Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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?

Accepted Answer

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. 
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 4

Which set has the largest standard deviation?

Accepted Answer

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. 
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 5

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.

Accepted Answer

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. 
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.

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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. 
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 9

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?

Accepted Answer

A) Class 1 
B) Class 2 
C) Class 1 and class 3 
D) Class 3 
E) None,because the classes had the same mean. 
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 10

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

Accepted Answer

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. 
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 11

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.

Accepted Answer

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. 
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 12

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

Accepted Answer

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

Question 13

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.

Accepted Answer

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. 
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 14

Which set has the largest standard deviation?

Accepted Answer

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. 
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 15

For class 2,compare the mean and the median.

Accepted Answer

A) Mean is higher than median. 
B) Median is lower than mean. 
C) Median is higher than mean. 
D) Mean is equal to median. 
E) No comparison possible 
A) Mean is higher than median. 
B) Median is lower than mean. 
C) Median is higher than mean. 
D) Mean is equal to median. 
E) No comparison possible

Question 16

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 smallest standard deviation?

Accepted Answer

A) Class 3,because the shape is symmetric and unimodal. 
B) Class 3,because the shape has the highest number of students. 
C) Class 1,because the shape is fairly symmetric and uniform. 
D) Class 2,because the shape is skewed. 
E) None,because the classes had the same standard deviation. 
A) Class 3,because the shape is symmetric and unimodal. 
B) Class 3,because the shape has the highest number of students. 
C) Class 1,because the shape is fairly symmetric and uniform. 
D) Class 2,because the shape is skewed. 
E) None,because the classes had the same standard deviation.

Question 17

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?

Accepted Answer

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. 
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 18

Students were asked to make a histogram of the number of corn snakes collected in Will County,Illinois from 1985 to 2006.They were given the data in the form of a stem-and-leaf display shown below:   
One student submitted the following display:   
a)Comment on this graph.
b)Create your own histogram of the data.

Accepted Answer

a)This is not a histogram.The

Question 19

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.

Accepted Answer

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. 
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 20

A clerk entering salary data into a company spreadsheet accidentally omitted a "0" in the CEO's salary,listing it as $155,000 instead of $1,550,000.Explain how this error will affect these summary statistics for the company payroll: a)measures of centre: median and mean;and b)measures of spread: range,IQR,and standard deviation.

Accepted Answer

a)Median will probably be unaf

Exam 3: Displaying and Summarizing Quantitative Data

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

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

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?

Which set has the largest standard deviation?

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

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

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

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?

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

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.

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

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.

Which set has the largest standard deviation?

For class 2,compare the mean and the median.

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 smallest standard deviation?

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?

Data

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Understanding and Comparing Distributions

The Standard Deviation As a Ruler and the Normal Model

Scatterplots, association, and Correlation

Linear Regression

Regression Wisdom

Re-Expressing Data: Get It Straight

Understanding Randomness

Sample Surveys

Experiments and Observational Surveys

From Randomness to Probability

Probability Rules

Random Variables

Probability Models

Sampling Distribution Models

Confidence Intervals for Proportions

Testing Hypotheses About Proportions

More About Tests

Comparing Two Proportions

Inferences About Means

Comparing Means

Paired Samples and Blocks

Comparing Counts

Inferences for Regression

Analysis of Variance

Multifactor Analysis of Variance

Multiple Regression

Multiple Regression Wisdom

Rank-Based Nonparametric Tests

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