Deck 3: Numerical Summaries of Center and Variation

Question 1

Two algebra classes at University High School took the same quiz. Mr. Athens had 25 students in his class with a mean score of 80. Mrs. Sutton's class of 30 students had a mean score of 75. Overall, what was the mean score for all students on the quiz?

Answer 1

Question 2

The boxplots below represent critics' movie ratings (from 0 to 100) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List the movie ratings according to their median critics' rating, from worst to best.

Answer 2

Worst to best: PG, PG-13, R, G.

Question 3

[Be able to calculate the mean for a small set of data.] The ages of five college students are listed below. Calculate the mean age of these students.

Answer 3

Question 4

Use the following information for following questions
A math professor has two routes he can take to campus. The length of time it takes to drive each
of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard
deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation
of 3 minutes. Assume that both distributions are unimodal and roughly symmetric.
Explain what a z-score of 1.3 would mean if the professor took Route A.

Question 5

The mean can be thought of as the balancing point of a distribution.According to this description, at approximately what value is the following distribution balanced?

Question 6

Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 1500 car accidents; but there were actually only 150 that day. How will this error affect the measures of center for this data?

Question 7

For the pair of histograms below, which distribution has the smaller standard deviation. Why?

Question 8

The fastest 25% of men participants ran the marathon how quickly?

Question 9

What do the dots on the right side of the boxplot represent? What does this mean in terms of marathon times?

Question 10

Ten parents were asked the ages of their youngest child. The results are shown below. What is the IQR for this set of data?

Question 11

For a left-skewed distribution, how will the median value compare to the mean value?

Question 12

Suppose we have the distribution of household income in the United States. What measures of center and spread would be best to describe this data?

Question 13

What is one feature of a distribution that can NOT be determined from a boxplot? The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics. Use the plot for Questions (19) and (20).

Question 14

A class of 20 history students took a quiz worth 100 points. The standard deviation of the scores was 0. What can you say about the scores of the students on this quiz?

Question 15

The number of dogs available at a local animal shelter was recorded for the past 8 days. Find the median.

Question 16

Use the following information for following questions
A math professor has two routes he can take to campus. The length of time it takes to drive each
of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard
deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation
of 3 minutes. Assume that both distributions are unimodal and roughly symmetric.
If it took the professor 24 minutes to drive to campus using Route B one day, would you consider this an unusual drive time? Why?

Question 17

Use the following information for following questions
A math professor has two routes he can take to campus. The length of time it takes to drive each
of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard
deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation
of 3 minutes. Assume that both distributions are unimodal and roughly symmetric.
Today, the z-score for the professor's travel time was −2.1. How many minutes did it take him to drive to campus if he took Route B?

Question 18

Use the following information for following questions
A math professor has two routes he can take to campus. The length of time it takes to drive each
of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard
deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation
of 3 minutes. Assume that both distributions are unimodal and roughly symmetric.
If the professor takes Route A, how often will he be able to drive to campus between 16 and 24 minutes?

Question 19

The five-number summary of the length of phone calls of 100 people is listed below. Consider the following two statements regarding outliers for this data and determine which, if any, are correct. Explain your reasoning. (i) There is at least one person made a phone call that is a low outlier. (ii) There is at least one person made a phone call that is a high outlier.

Question 20

Approximately what value corresponds to the first quartile of the following boxplot?

Question 21

The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from longest to shortest.

A)
B)
C)
D)

Question 22

Suppose we have a distribution of student exam scores on an easy test. What measure of spread would be best to describe this data?

A)The spread should be described with the standard deviation because the distribution will be symmetric.
B)The spread should be described with the IQR because the distribution will be symmetric.
C)The spread should be described with the standard deviation because the distribution will be skewed to the left.
D)The spread should be described with the IQR because the distribution will be skewed to the left.

Question 23

Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 14 car accidents; but there were actually 140 that day. How will this error affect the measures of center for this data?

A)The mean and the median will be lower than they should be.
B)The mean and the median will not be affected by this error.
C)The mean will be lower than it should be, but the median will not be affected.
D)The median will be lower than it should be, but the mean will not be affected.

Question 24

The following boxplot contains information about the length of time (in minutes) it took women participants to finish the marathon race at the 2012 London Olympics.

What can be said about the shape of the distribution of men's running times for the marathon?

A) The distribution is symmetric.
B) The distribution is unimodal.
C) The distribution is left-skewed.
D) The distribution is right-skewed.

Question 25

The five-number summary of the ages of a group of 100 adults is listed below. Consider the following two statements regarding outliers for this data and determine which, if any, are correct. (i) There is at least one adult whose age is a low outlier. (ii) There is at least one adult whose age is a high outlier.

A)Only statement (i) is correct.
B)Only statement (ii) is correct.
C)Both statements (i) and (ii) are correct.
D)Neither statement (i) or (ii) is correct.

Question 26

The distribution of the number of "friends" all users of a popular social media site have is strongly skewed to the right. Which of the following is true?

A)The median number of friends is smaller than the mean.
B)The median number of friends is larger than the mean.
C)The median number of friends is equal to the mean.
D)There is not enough information to compare the median and mean values.

Question 27

A class of 30 French students took a quiz worth 50 points. The standard deviation of the scores was 0. What must be true about the students' scores?

A)The mean, median, and mode must all be 0.
B)Every student received the same score.
C)Every student scored 50 on the quiz.
D)There was an error in the calculation for standard deviation.

Question 28

The number of students enrolled in a college algebra class for the last seven semesters are listed below. Find the median.

A)57
B)58
C)59
D)60

Question 29

For the pair of histograms below, determine which distribution has the smaller standard deviation.

A)(i) has a smaller standard deviation than (ii).
B)(ii) has a smaller standard deviation than (i).
C)Both histograms have the same standard deviation.
D)There is no way to determine which one is smaller.

Question 30

[Be able to calculate the mean for a small set of data.] The ages of five adults are listed below. Calculate the mean age of these adults.

A)44
B)45
C)46
D)47

Question 31

Use the following information for following questions .
The distribution of the number of hours people spend at work per day is unimodal
and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.
If Anthony's z-score for his work hours was −1.3, how many hours did he work?

A)7.20 hours
B)7.35 hours
C)7.50 hours
D)8.65 hours

Question 32

Two Physics classes at Jefferson High School took the same quiz. Mr. Spears had 20 students in his class with a mean score of 80. Mrs. Guyton's class of 30 students had a mean score of 90. Overall, what was the mean score for all students on the quiz?

A)84
B)85
C)86
D)87

Question 33

Ten parents were asked the ages of their oldest child. The results are shown below. What is the IQR for this set of data?

A)10
B)12
C)15
D)27

Question 34

Which boxplot represents the same data as the histogram shown below?

A)
B)
C)
D)

Question 35

Use the following information for following questions .
The distribution of the number of hours people spend at work per day is unimodal
and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.
95% of all people work between and hours per day?

A)7.5 and 8.5 hours
B)7 and 8.5 hours
C)7.5 and 9 hours
D)7 and 9 hours

Question 36

The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the following distribution balanced?

A)About 85
B)About 95
C)About 105
D)About 115

Question 37

The slowest 25% of men participants ran the marathon how quickly?

A)Less than 136 minutes.
B)Less than 139 minutes.
C)More than 139 minutes.
D)More than 143 minutes.

Question 38

The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the following distribution balanced?

A)About 20
B)About 30
C)About 40
D)About 50

Question 39

Use the following information for following questions .
The distribution of the number of hours people spend at work per day is unimodal
and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.
If Stacy worked 8.7 hours yesterday, would you consider this unusual?

A)No, 8.7 hours is less than 2 standard deviations above the mean.
B)No, 8.7 hours is less than 1 standard deviations above the mean.
C)Yes, 8.7 hours is more than 2 standard deviations above the mean.
D)Yes, 8.7 hours is more than 1 standard deviations above the mean.

Question 40

Use the following information for following questions .
The distribution of the number of hours people spend at work per day is unimodal
and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.
If Anthony's z-score for his work hours was −1.3, explain what this value means in terms of the number of hours he works.

A)Anthony works 1.3 hours less than the average person.
B)Anthony works 1.3 hours more than the average person.
C)The number of hours Anthony works is 1.3 standard deviations below the mean.
D)The number of hours Anthony works is 1.3 standard deviations above the mean.

Question 41

The distributions of income in the United States is strongly skewed to the right. Which of the following is true?

A)The median income is smaller than the mean income.
B)The median income is larger than the mean income.
C)The median income is equal to the mean income.
D)There is not enough information to compare the median and mean values.

Question 42

Suppose we have a distribution of the number of "friends" all users of a popular social media site have. What measure of spread would be best to describe this data?

A)The spread should be described with the standard deviation because the distribution will be symmetric.
B)The spread should be described with the IQR because the distribution will be symmetric.
C)The spread should be described with the standard deviation because the distribution will be skewed to the right.
D)The spread should be described with the IQR because the distribution will be skewed to the right.

Question 43

For the pair of histograms below, determine which distribution has the larger standard deviation.

A)(i) has a larger standard deviation than (ii).
B)(ii) has a larger standard deviation than (i).
C)Both histograms have the same standard deviation.
D)There is no way to determine which one is larger.

Question 44

Which boxplot represents the same data as the histogram shown below?

A)
B)
C)
D)

Question 45

Use the following information for following questions .
The distribution of the number of hours of sleep people get per night is unimodal
and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours.
Approximately what percent of people sleep between 6 and 7.5 hours per night?

A)16%
B)24%
C)34%
D)68%

Question 46

Ten households were asked how many pets they currently own. The results are shown below. What is the IQR for this set of data?

A)1
B)2
C)3
D)4

Question 47

What feature of a distribution can NOT be determined from a boxplot?

A)Skewness
B)Modality
C)Center
D)Spread

Question 48

Use the following information for following questions .
The distribution of the number of hours of sleep people get per night is unimodal
and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours.
If James had a z-score of 1.2, explain what this value means in terms of the number of hours of sleep he gets.

A)James sleeps 1.2 hours less than the average person.
B)James sleeps 1.2 hours more than the average person.
C)The number of hours James sleeps is 1.2 standard deviations below the mean.
D)The number of hours James sleeps is 1.2 standard deviations above the mean.

Question 49

The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from shortest to longest.

A)
B)
C)
D)

Question 50

The five-number summary of the ages of passengers on a cruise ship is listed below. Consider the following two statements regarding outliers for this data and determine which, if any, are correct. (i) There is at least one passenger whose age is a low outlier. (ii) There is at least one passenger whose age is a high outlier.

A)Only statement (i) is correct.
B)Only statement (ii) is correct.
C)Both statements (i) and (ii) are correct.
D)Neither statement (i) or (ii) is correct.

Question 51

Use the following information for following questions .
The distribution of the number of hours of sleep people get per night is unimodal
and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours.
If Amanda slept 9.2 hours last night, would you consider this unusual?

A)No, 9.2 hours is less than 2 standard deviations above the mean.
B)No, 9.2 hours is less than 3 standard deviations above the mean.
C)Yes, 9.2 hours is more than 2 standard deviations above the mean.
D)Yes, 9.2 hours is more than 3 standard deviations above the mean.

Question 52

The number of students enrolled in a college algebra class for the last seven semesters are listed below. Find the median.

A)68
B)70
C)71
D)76

Question 53

A class of 30 introductory statistics students took a quiz worth 100 points. The standard deviation of the scores was 0. What must be true about the students' scores?

A)The mean, median, and mode must all be 0.
B)Every student received the same score.
C)Every student scored 100 on the quiz.
D)There was an error in the calculation for standard deviation.

Question 54

Use the following information for following questions .
The distribution of the number of hours of sleep people get per night is unimodal
and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours.
If James had a z-score of 1.2, how many hours did he sleep?

A)7.5 hours
B)7.8 hours
C)8.0 hours
D)8.2 hours

Question 55

Two Geometry classes at North Hollywood High School took the same quiz. Mr. Davis had 15 students in his class with a mean score of 70. Mrs. Brown's class of 25 students had a mean score of 80. Overall, what was the mean score for all students on the quiz?

A)74.50
B)75.00
C)76.25
D)75.75

Question 56

Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013. The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in June 2013, he input that there were 1230 car accidents; but there were actually only 123 that day. How will this error affect the measures of center for this data?

A)The mean and the median will be higher than they should be.
B)The mean and the median will not be affected by this error.
C)The mean will be higher than it should be, but the median will not be affected.
D)The median will be higher than it should be, but the mean will not be affected.

Question 57

[Be able to calculate the mean for a small set of data.] The heights (in meters) of five adults are listed below. Calculate the mean height of these adults.

A)1.70 meters
B)1.71 meters
C)1.72 meters
D)1.73 meters

Question 58

The following boxplot contains information about the length of time (in minutes) it took women
participants to finish the marathon race at the 2012 London Olympics.Use the plot for following questions

What can be said about the shape of the distribution of women's running times for the marathon?

A)The distribution is symmetric.
B)The distribution is unimodal.
C)The distribution is left-skewed.
D)The distribution is right-skewed.

Question 59

The following boxplot contains information about the length of time (in minutes) it took women
participants to finish the marathon race at the 2012 London Olympics.Use the plot for following questions

The fastest 25% of women participants ran the marathon how quickly?

A)Less than 150 minutes.
B)Less than 155 minutes.
C)More than 155 minutes
D)More than 160 minutes