Question 1

The frequency table shows the weight,in kilograms,of 120 adults,rounded to the nearest kilogram. $$\begin{array} { c | c | c | c } 
\text { Weight } & \text { Count } & \text { Weight } & \text { Count } \
\hline 60 & 1 & 68 & 12 \
61 & 6 & 69 & 6 \
62 & 7 & 70 & 3 \
63 & 5 & 71 & 12 \
64 & 8 & 72 & 10 \
65 & 7 & 73 & 2 \
66 & 7 & 74 & 4 \
67 & 25 & 75 & 5
\end{array}$$

Accepted Answer

A) 60,65,67,70,75 kg 
B) 60,65,66,70,75 kg 
C) 60,65,67,71,75 kg 
D) 60,66,67,70,75 kg 
E) 60,65,66,71,75 kg

Question 2

The weekly salaries (in dollars)of sixteen government workers are listed below. $$\begin{array} { l l l l } 
690 & 594 & 813 & 636 \
728 & 585 & 486 & 634 \
534 & 679 & 685 & 451 \
558 & 787 & 503 & 826
\end{array}$$

Accepted Answer

A) 451,540,635,718.5,826 dollars 
B) 451,540,634,718.5,826 dollars 
C) 451,546,635,709,826 dollars 
D) 451,534,634,690,826 dollars

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.

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.

Question 4

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

Accepted Answer

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

Question 5

Office workers were asked how long it took them to travel to work one morning.Here is the stem-and-leaf display. $$\begin{array} { l } 
2 \
3 \
4 \
5 \
6
\end{array}$$ $$\begin{array} { | l } 
0002344578 \
0257 \
12789 \
028 \
05
\end{array}$$ Would you use the median or the mean to describe the centre of this distribution?

Accepted Answer

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 6

Ages of high school students.

Accepted Answer

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 7

Here is the boxplot and an ogive of the distribution of students marks on their statistics test.  Write a few sentences describing this distribution.

Accepted Answer

A) The distribution of the marks is slightly skewed to the left.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 18 to 75,for an IQR of 57.55% of the students had a mark less than 50. 
B) The distribution of the marks is slightly skewed to the left.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark less than 50. 
C) The distribution of the marks is slightly skewed to the right.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark greater than 50. 
D) The distribution of the marks is slightly skewed to the left.The median mark was about 48,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark greater than 50. 
E) The distribution of the marks is slightly skewed to the right.The median mark was about 55,with a max of 100 and a min of 0.The middle 50% of the marks appeared to range from 26 to 66,for an IQR of 40.About 55% of the students had a mark less than 50.

Question 8

The free throw percentages for participants in a basketball tournament were compiled.The percents ranged from 31% to 91% with a mean of 63% and a standard deviation of 6%.The quartiles and median percentages were 41%,79%,and 63%.Suppose one participant did not make any of his attempted free throws (0%).Which of the summary statistics might not change if that data value was added to the distribution?

Accepted Answer

A) Median,range 
B) Q1,Q3 
C) Range,SD 
D) Mean,IQR 
E) Median,IQR

Question 9

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

Accepted Answer

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 10

Heights of adult women attending a concert.

Accepted Answer

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 11

The weekly salaries,in dollars,of 16 government workers are listed below.Find the upper quartile (Q3)by hand. $492 $791 $545 $840
$506 $734 $620 $815
$676 $874 $450 $561
$713 $473 $654 $527

Accepted Answer

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

Question 12

Here are the summary statistics for mathematics scores for one high-school graduating class. $$\begin{array} { l | c | c | c | c | c | c | c | c } 
& \mathbf { n } & \text { Mean } & \text { Median } & \text { SD } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline \text { Male } & 17 & 60 & 63 & 18.6 & 30 & 100 & 52 & 78 \
\text { Female } & 18 & 65 & 66 & 17.7 & 36 & 98 & 50 & 80
\end{array}$$ Choose the boxplot that represents the given data. 
I   
II 
 
III
 
IV   
V

Accepted Answer

A) I 
B) II 
C) III 
D) IV 
E) V

Question 13

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.

Question 14

The test scores of 15 students are listed below.Find the lower quartile (Q1)by hand. 41 49 50 55 58
64 65 68 72 76
85 87 90 94 95

Accepted Answer

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

Question 15

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.

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.

Accepted Answer

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

Here are summary statistics of the four last digits of social security number of 500 customers,corresponding to the following histogram. $$\begin{array}{l}
\begin{array} { l | l } 
\text { Count } & 500 \
\hline \text { Mean } & 4919 \
\hline \text { StdDev } & 1556 \
\hline \text { Median } & 5009 \
\hline \text { IQR } & 2009 \
\hline \text { Q1 } & 4018 \
\hline \text { Q3 } & 6027
\end{array}\
\end{array}$$
 Is the mean or median a "better" summary of the centre of the distribution?

Accepted Answer

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 18

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest $\text { time } = 121$ minutes $\text { mean } = 76$ minutes $\text { median } = 76$ minutes $\text { range } = 91$ minutes $\mathrm { IQR } = 57$ $\mathrm { Q } 1 = 30$ standard $\text { deviation } = 13$ minutes
Between what two values are the middle 50% of times?

Accepted Answer

A) 30 and 87 
B) 38 and 76 
C) 15.2 and 60.8 
D) 19 and 57 
E) 121 and 30

Question 19

The weekly salaries,in dollars,of 16 government workers are listed below.Find the lower quartile (Q1)by hand. $$\begin{array} { l l l l l } 
\$ 690 & \$ 589 & \$ 813 & \$ 656 \
\$ 728 & \$ 556 & \$ 491 & \$ 614 \
\$ 532 & \$ 662 & \$ 685 & \$ 462 \
\$ 542 & \$ 787 & \$ 511 & \$ 826
\end{array}$$

Accepted Answer

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

Question 20

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 1995-2014. Animal Totals 90
89 
88 
87 
86
85 
84 
83 
82 
81 $$\begin{array} { l } 
2 \
3 \
5557 \
157 \\
2 \\
3357 \
223556
\end{array}$$ Key:
87 $|~5$ = 87,500 cats and dogs euthanized

Accepted Answer

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.

Exam 3: Displaying and Summarizing Quantitative Data

The weekly salaries (in dollars) of sixteen government workers are listed below. $\begin{array} { l l l l } 690 & 594 & 813 & 636 \\728 & 585 & 486 & 634 \\534 & 679 & 685 & 451 \\558 & 787 & 503 & 826\end{array}$

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

Ages of high school students.

Here is the boxplot and an ogive of the distribution of students marks on their statistics test. Write a few sentences describing this distribution.

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

Heights of adult women attending a concert.

The weekly salaries,in dollars,of 16 government workers are listed below.Find the upper quartile (Q3) by hand. $492 $791 $545 $840 $506 $734 $620 $815 $676 $874 $450 $561 $713 $473 $654 $527

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 test scores of 15 students are listed below.Find the lower quartile (Q1) by hand. 41 49 50 55 58 64 65 68 72 76 85 87 90 94 95

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.

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.

The weekly salaries,in dollars,of 16 government workers are listed below.Find the lower quartile (Q1) by hand. $\begin{array} { l l l l l } \$ 690 & \$ 589 & \$ 813 & \$ 656 \\\$ 728 & \$ 556 & \$ 491 & \$ 614 \\\$ 532 & \$ 662 & \$ 685 & \$ 462 \\\$ 542 & \$ 787 & \$ 511 & \$ 826\end{array}$