Deck 3: Displaying and Summarizing Quantitative Data

Question 1

Heights of a group of male professional athletes,half of whom are gymnasts and half of whom are basketball players.

A)The distribution would likely be unimodal and slightly skewed right.The average height of the gymnasts and basketball players would be about the same.The distribution would be slightly skewed to the right,since it is possible to have some exceptionally tall basketball players.
B)The distribution would likely be uniform,with heights of the professional athletes evenly distributed.
C)The distribution would likely be bimodal and slightly skewed right.The average height of the gymnasts would be at one mode,and the average height of the basketball players would be at the other mode,since basketball players are taller than gymnasts.The distribution would be slightly skewed to the right,since it is possible to have some exceptionally tall basketball players,and it is less likely that the heights of gymnasts would vary significantly.
D)The distribution would likely be bimodal and slightly skewed left.The average height of the gymnasts would be at one mode,and the average height of the basketball players would be at the other mode,since basketball players are taller than gymnasts.The distribution would be slightly skewed to the left,since it is possible to have some exceptionally tall basketball players,and it is less likely that the heights of gymnasts would vary significantly.
E)The distribution would likely be unimodal and symmetric.The average height of the gymnasts and basketball players would be about the same.The distribution would be symmetric,since it is possible to have some exceptionally tall basketball players,and exceptionally short gymnasts.

Answer 1

The distribution would likely be bimodal and slightly skewed right.The average height of the gymnasts would be at one mode,and the average height of the basketball players would be at the other mode,since basketball players are taller than gymnasts.The distribution would be slightly skewed to the right,since it is possible to have some exceptionally tall basketball players,and it is less likely that the heights of gymnasts would vary significantly.

Question 2

Here is the stem-and-leaf display of the midterm test scores for the seventh-period typing class.
Would you use the median or the mean to describe the centre of this distribution?

A)Median,because the data are skewed to the left.
B)Mean,because the data are skewed to the left.
C)Mean,because the data are quite symmetric.
D)Mean,because the data are skewed to the right.
E)Median,because the data are skewed to the right.

Answer 2

Mean,because the data are quite symmetric.

Question 3

A university instructor created a website for her Chemistry course.The students in her class were encouraged to use the website as an additional resource for the course.At the end of the semester,the instructor asked each student how many times he or she visited the website and recorded the counts.Based on the histogram below,describe the distribution of website use.

A)The distribution of the number of visits to the course website by each student for the semester is skewed to the left,with the number of visits ranging from 1 to 15 visits.The distribution is centred at about 14 visits,with many students visiting 15 times.
B)The distribution of the number of visits to the course website by each student for the semester is skewed to the left,with the number of visits ranging from 1 to 16 visits.The distribution is centred at about 14 visits,with many students visiting 15 times.There is an outlier in the distribution,two students who visited the site only once.The next highest number of visits was 8.
C)The distribution of the number of visits to the course website by each student for the semester is skewed to the right,with the number of visits ranging from 1 to 15 visits.The distribution is centred at about 14 visits,with many students visiting 15 times.There is an outlier in the distribution,two students who visited the site only once.The next highest number of visits was 8.
D)The distribution of the number of visits to the course website by each student for the semester is skewed to the left,with the number of visits ranging from 1 to 15 visits.The distribution is centred at about 14 visits,with many students visiting 15 times.There is an outlier in the distribution,two students who visited the site only once.The next highest number of visits was 8.
E)The distribution of the number of visits to the course website by each student for the semester is skewed to the left,with the number of visits ranging from 1 to 15 visits.The distribution is centred at about 12 visits,with many students visiting 15 times.There is an outlier in the distribution,two students who visited the site only once.The next highest number of visits was 8.

Answer 3

The distribution of the number of visits to the course website by each student for the semester is skewed to the left,with the number of visits ranging from 1 to 15 visits.The distribution is centred at about 14 visits,with many students visiting 15 times.There is an outlier in the distribution,two students who visited the site only once.The next highest number of visits was 8.

Question 4

The histogram displays the body fat percentages of 65 students taking a college health course.In addition to describing the distribution,give a reason to account for the shape of this distribution.

A)The distribution of body fat percentages is bimodal,with a cluster of body fat percentages around 16% and another cluster of body fat percentages around 26%.The upper cluster shows a bit of a skew to the right.Most students in the lower cluster have body fat percentages between 16% and 20%,and most students in the upper cluster have body fat percentages between 22% and 26%.Men and women have different body fat percentages: the lower cluster would likely represent male students,and the upper cluster would likely represent female students.
B)The distribution of body fat percentages is unimodal,with a bit of a skew to the right.The body fat percentages are centred around 20%,with a range of 10% to 35%.Most students have body fat percentages between 12% and 28%.Men and women have different body fat percentages,but the average of body fat percentages for men and women would be around 20%.
C)The distribution of body fat percentages is unimodal,with a bit of a skew to the right.The body fat percentages are centred around 24%,with a range of 10% to 34%.Most students have body fat percentages between 12% and 28%.Men and women have different body fat percentages,but the average of body fat percentages for men and women would be around 24%.
D)The distribution of body fat percentages is bimodal,with a cluster of body fat percentages around 16% and another cluster of body fat percentages around 26%.The upper cluster shows a bit of a skew to the right.Most students in the lower cluster have body fat percentages between 12% and 18%,and most students in the upper cluster have body fat percentages between 22% and 28%.Men and women have different body fat percentages: the lower cluster would likely represent male students,and the upper cluster would likely represent female students.
E)The distribution of body fat percentages is bimodal,with a cluster of body fat percentages around 12% and another cluster of body fat percentages around 28%.The upper cluster shows a bit of a skew to the right.Most students in the lower cluster have body fat percentages between 12% and 18%,and most students in the upper cluster have body fat percentages between 22% and 28%.Men and women have different body fat percentages: the lower cluster would likely represent male students,and the upper cluster would likely represent female students.

Question 5

Shown below are the histogram and summary statistics for the reading scores of 29 fifth graders.

Which measures of centre and spread would you use for this distribution?

A)Mean and IQR,because the data is skewed to the left.
B)Median and standard deviation,because the data is skewed to the left.
C)Mean and standard deviation,because the data is skewed to the left.
D)Mean and standard deviation,because the data is symmetric.
E)Median and IQR,because the data is skewed to the left.

Question 6

A small company employs a supervisor at $1,100 a week,an inventory manager at $700 a week,6 stock boys at $400 a week,and 4 drivers at $600 a week.Which measure of spread,would best describe the payroll,the range,the IQR,or the standard deviation?

A)IQR,because the distribution is symmetric.
B)Range,because it would be least sensitive to the outlier at $1,100.
C)Standard deviation,because it would be least sensitive to the outlier at $1,100.
D)IQR,because it would be least sensitive to the outliers at $700 and $1,100.
E)IQR,because it would be least sensitive to the outlier at $1,100.

Question 7

Ages of high school students.

A)The distribution would likely be unimodal and slightly skewed to the left.The average age of the high school students would be about the same.The distribution would be slightly skewed to the left,since there are more freshmen.
B)The distribution would likely be unimodal and slightly skewed to the right.The average age of the high school students would be about the same.The distribution would be slightly skewed to the right,since there are more seniors.
C)The distribution would likely be bimodal and slightly skewed to the right.The average age of the freshman and sophomores would be at one mode,and the average age of the juniors and seniors would be at the other mode.The distribution would be slightly skewed to the right,since there are more seniors.
D)The distribution would likely be uniform.Freshmen tend to be about 14 years old;sophomores,15;juniors,16;and seniors,17.Since there is about an equal number of students in each class,the distribution is uniform.
E)The distribution would likely be unimodal and symmetric.The average age of the high school students would be about the same,with some students that are older and some that are younger than the average age.

Question 8

Number of times each face of a fair six-sided die shows in 60 tosses.

A)The distribution would likely be unimodal and skewed left.The average of the numbers on the face of the die would be around 3.5,with more tosses less than 3.5.
B)The distribution would likely be uniform,with around 10 occurrences of each side.
C)The distribution would likely be unimodal and symmetric.The average of the numbers on the face of the die would be around 3.5,with a some tosses greater than 3.5 and some less than 3.5.
D)The distribution would likely be unimodal and skewed right.The average of the numbers on the face of the die would be around 3.5,with more tosses greater than 3.5.
E)The distribution would likely be uniform,with around 60 occurrences of each side.

Question 9

Heights of adult women attending a concert.

A)The distribution would likely be unimodal and symmetric.The average height of women at the concert will be about the same as the median height.The distribution will likely be symmetric,since there are some women who are taller than average and some that are shorter.
B)The distribution would likely be uniform,with the heights of women evenly distributed.
C)The distribution would likely be unimodal and slightly skewed right.The average height of women at the concert will be about the same as the median height.The distribution will likely be slightly skewed right,since there are more women who are tall than short.
D)The distribution would likely be bimodal and slightly skewed left.The average height of shorter women will be at one mode,and the average height of taller women at the other mode.The distribution will likely be slightly skewed left,since there are more women who are short than tall.
E)The distribution would likely be bimodal and slightly skewed right.The average height of shorter women will be at one mode,and the average height of taller women at the other mode.The distribution will likely be slightly skewed right,since there are more women who are tall than short.

Question 10

Ages of patients who had their tonsils removed at a hospital over the course of a year.

A)The distribution would likely be bimodal and skewed right.The procedure is much more common among young people,so most patients would be younger,perhaps 8-12 years old.Eight-year-olds would be at one mode,and twelve-year-olds would be at the other mode.The distribution would be skewed right,since it is possible to have a greater variety of ages among older people,while there is a natural left endpoint to the distribution at zero years of age.
B)The distribution would likely be unimodal and symmetric.The procedure is much more common among young people,so most patients would be younger,perhaps 8-12 years old.The distribution would be symmetric,since it is possible to have this procedure done earlier or later than the average age.
C)The distribution would likely be unimodal and skewed left.The procedure is much more common among young people,so most patients would be younger,perhaps 8-12 years old.The distribution would be skewed left,since it is possible to have a greater variety of ages among younger people
D)The distribution would likely be unimodal and skewed right.The procedure is much more common among young people,so most patients would be younger,perhaps 8-12 years old.The distribution would be skewed right,since it is possible to have a greater variety of ages among older people,while there is a natural left endpoint to the distribution at zero years of age.
E)The distribution would likely be bimodal and symmetric.The procedure is much more common among young people,so most patients would be younger,perhaps 8-12 years old.Eight-year-olds would be at one mode,and twelve-year-olds would be at the other mode.The distribution would be symmetric,since it is possible to have this procedure done earlier or later than the average age.

Question 11

Office workers were asked how long it took them to travel to work one morning.Here is the stem-and-leaf display.
Without actually finding the mean and the median,would you expect the mean to be higher or lower than the median?

A)Lower,because the data are skewed to the right.
B)Lower,because the data are skewed to the left.
C)Higher,because the data are skewed to the left.
D)Higher,because the data are skewed to the right.
E)Neither,because the mean would be equal to the median.

Question 12

A small company employs a supervisor at $1,300 a week,an inventory manager at $800 a week,7 stock boys at $400 a week,and 5 drivers at $700 a week.Which measure of centre best describes a typical wage at this company,the mean at $600 or the median at $550?

A)Mean,because the distribution is symmetric.
B)Median,because of the outlier $1,300.
C)Mean,because there are no outliers.
D)Median,because the distribution is skewed to the left.
E)Median,because of the outliers $800 and $1,300.

Question 13

The histogram shows the cost of living,in dollars,in 32 Canadian towns.

A)The distribution of the cost of living in the 32 Canadian cities is unimodal and skewed to the right.The distribution is centred around $100,and spread out,with values ranging from $80 to $139.99.
B)The distribution of the cost of living in the 32 Canadian cities is unimodal and skewed to the right.The distribution is centred around $110,and spread out,with values ranging from $80 to $140.
C)The distribution of the cost of living in the 32 Canadian cities is unimodal and skewed to the right.The distribution is centred around $90,and spread out,with values ranging from $80 to $139.99.
D)The distribution of the cost of living in the 32 Canadian cities is unimodal and skewed to the left.The distribution is centred around $100,and spread out,with values ranging from $80 to $139.99.
E)The distribution of the cost of living in the 32 Canadian cities is unimodal.The distribution is centred around $100,and spread out,with values ranging from $80 to $140.

Question 14

Number of innings in the baseball games a major league team plays over the course of a season.

A)The distribution would likely be bimodal and skewed right.The great majority of the games will be nine innings and this would represent one mode.However,if the score of a game is tied after nine innings,extra innings are played,so some games will last 10,11,12,or more innings;and,this will represent the other mode.Some games will be 5-8 innings,if for example rain cuts them short,and this is more common than extra-inning games,so the distribution would be skewed to the left.
B)The distribution would likely be bimodal and skewed right.The great majority of the games will be nine innings and this would represent one mode.However,if the score of a game is tied after nine innings,extra innings are played,so some games will last 10,11,12,or more innings;and,this will represent the other mode.Some games will be 5-8 innings,if for example rain cuts them short,but extra-inning games are much more common,so the distribution would be skewed to the right.
C)The distribution would likely be unimodal and skewed right.The great majority of the games will be nine innings.However,if the score of a game is tied after nine innings,extra innings are played,so some games will last 10,11,12,or more innings.Some games will be 5-8 innings,if for example rain cuts them short,but extra-inning games are much more common,so the distribution would be skewed to the right.
D)The distribution would likely be unimodal and skewed left.The great majority of the games will be nine innings.However,if the score of a game is tied after nine innings,extra innings are played,so some games will last 10,11,12,or more innings.Some games will be 5-8 innings,if for example rain cuts them short,and this is more common than extra-inning games,so the distribution would be skewed to the left.
E)The distribution would likely be uniform.Some games will be nine innings.However,if the score of a game is tied after nine innings,extra innings are played,so some games will last 10,11,12,or more innings.Some games will be 5-8 innings,if for example rain cuts them short.The number of innings in the games would be evenly distributed.

Question 15

The display shows the heights of Grade 12 students at a local high school,collected so that the students could be arranged with shorter ones in front and taller ones in back for a class photograph.In addition to describing the distribution,give a reason to account for the shape of this distribution.

A)The distribution of the heights of Grade 12 students is bimodal,with a mode at around 65 inches and the other mode around 71 inches.The students' heights are between 60 inches and 74 inches.The two modes would likely represent the average heights of the male and female students.
B)The distribution of the heights of Grade 12 students is unimodal centred at 68,with a heights ranging from 60 inches to 76 inches.The two peaks would likely represent the average heights of the male and female students.
C)The distribution of the heights of Grade 12 students is bimodal,with a mode at around 62 inches and the other mode around 74 inches.No student has a height below 60 inches or above 76 inches.The two modes would likely represent the average heights of the male and female students.
D)The distribution of the heights of Grade 12 students is bimodal,with a mode at around 65 inches and the other mode around 71 inches.No student has a height below 60 inches or above 76 inches.The two modes would likely represent the average heights of the male and female students.
E)The distribution of the heights of Grade 12 students is uniform centred at 68,with a heights ranging from 60 inches to 76 inches.The two peaks would likely represent the average heights of the male and female students.

Question 16

The histograms display the body fat percentages of 42 female students and 48 male students taking a college health course.For which of the variables depicted in the histograms would you be most satisfied to summarize the centre with a mean? Explain.

A)The histogram of Women's Body Fat is skewed on the left.That makes it the best candidate of summarizing with a mean.
B)The histogram of Women's Body Fat shows no outliers.That makes it the best candidate of summarizing with a mean.
C)The histogram of Men's Body Fat is most nearly symmetric,is not strongly skewed and shows no outliers.That makes it the best candidate of summarizing with a mean.
D)The histogram of Women's Body Fat is most nearly symmetric,is not strongly skewed and shows no outliers.That makes it the best candidate of summarizing with a mean.
E)The histogram of Men's Body Fat is skewed on the left.That makes it the best candidate of summarizing with a mean.

Question 17

The histogram shows the sizes (in acres)of 169 farms in Ontario.In addition to describing the distribution,approximate the percentage of farms that are under 100 acres.

A)The distribution of the size of farms in Ontario is skewed to the right.Most of the farms are smaller than 150 acres,with some larger ones,from 150 to 300 acres.Five farms were larger than the rest,over 400 acres.The mode of the distribution is between 0 and 50 acres.It appears that 118 of 169 farms are under 100 acres,approximately 70%.
B)The distribution of the size of farms in Ontario is symmetric,with farm sizes ranging from 0 to 450 acres.The mode of the distribution is between 0 and 50 acres.It appears that 118 of 169 farms are under 100 acres,approximately 70%.
C)The distribution of the size of farms in Ontario is symmetric,with farm sizes ranging from 0 to 450 acres.The mode of the distribution is between 100 and 150 acres.It appears that 118 of 169 farms are under 100 acres,approximately 70%.
D)The distribution of the size of farms in Ontario is skewed to the right.Most of the farms are smaller than 50 acres,with some larger ones,from 150 to 300 acres.Five farms were larger than the rest,over 400 acres.The mode of the distribution is between 0 and 50 acres.It appears that 118 of 169 farms are under 100 acres,approximately 70%.
E)The distribution of the size of farms in Ontario is skewed to the right.Most of the farms are smaller than 150 acres,with some larger ones,from 150 to 300 acres.Five farms were larger than the rest,over 400 acres.The mode of the distribution is between 0 and 50 acres.It appears that 62 of 169 farms are under 100 acres,approximately 37%.

Question 18

Office workers were asked how long it took them to travel to work one morning.Here is the stem-and-leaf display.
Would you use the median or the mean to describe the centre of this distribution?

A)Mean,because the data are skewed to the right.
B)Median,because the data are skewed to the left.
C)Mean,because the data are skewed to the left.
D)Mean,because the data are symmetric.
E)Median,because the data are skewed to the right.

Question 19

The histogram shows the lengths of hospital stays (in hours)for pregnant women admitted to hospitals in Ontario who were having contractions upon arrival.

A)The distribution of the length of hospital stays for pregnant patients is skewed to the right,with stays ranging from 1 hour to 96 hours.The distribution is centred around 26 hours,with the majority of stays lasting between 1 to 48 hours.There are relatively few hospital stays longer than 72 hours.Many patients have a stay of only 1-4 hours,possibly because it was not time to deliver.
B)The distribution of the length of hospital stays for pregnant patients is skewed to the right,with stays ranging from 1 hour to 95 hours.The distribution is centred around 26 hours,with the majority of stays lasting between 1 to 48 hours.There are relatively few hospital stays longer than 72 hours.
C)The distribution of the length of hospital stays for pregnant patients is skewed to the right,with stays ranging from 1 hour to 96 hours.The distribution is centred around 26 hours,with the majority of stays lasting between 3 to 24 hours.There are relatively few hospital stays longer than 72 hours.Many patients have a stay of only 1-4 hours,possibly because it was not time to deliver.
D)The distribution of the length of hospital stays for pregnant patients is skewed to the right,with stays ranging from 1 hour to 95 hours.The distribution is centred around 48 hours,with the majority of stays lasting between 24 to 72 hours.There are relatively few hospital stays longer than 72 hours.Many patients have a stay of only 1-3 hours,possibly because it was not time to deliver.
E)The distribution of the length of hospital stays for pregnant patients is skewed to the right,with stays ranging from 1 hour to 95 hours.The distribution is centred around 26 hours,with the majority of stays lasting between 1 to 48 hours.There are relatively few hospital stays longer than 72 hours.Many patients have a stay of only 1-3 hours,possibly because it was not time to deliver.

Question 20

Here are summary statistics of the four last digits of social security number of 500 customers,corresponding to the following histogram.

Is the mean or median a "better" summary of the centre of the distribution?

A)Neither,because these are not categorical data.
B)Neither,because these are not quantitative data.
C)Median,because the IQR is smaller than the standard deviation.
D)Mean,because the distribution is quite symmetric.
E)Median,because of the outliers.

Question 21

The histograms show the cost of living,in dollars,for 32 U.S.cities.The histogram on the left shows the cost of living for the 32 cities using bins $10 wide,and the histogram on the right displays the same data using bins that are $6 wide.For which of the histograms would you most strenuously insist on using an IQR rather than a standard deviation to summarize spread? Explain.

A)The histogram on the right is most nearly symmetric and shows no outliers.That makes it the best candidate for summarizing with an IQR.
B)The histogram on the left shows a low outlier.The standard deviation is sensitive to outliers,so we'd prefer to use the IQR for this one.
C)The histogram on the right shows a high outlier.The standard deviation is sensitive to outliers,so we'd prefer to use the IQR for this one.
D)The histogram on the left is most strongly skewed to the right.That makes it the best candidate for summarizing with an IQR.
E)The histogram on the left is most nearly symmetric and shows no outliers.That makes it the best candidate for summarizing with an IQR.

Question 22

The annual incomes,in dollars,of several doctors are listed below.

A)$238,000
B)$188,000
C)$169,500
D)$264,000
E)$151,000

Question 23

A new business had the following monthly revenues,in dollars.

A)$4,919.10
B)$5,008.00
C)$4,841.00
D)$5,465.67
E)$5,175.00

Question 24

The students in a math class took the Scholastic Aptitude Test.Their math scores are shown below.

A)461.7
B)476.0
C)552.1
D)452.6
E)471.1

Question 25

The employees at Frank's Furniture earned the following amounts,in dollars,last week.
Round your answer to the nearest cent.

A)$423.42
B)$435.42
C)$544.28
D)$533.66
E)$362.85

Question 26

The number of cars passing through a Tim Hortons "drive-thru" during each 15-minute period was recorded.The results are shown below.

A)20 cars
B)23 cars
C)22 cars
D)21.85 cars
E)26 cars

Question 27

The local Tupperware dealers earned the following commissions,in dollars,last month.
Round your answer to the nearest cent.

A)$4,073.77
B)$3,660.40
C)$2,342.19
D)$3,666.40
E)$4,583.00

Question 28

Here are the number of hours that Bill has exercised each week since he started keeping records.
Round your answer to the nearest tenth.

A)8.3 hours
B)9.3 hours
C)8.0 hours
D)7.8 hours
E)7.4 hours

Question 29

Here are the number of baseball games that Dave attended over the last several seasons.
1 15 17 21 30 30 49

A)17 games
B)24 games
C)21 games
D)30 games
E)25.5 games

Question 30

The back-to-back dotplot shows the number of fatalities per year caused by tornadoes in a certain state for two periods: 1950-1974 and 1975-1999.Explain how you would summarize the centre and spread of each of the variables depicted in the dotplots.

A)The distribution of the number of fatalities per year for the period 1950-1974 is unimodal and approximately symmetric.Therefore,we would be satified using the mean to summarize the centre and the standard deviation to summarize spread.For the period 1975-1999,the distribution of the number of fatalities per year is also unimodal,but skewed to the right.Therefore,we would prefer to use a median for centre and an IQR to summarize spread.
B)The distribution of the number of fatalities per year for the period 1950-1974 is unimodal,but skewed to the right.Therefore,we would prefer to use a median for centre and an IQR to summarize spread.For the period 1975-1999,the distribution is also unimodal and approximately symmetric.Therefore,we would be satisfied using the mean to summarize the centre and the standard deviation to summarize spread.
C)The distribution of the number of fatalities per year for the period 1950-1974 is bimodal.Therefore,we would prefer to use a median to summarize the centre and an IQR to summarize spread.For the period 1975-1999,the distribution of the number of fatalities per year is also bimodal,but skewed to the left.Therefore,we would prefer to use a mean for centre and an standard deviation to summarize spread.
D)The distribution of the number of fatalities per year for the period 1950-1974 is unimodal and approximately symmetric.Therefore,we would prefer to use the median to summarize the centre and the standard deviation to summarize spread.For the period 1975-1999,the distribution of the number of fatalities per year is also unimodal,but skewed to the right.Therefore,we would prefer to use the mean for centre and an IQR to summarize spread.
E)The distribution of the number of fatalities per year for the period 1950-1974 is unimodal but skewed to the right.Therefore,we would prefer to use a median to summarize the centre and and IQR to summarize spread.For the period 1975-1999,the distribution of the number of fatalities per year is also unimodal and skewed to the right.Therefore,we would prefer to use a median for centre and an IQR to summarize spread.

Question 31

The precipitation,in millimetres,for August is given for 20 different Canadian cities.

A)67
B)56
C)58
D)65
E)36

Question 32

A small company employs a supervisor at $1,400 a week,an inventory manager at $800 a week,8 stock boys at $300 a week each,and 6 drivers at $700 a week each.

A)$2,200
B)$733
C)$500
D)$300
E)$550

Question 33

Here are the amounts,in dollars,spent by six students at a university book store.
Round your answer to the nearest cent.

A)$242.94
B)$318.67
C)$254.94
D)$167.42
E)$212.45

Question 34

A substitute teacher traveled the following distances,in kilometres,to arrive at work.

A)21
B)24
C)26
D)20
E)55

Question 35

Here are the weights,in grams,of several snack crackers.

A)25.23
B)22.40
C)27.22
D)34.59
E)13.32

Question 36

Last year,nine employees of an electronics company retired.Their ages at retirement,in years,are listed below.
Round your answer to the nearest tenth.

A)61.0 years old
B)55.5 years old
C)56.8 years old
D)57.4 years old
E)56.2 years old

Question 37

John liked to order the all-you-can-eat shrimp at his favorite restaurant.Here are the number of shrimp he ate during his last five visits to the restaurant.
15,16,13,15,10

A)15 shrimp
B)13 shrimp
C)13.8 shrimp
D)17.3 shrimp
E)10 shrimp

Question 38

A store manager kept track of the number of newspapers sold each week.The results are shown below.

A)182 newspapers
B)203 newspapers
C)261 newspapers
D)193 newspapers
E)246 newspapers

Question 39

Jody got a bank statement each month that listed the balance,in dollars,in her checking account.Here are the balances on several statements.
Round your answer to the nearest cent.

A)$497.10
B)$381.72
C)$435.20
D)$441.87
E)$568.11

Question 40

Here are the grocery bills,in dollars,for six shoppers.
Round your answer to the nearest cent.

A)$91.86
B)$46.02
C)$73.49
D)$61.49
E)$61.24

Question 41

Here are the average mathematics achievement scores for ninth graders in 32 counties.Find the standard deviation.

A)75.3
B)75
C)73.3
D)74.3
E)75.5

Question 42

The weekly salaries,in dollars,of 16 government workers are listed below.Find the lower quartile (Q1)by hand.

A)$542.00
B)$537.00
C)$491.00
D)$534.50
E)$532.00

Question 43

The test scores of 19 students are listed below.Find the upper quartile (Q3)by hand.

A)55.5
B)83.0
C)65.0
D)80.0
E)81.5

Question 44

Which set has the largest standard deviation?

A)Neither,because set 1 and set 2 have the same standard deviation.
B)Set 1,because 7 and 7 in set 1 are farther from 7 than 6 and 8 in set 2.
C)Set 1,because 6 and 8 in set 1 are farther from 7 than 7 and 7 in set 2.
D)Set 2,because 6 and 8 in set 2 are farther from 7 than 7 and 7 in set 1.
E)Set 2,because 7 and 7 in set 2 are farther from 7 than 6 and 8 in set 1.

Question 45

A small company employs a supervisor at $1,300 a week,an inventory manager at $600 a week,5 stock boys at $300 a week each,and 3 drivers at $500 a week each.

A)$300
B)$500
C)$400
D)$600
E)$490

Question 46

The semester point totals of 16 students are listed below.Find the interquartile range (IQR)by hand.

A)297
B)169
C)165.5
D)588
E)616

Question 47

Here are costs (in dollars)of 12 refrigerators.Find the range.

A)$905
B)$920
C)$915
D)$900
E)$910

Question 48

The weights,in kilograms,of 17 randomly selected adults are given below.Find the interquartile range (IQR)by hand.

A)21.3 kg
B)51.7 kg
C)17.5 kg
D)13.6 kg
E)39.9 kg

Question 49

Which set has the largest standard deviation?

A)Set 2,because 80 and 180 in set 1 are larger than 10 and 110 in set 2.
B)Neither,because the values in set 1 are just the values in set 2 plus 70.
C)Set 1,because 180 in set 1 is larger than 110 in set 2.
D)Set 1,because 80 and 180 in set 1 are larger than 10 and 110 in set 2.
E)Set 2,because set 2 has a smaller range than set 1.

Question 50

The stem-and-leaf display shows the results of a math test written by 30 students.

A)79
B)81.5
C)87
D)80.5
E)88.5

Question 51

The test scores of 19 students are listed below.Find the range.

A)(54,99)
B)(66,99)
C)33
D)45
E)44

Question 52

The weekly salaries,in dollars,of 16 government workers are listed below.Find the upper quartile (Q3)by hand.

A)$734.00
B)$776.75
C)$791.00
D)$654.00
E)$762.50

Question 53

Here are the prices for 8 different CD players.Find the standard deviation.

A)$87.65
B)$648,660.50
C)$183.00
D)$702,438.00
E)$222

Question 54

The ages of the 21 members of a track and field team are listed below.Find the standard deviation.

A)6.5
B)6.6
C)6.7
D)6.4
E)6.3

Question 55

The test scores of 15 students are listed below.Find the lower quartile (Q1)by hand.

A)55
B)56.5
C)58
D)85
E)86

Question 56

The weights,in kilograms,of 18 randomly selected adults are given below.Find the range.

A)(51.7 kg,91.6 kg)
B)(54.4 kg,91.6 kg)
C)91.6 kg
D)37.2 kg
E)39.9 kg

Question 57

Here are the average mathematics achievement scores for ninth graders in 34 counties.Find the standard deviation.

A)55.8
B)57.5
C)54.2
D)56.2
E)55.2

Question 58

The test scores of 19 students are listed below.Find the interquartile range (IQR)by hand.

A)25
B)31.5
C)31
D)30.5
E)28.5

Question 59

Here are the commutes (in kilometres)for a group of six employees.Find the standard deviation.

A)421.6
B)214.6
C)72.6
D)20.5
E)98.9

Question 60

The weights (in kilograms)of 27 dogs are listed below.Find the standard deviation.

A)0.50 kg
B)0.49 kg
C)0.24 kg
D)6.27 kg
E)0.51 kg

Question 61

The following stem-and-leaf display shows the number of homeless cats and dogs that had to be euthanized each year in a large city for the period 1985-2004.
Key:
87 | 5 = 87,500 cats and dogs euthanized

A)The distribution of the number of cats and dogs that were euthanized is skewed to the right,and has several modes,with gaps in between.One mode is clustered between 87,000 and 90,000 euthanized,a second mode at 84,000,and a third mode with a cluster between 81,000 and 82,000.
B)The distribution of the number of cats and dogs that were euthanized is bimodal.The upper cluster is between 89,000 and 90,000 euthanized,with a centre at around 89,500.The lower cluster is between 81,000 and 82,000 euthanized,with a centre at around 81,200.
C)The distribution of the number of cats and dogs that were euthanized is bimodal.The upper cluster is between 87,000 and 90,000 euthanized,with a centre at around 88,500.The lower cluster is between 81,000 and 83,000 euthanized,with a centre at around 81,200.
D)The distribution of the number of cats and dogs that were euthanized is skewed to the right,with a centre at around 85,500.The number of cats and dogs euthanized each year ranges from 81,200 to 90,200.
E)The distribution of the number of cats and dogs that were euthanized is unimodal,ranging from 81,200 to 90,200 euthanized.The centre of the distribution is at around 85,500.

Question 62

Ontario wanted to find the typical size of farms in the province.The data below shows the sizes (in acres)of the 84 farms located in Ontario.Create a histogram of the data using bins that are 50 acres wide.

Question 63

The number of days off that 30 police officers took in a given year are provided below.Create a histogram of the data using bins 2 days wide.

Question 64

The mathematics department at a Canadian university collected data for the number of students enrolled in 40 math courses over the course of one year.The following stem-and-leaf display shows the total number of students enrolled in each class.
Key:
10 | 6 = 106 students

A)The distribution of the number of students enrolled in each of 40 math courses is skewed to the left,with a typical class size of 89 students.The smallest class size was 36 and the largest was 123.
B)The distribution of the number of students enrolled in each of 40 math courses is unimodal and symmetric.The smallest class size was 36 and the largest was 123.The centre of the distribution was around 75 students.
C)The distribution of the number of students enrolled in each of 40 math courses is nearly uniform.The smallest class size was 36 and the largest was 123.The centre of the distribution was around 89 students.
D)The distribution of the number of students enrolled in each of 40 math courses is nearly uniform.The smallest class size was 36 and the largest was 123.The centre of the distribution was around 75 students.
E)The distribution of the number of students enrolled in each of 40 math courses is skewed to the right,with a typical class size of 69 students.The smallest class size was 36 and the largest was 123.

Question 65

In a college health course,65 students participated in a physical fitness assessment.One measure used in the assessment was body fat.The body fat percentages for the 65 students is given below.Create a histogram of the data using bins that are 2% wide.

Question 66

The diastolic blood pressures,in mm Hg,for a sample of patients at a clinic are given.Create a stem-and-leaf display of the data.Do not use split stems.

Question 67

The data below represent the midterm grades for 24 students enrolled in an electrical engineering course.Create a stem-and-leaf display of the data.Use split stems.Let the lower leaf represent digits 0-4 and the upper leaf represent 5-9.

Question 68

In a survey,26 voters were asked their ages.The results are shown below.Construct a histogram to represent the data (with 5 bins beginning with a lower bin limit of 19.5 and a bin width of 10).What is the approximate age at the centre?

Question 69

A dotplot of the number of tornadoes each year in a certain county from 1948 to 2004 is given.Each dot represents a year in which there were that many tornadoes.

A)The distribution of the number of tornadoes per year is unimodal and symmetric,with a centre around 5 tornadoes per year.The number of tornadoes per year ranges from 0 to 7.
B)The distribution of the number of tornadoes per year is unimodal and skewed to the left,with a centre around 3.5 tornadoes per year.The number of tornadoes per year ranges from 0 to 7.
C)The distribution of the number of tornadoes per year is unimodal and symmetric,with a centre around 3.5 tornadoes per year.The number of tornadoes per year ranges from 0 to 7.
D)The distribution of the number of tornadoes per year is unimodal and skewed to the left,with a centre around 5 tornadoes per year.The number of tornadoes per year ranges from 0 to 7.
E)The distribution of the number of tornadoes per year is unimodal and skewed to the right,with a centre around 5 tornadoes per year.The number of tornadoes per year ranges from 0 to 7.

Question 70

A student at a local university took a total of 20 exams during freshman year.The student recorded the exam scores as percentages and created the following stem-and-leaf display.The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9.In addition to describing the distribution,give a reason to account for the shape of this distribution.
Key:
9 | 3 = 93%

A)The distribution of exam scores is skewed to the left.Typically,the student scored 94% on exams,and the exam scores are tightly clustered in the 90s.Two exam scores are outliers,when the student scored below 65%.It is possible that the student had a difficult time with one of his or her courses in that year.Regardless of the possible reasons,these two scores were unusual compared to the student's other exam scores.
B)The distribution of exam scores is skewed to the left.Typically,the student scored 95% on exams,and the exam scores are tightly clustered in the 90s.Two exam scores are outliers,when the student scored below 65%.It is possible that the student had a difficult time with one of his or her courses in that year.Regardless of the possible reasons,these two scores were unusual compared to the student's other exam scores.
C)The distribution of exam scores is skewed to the right.Typically,the student scored 95% on exams,and the exam scores are tightly clustered in the 90s.Two exam scores are outliers,when the student scored below 65%.It is possible that the student had a difficult time with one of his or her courses in that year.Regardless of the possible reasons,these two scores were unusual compared to the student's other exam scores.
D)The distribution of exam scores is skewed to the left.Typically,the student scored 95% on exams,and the exam scores are tightly clustered in the upper 80s and lower 90s.Two exam scores are outliers,when the student scored below 65%.It is possible that the student had a difficult time with one of his or her courses in that year.Regardless of the possible reasons,these two scores were unusual compared to the student's other exam scores.
E)The distribution of exam scores is skewed to the left.Typically,the student scored 95% on exams,and the exam scores are tightly clustered in the 90s.

Question 71

The stem-and-leaf diagram shows the ages of 17 people at a playground in London,Ontario.
Key:
3 | 3 = 33 years

A)The distribution of the ages of people at the playground is skewed to the left,with a typical age between 32 and 38.With the exception of the 3 people less than 10 years old,the ages are between 27 and the maximum 71 .
B)The distribution of the ages of people at the playground is skewed to the right,with a typical age between 42 and 54.With the exception of the 3 people less than 10 years old,the ages are between 27 and the maximum 71.
C)The distribution of the ages of people at the playground is skewed to the right,with a typical age between 27 and 71 .There are 3 outliers,when people are less than 10 years old.
D)The distribution of the ages of people at the playground is skewed to the right,with a typical age between 32 and 38 .
E)The distribution of the ages of people at the playground is skewed to the right,with a typical age between 32 and 38.With the exception of the 3 people less than 10 years old,the ages are between 27 and the maximum 71.

Question 72

The diastolic blood pressures,in mm Hg,for a sample of patients at a clinic are given.Create a stem-and-leaf display of the data.Use split stems.Let the lower leaf represent digits 0-4 and the upper leaf represent 5-9.

Question 73

The weights,in kilograms,of the members of the varsity football team are listed below.Create a stem-and-leaf display of the data.Use split stems by separating each stem into 5 stems.

Question 74

Three statistics classes (50 students each)took the same test.Shown below are histograms of the scores for the classes.Use the histograms to answer the question.
Which class had the highest mean score?

A)Class 1
B)Class 2
C)Class 1 and class 3
D)Class 3
E)None,because the classes had the same mean.

Question 75

Which set has the largest standard deviation?

A)Set 2,because set 2 has a wider range and will have a smaller SD.
B)Set 1,because set 1 has a narrower range and will have a larger SD.
C)Set 1,because the minimum and maximum in set 1 are farther from the centre.
D)Neither,because the values in set 2 are just the values in set 1 plus 45.
E)Set 2,because the minimum and maximum in set 2 are farther from the centre.

Question 76

The data below give the number of tornadoes that happened each year in a certain county from 1948 through 2004.Create a dotplot of these data.

Question 77

In May 2011,17 coffee shops in Toronto charged the following amounts,in dollars,for a large cup of coffee (including tax).The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9.
Key:
1.9 | 6 = $1.96

A)The distribution of large coffee prices is skewed to the right,centred around $2.00 ,with most coffee shops charging between $1.95 and $2.03.The lowest and highest prices were $1.93 and $2.18.There is a gap in the distribution,no coffee shops charged between $2.08 and $2.16.
B)The distribution of large coffee prices is skewed to the right,centred around $2.00,with most coffee shops charging between $1.95 and $2.03.The lowest and highest prices were $1.93 and $2.03.
C)The distribution of large coffee prices is skewed to the right,centred around $1.95,with most coffee shops charging between $1.93 and $1.98.The lowest and highest prices were $1.93 and $2.03.There is a gap in the distribution,no coffee shops charged between $2.08 and $2.16.
D)The distribution of large coffee prices is skewed to the left,centred around $1.95,with most coffee shops charging between $1.93 and $1.98.The lowest and highest prices were $1.93 and $2.03.There is a gap in the distribution,no coffee shops charged between $2.08 and $2.16.
E)The distribution of large coffee prices is skewed to the left,centred around $2.00,with most coffee shops charging between $1.95 and $2.03.The lowest and highest prices were $1.93 and $2.03.There is a gap in the distribution,no coffee shops charged between $2.08 and $2.16.

Question 78

A business owner recorded her annual profits for the first 12 years since opening her business.The stem-and-leaf display below shows the annual profits in thousands of dollars.
Key:
13 | 8 = $138,000 profit

A)The distribution of the business owner's profits is skewed to the left,and is multimodal,with gaps in between.Five years the business had profits near $140,000,another four years the business had profits near $110,000,and three years the business had profits near $80,000.
B)The distribution of the business owner's profits is skewed to the right,and is unimodal,with gaps in between.The centre is at around $110,000.
C)The distribution of the business owner's profits is skewed to the right,and is multimodal,with gaps in between.Five years the business had profits near $140,000,another four years the business had profits near $110,000,and three years the business had profits near $80,000.
D)The distribution of the business owner's profits is skewed to the left,and is unimodal,with gaps in between.The centre is at around $110,000.
E)The distribution of the business owner's profits is skewed to the left,and is multimodal,with gaps in between.Five years the business had profits near $130,000,another four years the business had profits near $100,000,and three years the business had profits near $70,000.

Question 79

Members of the Ontario Field Ornithologists (OFO)observe birds at various locations within the province to see how many different species of bird they can spot.Suppose that 21 members have reported spotting the following number of species in 2010.The lower stem contains leaves with the digits 0-4 and the upper stem contains leaves with digits 5-9.
Key:
11 | 7 = 117 birds

A)The distribution of the number of birds spotted by OFO members in 2010 is skewed right,with a centre at around 125 birds.There are several high outliers,with two members spotting 158 birds and another spotting 178.With the exception of these outliers,most members saw between 102 and 139 birds.
B)The distribution of the number of birds spotted by OFO members in 2010 is skewed right,with a centre at around 111 birds.There are several high outliers,with two members spotting 158 birds and another spotting 178.With the exception of these outliers,most members saw between 102 and 139 birds.
C)The distribution of the number of birds spotted by OFO members in 2010 is skewed left,with a centre at around 111 birds.Most members saw between 102 and 178 birds.
D)The distribution of the number of birds spotted by OFO members in 2010 is skewed left,with a centre at around 111 birds.There are several high outliers,with two members spotting 158 birds and another spotting 178.With the exception of these outliers,most members saw between 102 and 139 birds.
E)The distribution of the number of birds spotted by OFO members in 2010 is skewed right,with a centre at around 111 birds.Most members saw between 102 and 178 birds.

Question 80

In a survey,20 people were asked how many magazines they had purchased during the previous year.The results are shown below.Construct a histogram to represent the data.Use 4 bins with a bin width of 10,and begin with a lower bin limit of -0.5.What is the approximate amount at the centre?