Max: 790 The following graph shows the box-and-whisker plot. Figure 2.15 2.25 Follow the steps you used to graph a box-and-whisker plot for the data values shown. 0; 5; 5; 15; 30; 30; 45; 50; 50; 60; 75; 110; 140; 240; 330 2.5 | Measures of the Center of the Dat... |
; 4; 4; 4; 4; 4 x 11 3(1) + 2(2) + 1(3) + 5(4) 11 x¯ = = 2.7 = 2.7 In the second example, the frequencies are 3(1) + 2(2) + 1(3) + 5(4). You can quickly find the location of the median by using the expression n + 1 2. The letter n is the total number of data values in the sample. If n is an odd number, the median is th... |
21st values (the two 24s): 3; 4; 8; 8; 10; 11; 12; 13; 14; 15; 15; 16; 16; 17; 17; 18; 21; 22; 22; 24; 24; 25; 26; 26; 27; 27; 29; 29; 31; 32; 33; 33; 34; 34; 35; 37; 40; 44; 44; 47; M = 24 + 24 2 = 24 To find the mean and the median: Clear list L1. Pres STAT 4:ClrList. Enter 2nd 1 for list L1. Press ENTER. Enter data... |
of the rest are worth $280,000, and all the others are worth $315,000. Which is the better measure of the “center”: the mean or the median? Another measure of the center is the mode. The mode is the most frequent value. There can be more than one mode in a data set as long as those values have the same frequency and t... |
. Consider the annual earnings of workers at a factory. The mode is $25,000 and occurs 150 times out of 301. The median is $50,000 and the mean is $47,500. What would be the best measure of the “center”? The Law of Large Numbers and the Mean The Law of Large Numbers says that if you take samples of larger and larger si... |
ount’s last statistic test is shown. Find the best estimate of the class mean. Grade Interval Number of Students 50–56.5 56.5–62.5 62.5–68.5 68.5–74.5 74.5–80.5 80.5–86.5 86.5–92.5 92.5–98.5 Table 2.25 1 0 4 4 2 3 4 1 Solution 2.30 • Find the midpoints for all intervals This content is available for free at http://text... |
, and each value is located in the middle of an interval. 104 CHAPTER 2 | DESCRIPTIVE STATISTICS Figure 2.16 The histogram displays a symmetrical distribution of data. A distribution is symmetrical if a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertic... |
Example 2.31 Statistics are used to compare and sometimes identify authors. The following lists shows a simple random sample that compares the letter counts for three authors. Terry: 7; 9; 3; 3; 3; 4; 1; 3; 2; 2 Davis: 3; 3; 3; 4; 1; 4; 3; 2; 3; 1 Maris: 2; 3; 4; 4; 4; 6; 6; 6; 8; 3 a. Make a dot plot for the three au... |
of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean. The standard deviation • provides a numerical measure of the overall amount of variation in a data set, and • can be used to determine whether a particular data value is close t... |
it is more than two standard deviations away is more of an approximate "rule of thumb" than a rigid rule. In general, the shape of the distribution of the data affects how much of the data is further away than two standard deviations. (You will learn more about this in later chapters.) The number line may help you und... |
a population or a sample. The lower case letter s represents the sample standard deviation and the Greek letter σ (sigma, lower case) represents the population standard deviation. If the sample has the same characteristics as the population, then s should be a good estimate of σ. To calculate the standard deviation, w... |
You will cover the standard error of the mean in the chapter The Central Limit Theorem (not now). The notation for the standard error of the mean is σ where σ is the standard deviation of the population and n is the size of the sample. n NOTE In practice, USE A CALCULATOR OR COMPUTER SOFTWARE TO CALCULATE THE STANDARD... |
.050625 2 × 1.050625 = 2.101250 10 – 10.525 = –0.525 (–0.525)2 = 0.275625 4 × 0.275625 = 1.1025 10.5 – 10.525 = –0.025 (–0.025)2 = 0.000625 4 × 0.000625 = 0.0025 11 – 10.525 = 0.475 (0.475)2 = 0.225625 6 × 0.225625 = 1.35375 11.5 – 10.525 = 0.975 (0.975)2 = 0.950625 3 × 0.950625 = 2.851875 The total is 9.7375 The sampl... |
32 a. ◦ Clear lists L1 and L2. Press STAT 4:ClrList. Enter 2nd 1 for L1, the comma (,), and 2nd 2 for L2. ◦ Enter data into the list editor. Press STAT 1:EDIT. If necessary, clear the lists by arrowing up into the name. Press CLEAR and arrow down. ◦ Put the data values (9, 9.5, 10, 10.5, 11, 11.5) into list L1 and the ... |
If you add the deviations, the sum is always zero. (For Example 2.32, there are n = 20 deviations.) So you cannot simply add the deviations to get the spread of the data. By squaring the deviations, you make them positive numbers, and the sum will also be positive. The variance, then, is the average squared deviation.... |
.33 Use the following data (first exam scores) from Susan Dean's spring pre-calculus class: 33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100 a. Create a chart containing the data, frequencies, relative frequencies, and cumulative relative freque... |
the upper 50% (100 – 73 = 27). The histogram, box plot, and chart all reflect this. There are a substantial number of A and B grades (80s, 90s, and 100). The histogram clearly shows this. The box plot shows us that the middle 50% of the exam scores (IQR = 29) are Ds, Cs, and Bs. The box plot also shows us that the low... |
m = interval midpoints. Just as we could not find the exact mean, neither can we find the exact standard deviation. Remember that standard deviation describes numerically the expected deviation a data value has from the mean. In simple English, the standard deviation allows us to compare how “unusual” individual data ... |
Enter Figure 2.29 You will see displayed both a population standard deviation, σx, and the sample standard deviation, sx. Comparing Values from Different Data Sets The standard deviation is useful when comparing data values that come from different data sets. If the data sets have different means and standard deviatio... |
GPA when compared to his school. 2.35 Two swimmers, Angie and Beth, from different teams, wanted to find out who had the fastest time for the 50 meter freestyle when compared to her team. Which swimmer had the fastest time when compared to her team? Swimmer Time (seconds) Team Mean Time Team Standard Deviation Angie B... |
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ Table 2.36 Survey Results 2. Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil and scale the axes. Figure 2.30 3. Calculate the following values. a. b. x¯ = _____ s = _____ 4. Are t... |
quartile Range or IQR, is the range of the middle 50 percent of the data values; the IQR is found by subtracting the first quartile from the third quartile. Interval also called a class interval; an interval represents a range of data and is used when displaying large data sets Mean a number that measures the central t... |
data are skewed to the left. When the greater values are more spread out, the data are skewed to the right. Standard Deviation a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviatio... |
the x-axis. Time series graphs can be helpful when looking at large amounts of data for one variable over a period of time. 2.3 Measures of the Location of the Data The values that divide a rank-ordered set of data into 100 equal parts are called percentiles. Percentiles are used to compare and interpret data. For exa... |
and the mode. There are three types of distributions. A right (or positive) skewed distribution has a shape like Figure 2.17. A left (or negative) skewed distribution has a shape like Figure 2.18. A symmetrical distrubtion looks like Figure 2.16. 2.7 Measures of the Spread of the Data This content is available for fre... |
For each of the following data sets, create a stem plot and identify any outliers. 1. The miles per gallon rating for 30 cars are shown below (lowest to highest). 19, 19, 19, 20, 21, 21, 25, 25, 25, 26, 26, 28, 29, 31, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 38, 38, 38, 41, 43, 43 2. The height in feet of 25 trees is ... |
’s math class have birthdays in each of the four seasons. Table 2.40 shows the four seasons, the number of students who have birthdays in each season, and the percentage (%) of students in each group. Construct a bar graph showing the number of students. Seasons Number of students Proportion of population Spring Summer... |
frequency for each data value? 17. To construct the histogram for the data in Table 2.42, determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram. Label the horizontal and vertical axes with words. Include numerical scaling. Figure 2.31 18. Construct a frequency polygon for the f... |
,239 53,158 53,694 54,628 54,409 54,606 93,349 101,821 103,415 104,018 106,543 105,629 107,009 Male Total Table 2.49 Sex/Year 1862 1863 1864 1865 1866 1867 1868 1869 Female 51,812 53,115 54,959 54,850 55,307 55,527 56,292 55,033 55,257 56,226 57,374 58,220 58,360 58,517 59,222 58,321 107,069 109,341 112,333 113,070 113... |
; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 a. Find the 40th percentile. b. Find the 78th percentile. 24. Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. 18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 7... |
.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 129 31. In a study collecting data about the repair costs of damage to automobiles in a certain type of crash tests, a certain model of car had $1,700 in damage and was in the 90th percentile. Should the manufactu... |
Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell? 2.5 Measures of the Center of the Data 42. Find the mean for the following frequency tables. a. b. Grade Frequency 49.5–59.5 2 59.5–69.5 3 69.5–79.5 8... |
; 4; 5; 5 50. 16; 17; 19; 22; 22; 22; 22; 22; 23 51. 87; 87; 87; 87; 87; 88; 89; 89; 90; 91 52. When the data are skewed left, what is the typical relationship between the mean and median? 53. When the data are symmetrical, what is the typical relationship between the mean and median? 54. What word describes a distribu... |
56; 56; 56; 58; 59; 60; 62; 64; 64; 65; 67 67. Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why? 68. In a perfectly symmetrical distribution, when would the mode be different from the mean and median? 2.7 Measures of the Spread of the Data Use the following informa... |
69.5 69.5–79.5 79.5–89.5 89.5–99.5 Table 2.60 14 32 15 23 2 HOMEWORK 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs 74. Student grades on a chemistry exam were: 77, 78, 76, 81, 86, 51, 79, 82, 84, 99 a. Construct a stem-and-leaf plot of the data. b. Are there any potential outliers? If so, which scor... |
they had purchased the previous month. The results are as follows: # of books Freq. Rel. Freq. 0 1 2 3 4 5 6 8 10 12 16 12 8 6 2 2 Table 2.62 Publisher A # of books Freq. Rel. Freq. 0 1 2 3 4 5 7 9 18 24 24 22 15 10 5 1 Table 2.63 Publisher B # of books Freq. Rel. Freq. 0–1 2–3 4–5 6–7 8–9 20 35 12 2 1 Table 2.64 Publ... |
.66 Couples a. Fill in the relative frequency for each group. b. Construct a histogram for the singles group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis. c. Construct a histogram for the couples group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis. d. Compare the two gra... |
.1 24.0 21.0 22.5 28.0 Kentucky Louisiana Maine Maryland 31.3 31.0 26.8 27.1 North Dakota 27.2 Ohio Oklahoma Oregon 29.2 30.4 26.8 Massachusetts 23.0 Pennsylvania 28.6 Michigan Minnesota Mississippi 30.9 24.8 34.0 Rhode Island 25.5 South Carolina 31.5 South Dakota 27.3 This content is available for free at http://textb... |
–75,000 0.17 75,000–99,999 0.02 100,000+ 0.01 Table 2.69 a. What percentage of the survey answered "not sure"? b. What percentage think that middle-class is from $25,000 to $50,000? c. Construct a histogram of the data. i. Should all bars have the same width, based on the data? Why or why not? ii. How should the <20,00... |
istics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 141 Figure 2.44 a. Think of an example (in words) where the data might fit into the above box plot. In 2–5 sentences, write down the example. b. What does it mean to have the first and second quartiles so close together, while the seco... |
movies they watched the previous week. The results are as follows: # of movies Frequency 0 1 2 3 4 Table 2.70 5 9 6 4 1 Construct a box plot of the data. 2.5 Measures of the Center of the Data 91. The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in the fo... |
FTES • median = 1,014 FTES • σ = 474 FTES • • first quartile = 528.5 FTES third quartile = 1,447.5 FTES • n = 29 years 94. A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer. 95. 75% of all years have an FTES: a. at or below: _____ b. at o... |
. The mean cost for a guitar is $500 with a standard deviation of $200. The mean cost for drums is $700 with a standard deviation of $100. Which cost is the lowest, when compared to other instruments of the same type? Which cost is the highest when compared to other instruments of the same type. Justify your answer. 10... |
APTER 2 | DESCRIPTIVE STATISTICS 145 Percent of Underweight Children Number of Countries 37.8–43.25 43.25–48.7 Table 2.76 6 1 What is the best estimate for the mean percentage of underweight children? What is the standard deviation? Which interval(s) could be considered unusual? Explain. BRINGING IT TOGETHER: HOMEWORK ... |
-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 147 110. What is the IQR? a. 8 b. 11 c. 15 d. 35 111. What is the mode? a. 19 b. 19.5 c. 14 and 20 d. 22.65 112. Is this a sample or the entire population? sample a. b. entire population c. neither 113. Twenty-five randomly select... |
f. The middle 50% of the weights are from _______ to _______. g. h. If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why? If our population included every team member who ever played for the San Francisco 49ers, would the above data be ... |
six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days. Let X = the length (in days) of an engineering conference. CHAPTER 2 | DESCRIPTIVE STATISTICS 149 a. Organize the data in a chart. b. Find the median, th... |
b. 80 c. 3 d. 4 121. The number that is 1.5 standard deviations BELOW the mean is approximately _____ a. 0.7 b. 4.8 c. –2.8 d. Cannot be determined 150 CHAPTER 2 | DESCRIPTIVE STATISTICS 122. Suppose that a publisher conducted a survey asking adult consumers the number of fiction paperback books they had purchased in ... |
Histograms, Frequency Polygons, and Time Series Graphs Data on annual homicides in Detroit, 1961–73, from Gunst & Mason’s book ‘Regression Analysis and its Application’, Marcel Dekker “Timeline: Guide to the U.S. Presidents: Information on every president’s birthplace, political party, term of office, and more.” Schol... |
Adult Obesity Facts.” Centers for Disease Control and Prevention. Available online at http://www.cdc.gov/obesity/data/adult.html (accessed September 13, 2013). 2.3 Measures of the Location of the Data Cauchon, Dennis, Paul Overberg. “Census data shows minorities now a majority of U.S. births.” USA Today, 2012. http://... |
frequency shows the proportion of data points that have each value. The frequency tells the number of data points that have each value. 17 Answers will vary. One possible histogram is shown: 154 CHAPTER 2 | DESCRIPTIVE STATISTICS Figure 2.55 19 Find the midpoint for each class. These will be graphed on the x-axis. The... |
% of houses cost $240,000 or more. 35 4 37 6 – 4 = 2 39 6 41 More than 25% of salespersons sell four cars in a typical week. You can see this concentration in the box plot because the first quartile is equal to the median. The top 25% and the bottom 25% are spread out evenly; the whiskers have the same length. 156 CHAP... |
, so Fredo has a better batting average compared to his team. 73 a. s x = b. s x = c. s x = ∑ f m2 n ∑ f m2 n ∑ f m2 n 75 − x¯ 2 = 193157.45 30 − 79.52 = 10.88 − x¯ 2 = 380945.3 101 − 60.942 = 7.62 − x¯ 2 = 440051.5 86 − 70.662 = 11.14 a. Example solution for using the random number generator for the TI-84+ to generate... |
0.14 0.14 0.07 0.07 a. See Table 2.86 and Table 2.87. This content is available for free at http://textbookequity.org/introductory-statistics or at http://cnx.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 159 b. In the following histogram data values that fall on the right boundary are counted in the cl... |
c 81 Answers will vary. 83 a. 1 – (0.02+0.09+0.19+0.26+0.18+0.17+0.02+0.01) = 0.06 b. 0.19+0.26+0.18 = 0.63 c. Check student’s solution. d. 40th percentile will fall between 30,000 and 40,000 80th percentile will fall between 50,000 and 75,000 e. Check student’s solution. 85 a. more children; the left whisker shows th... |
x.org/content/col11562/1.16 CHAPTER 2 | DESCRIPTIVE STATISTICS 161 h. The interval from 31 to 35 years has the fewest data values. Twenty-five percent of the values fall in the interval 38 to 41, and 25% fall between 41 and 64. Since 25% of values fall between 31 and 38, we know that fewer than 25% fall between 31 and ... |
113 a. 1.48 b. 1.12 115 162 CHAPTER 2 | DESCRIPTIVE STATISTICS a. 174; 177; 178; 184; 185; 185; 185; 185; 188; 190; 200; 205; 205; 206; 210; 210; 210; 212; 212; 215; 215; 220; 223; 228; 230; 232; 241; 241; 242; 245; 247; 250; 250; 259; 260; 260; 265; 265; 270; 272; 273; 275; 276; 278; 280; 280; 285; 285; 286; 290; 290... |
on their assessment of likely results. You may have visited a casino where people play games chosen because of the belief that the likelihood of winning is good. You may have chosen your course of study based on the probable availability of jobs. You have, more than likely, used probability. In fact, you probably have... |
are: to list the possible outcomes, to create a tree diagram, or to create a Venn diagram. The uppercase letter S is used to denote the sample space. For example, if you flip one fair coin, S = {H, T} where H = heads and T = tails are the outcomes. An event is any combination of outcomes. Upper case letters like A and... |
There are two outcomes {5, 6}. P(E) = 2 6. If you were to roll the die only a few times, you would not be surprised if your observed results did not match the probability. If you were to roll the die a very large number of times, you of the rolls would result in an outcome of "at least five". You would not expect exac... |
"OR" Event: An outcome is in the event A OR B if the outcome is in A or is in B or is in both A and B. For example, let A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}. A OR B = {1, 2, 3, 4, 5, 6, 7, 8}. Notice that 4 and 5 are NOT listed twice. "AND" Event: An outcome is in the event A AND B if the outcome is in both A a... |
(B) = (the number of outcomes that are 2 or 3 and even inS) 6 (the number of outcomes that are even inS Understanding Terminology and Symbols It is important to read each problem carefully to think about and understand what the events are. Understanding the wording is the first very important step in solving probabilit... |
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