Question 1

Here are the summary statistics for mathematics scores for one high school graduating class,and the parallel boxplots comparing the scores of male and female students.Write a brief report on these results.Be sure to discuss shape,centre,and spread of the scores. $$\begin{array} { l | c | c | c | c | c | c | c | c } 
\mathbf { n } & \text { Mean } & \text { Median } & \text { SD } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline \text { Male } & 17 & 60 & 63 & 18.6 & 30 & 100 & 52 & 78 \
\text { Female } & 18 & 65 & 66 & 17.7 & 36 & 98 & 50 & 80
\end{array}$$

A)Median score by females at 66 points is 3 points higher than that by males,and female mean is higher by 5.The middle 50% for both group is close with a IQR at 26 for the males and 30 for the females.The males have a larger range from 30 to 100.The distribution is right-skewed for the females and symmetric for the males.
B)Median score by females at 66 points is 3 points higher than that by males,and female mean is higher by 5.The middle 50% for both group is close with a IQR at 26 for the males and 30 for the females.The males have a larger range from 30 to 100.Both distributions are right-skewed.
C)Median score by females at 66 points is 3 points higher than that by males,and female mean is higher by 5.The middle 50% for both group is close with a IQR at 26 for the males and 30 for the females.The males have a larger range from 30 to 100.The distribution is right-skewed for the males and symmetric for the females.
D)Median score by females at 66 points is 3 points higher than that by males,and male mean is higher by 5.The middle 50% for both group is close with a IQR at 30 for the males and 26 for the females.The males have a larger range from 30 to 100.The distribution is right-skewed for the males and symmetric for the females.
E)Median score by females at 66 points is 3 points higher than that by males,and female mean is higher by 5.The middle 50% for both group is close with a IQR at 26 for the males and 30 for the females.The males have a smaller range from 30 to 100.Both distributions are left-skewed.

Accepted Answer

The answer of Here are the summary statistics for mathematics...

Question 2

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.Use both the stemplot and timeplot to describe the distribution. Euthanized Animal Totals 90
89 
88 
87 
86 
85 
84 
83 
82 
81 $$\begin{array} { |l } 
0 \
3 \
4449 \
057\\
6\\
1157\
001338\
\end{array}$$\ Key:
$87 \mid 5 = 87,500$ 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.The timeplot shows that the number of animals euthanized has increased over the period 1985-2004,with a significant increase between 1994 and 1996.
B)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 88,400.The lower cluster is between 81,000 and 82,000 euthanized,with a centre at around 81,000.The timeplot shows that the number of animals euthanized has decreased over the period 1985-2004,with a significant decrease between 1994 and 1996.
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 88,400.The lower cluster is between 81,000 and 82,000 euthanized,with a centre at around 81,000.The timeplot shows that the number of animals euthanized has increased over the period 1985-2004,with a significant increase between 1994 and 1996.
D)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 88,400.The lower cluster is between 81,000 and 82,000 euthanized,with a centre at around 81,000.The timeplot shows that the number of animals euthanized has increased over the period 1985-2004,with a significant increase between 1994 and 1996.
E)The distribution of the number of cats and dogs that were euthanized is skewed to the left,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.The timeplot shows that the number of animals euthanized has increased over the period 1985-2004,with a significant increase between 1994 and 1996.

Accepted Answer

The stem-and-leaf display shows a bimodal distribution with one mode between 87,000 and 90,000 and another mode between 81,000 and 82,000. The timeplot indicates an increase in the number of animals euthanized over the period 1985-2004, with a significant increase between 1994 and 1996. Option C accurately describes both the distribution and the trend observed in the timeplot.

Question 3

The times,in minutes,it took for 21 students to finish writing a statistics test are given below. 32.4 30.5 34.6 64.9 22.1 31.8 16.6
27.7 36.2 60.6 24.3 47.2 45.6 9.2
27.1 18.9 14.2 31.4 24.2 12.5 35.4
A)9.2,60.6,64.9
B)60.6,64.9
C)64.9
D)24.3
E)None

Accepted Answer

The question asks for the highest time taken by the students to finish the test. Looking at the values, we can see that 64.9 is the highest value, followed by 60.6. Therefore, the best choice is B, as it includes both of these values. Option A includes one additional value, 9.2, which is not the highest. Option C only includes the highest value, 64.9, and option D includes a lower value than option B. Option E is not applicable as there is a best choice.

Question 4

The boxplots display case prices (in dollars)of white wines produced by three vineyards in south-western Ontario.Which vineyard produces the cheapest wine? 
A)Vineyard C,because it has the smallest range.
B)Vineyard B,because it does not have any outliers.
C)Vineyard C,because it has the smallest IQR.
D)Vineyard B,because it has the highest case price at about $150.
E)Vineyard A,because it has the smallest case price at about $60.

Accepted Answer

The boxplot for Vineyard A shows the smallest median and the smallest upper quartile, indicating that the case prices for this vineyard are generally lower than the other two vineyards. Additionally, the maximum price for Vineyard A is only slightly higher than the minimum price for the other two vineyards, further supporting the idea that Vineyard A produces the cheapest wine.

Question 5

The reaction time of 20 drivers at a stop light was measured,in seconds,as the time between the traffic light turning green and the time it took them to press the gas pedal. $\begin{array} { l l l l l } 0.4 & 1.0 & 1.5 & 1.6 & 2.0 \end{array}$
$\begin{array} { l l l l l } 2.2 & 2.4 & 2.7 & 3.4 & 3.4 \end{array}$
$\begin{array} { l l l l l } 3.5 & 3.6 & 3.6 & 3.7 & 3.7 \end{array}$
$\begin{array} { l l l l l } 3.9 & 4.1 & 4.2 & 4.2 & 7.0 \end{array}$
A)0.4,7.0
B)0.4
C)4.2,7.0
D)7.0
E)None

Accepted Answer

The outlier in the data set is 7.0 seconds, as it is significantly higher than the other reaction times.

Question 6

The weekly salaries (in dollars)of 24 randomly selected employees of a company are shown below. 310 320 450 460 470 500 520 540
580 600 650 700 710 840 870 900
1000 1200 1250 1300 1400 1720 2500 3700
A)3700
B)2500
C)310,2500,3700
D)2500,3700
E)None

Accepted Answer

The question is asking for the "best choice(s)" and not for a specific statistical calculation. Therefore, we need to look at the salaries and select the options that make the most sense.

Option A (3700) is the highest salary in the list, but it is only one person out of 24. Therefore, it does not represent the majority of the employees, and it might not be the best choice.

Option B (2500) is the second highest salary in the list, and it appears twice. This is significant because it represents two different people in the company who earn a high salary. However, it still does not represent the majority of the employees.

Option C (310, 2500, 3700) includes the lowest, second highest, and the highest salaries in the list. While this option covers a range of salary levels, it might not be the best because it leaves out many of the other salaries in the list.

Option D (2500, 3700) includes the two highest salaries in the list, and it represents two different people in the company who earn a high salary. This option is a good choice because it covers the top earners and represents a significant portion of the employees.

Option E (None) is incorrect because there are two choices that make sense, as explained above.

Question 7

Use the high closing values of Naristar Inc.stock from the years 2003-2014 to construct a timeplot. $$\begin{array} { c | c | c | c } 
\text { Year } & \text { High } & \text { Year } & \text { High } \
\hline 2003 & 48 & 2009 & 62 \
2004 & 53 & 2010 & 60 \
2005 & 47 & 2011 & 68 \
2006 & 55 & 2012 & 42 \
2007 & 58 & 2013 & 51 \
2008 & 61 & 2014 & 78
\end{array}$$

Accepted Answer

The answer of Use the high closing values of Naristar...

Question 8

Here are the heights,in centimetres,of 32 Grade 3 students. 100 100 105 105 106 106 107 107
108 110 110 112 112 112 114 114
114 115 116 117 118 118 118 118
118 119 120 121 122 125 128 142
A)142
B)100
C)128,142
D)100,142
E)None

Accepted Answer

The answer of Here are the heights,in centimetres,of 32 Grade...

Question 9

The ages of the 21 members of a track and field team are listed below. 15 18 18 19 22 23 24
24 24 25 25 26 26 27
28 28 30 32 33 40 42
A)42
B)25
C)15,42
D)40,42
E)None

Accepted Answer

The two highest ages in the list are 40 and 42, so option D (40,42) is the best choice. Option A can be eliminated because it only includes one age, but there are two ages that are higher than 25. Option B can also be eliminated because there are several ages that are higher than 25. Option C includes the lowest and highest ages in the list, but it doesn't include all of the ages that are higher than 25. Option D is the only choice that includes both of the highest ages in the list.

Question 10

The boxplots display case prices (in dollars)of white wines produced by three vineyards in south-western Ontario.Which vineyard produces the most expensive wine? 
A)Vineyard B,because it has the highest case price at about $150.
B)Vineyard A,because it has one outlier at about $145.
C)Vineyard C,because it has the smallest IQR.
D)Vineyard A,because it has the smallest case price at about $60.
E)Vineyard B,because it has the highest case price at about $120.

Accepted Answer

Based on the boxplots, Vineyard B has the highest median case price at around $150, indicating that their wines are generally more expensive than those produced by Vineyards A and C. Vineyard A does have an outlier at around $145, but that is just one data point and does not necessarily reflect the overall trend of their case prices. The size of the IQR (Interquartile Range) for Vineyard C does not indicate which vineyard produces the most expensive wine. The smallest case price belongs to Vineyard A, but that does not necessarily mean they produce the least expensive wine overall. Therefore, Vineyard B is the best choice as the producer of the most expensive wine in this scenario.

Question 11

The Ontario Ministry of Education collects data on the number of years of teaching experience of high school teachers.A sample taken this year of 19 high school teachers yielded the following data on number of years of teaching experience. 16 28 1 33 15
6 18 7 20 14
17 19 16 10 21
29 14 39 18
A)33,39
B)1
C)1,33,39
D)1,39
E)None

Accepted Answer

The data set includes the values 1, 33, and 39. Therefore, the best choice(s) is answer choice C. None of the other choices include all three values.

Question 12

A business owner recorded her annual profits for the first 12 years since opening her business in 1993.The stem-and-leaf display below shows the annual profits in thousands of dollars.Use both the stemplot and timeplot to describe the distribution. Annual Profit Totals 8
7
6
5
4
3
2
1 $$\begin{array} { l } 
0133 \
9 \\
023 \
8 \\
24 \
7
\end{array}$$ Key:
$7 \mid 9 = \$ 79,000 \text { profit }$ 
A)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 $50,000.The timeplot shows that the profits grew from 1993 to 1994,and were relatively steady from 1994 to 1998.After 1998,the profits declined significantly compared with those between 1993 and 1998.
B)The distribution of the business owner's profits is skewed to the left,and is multimodal,with gaps in between.One mode is at around $80,000,another at around $50,000,and a third mode at around $20,000.The timeplot shows that the profits grew from 1993 to 1994,and were relatively steady from 1994 to 2001.After 2001,the profits declined significantly compared with those between 1994 and 2001.
C)The distribution of the business owner's profits is skewed to the right,and is multimodal,with gaps in between.One mode is at around $80,000,another at around $50,000,and a third mode at around $20,000.The timeplot shows that the profits grew from 1993 to 1994,and were relatively steady from 1994 to 1998.After 1998,the profits declined significantly compared with those between 1993 and 1998.
D)The distribution of the business owner's profits is skewed to the left,and is multimodal,with gaps in between.One mode is at around $80,000,another at around $50,000,and a third mode at around $20,000.The timeplot shows that the profits grew from 1993 to 1994,and were relatively steady from 1994 to 1998.After 1998,the profits declined significantly compared with those between 1993 and 1998.
E)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 $50,000.The timeplot shows that the profits grew from 1993 to 1994,and were relatively steady from 1994 to 2001.After 2001,the profits declined significantly compared with those between 1994 and 2001.

Accepted Answer

The answer of A business owner recorded her annual profits...

Question 13

The weekly salaries (in dollars)of sixteen government workers are listed below. 690 578 813 630
728 546 469 614
502 677 685 350
530 787 477 1086
A)350,986
B)614
C)350
D)1086
E)None

Accepted Answer

The answer of The weekly salaries (in dollars)of sixteen government...

Question 14

Use the high closing values of Naristar Inc.stock from the years 2003-2014 to construct a timeplot. $$\begin{array} { c | c | c | c } 
\text { Year } & \text { High } & \text { Year } & \text { High } \
\hline 2003 & 42 & 2009 & 47 \
2004 & 40 & 2010 & 60 \
2005 & 31 & 2011 & 61 \
2006 & 42 & 2012 & 57 \
2007 & 44 & 2013 & 54 \
2008 & 47 & 2014 & 30
\end{array}$$

Accepted Answer

The answer of Use the high closing values of Naristar...

Question 15

The test scores of 15 students are listed below. 33 60 50 65 66
68 70 73 74 77
78 82 87 90 99
A)33
B)33,60
C)99
D)33,99
E)None

Accepted Answer

The answer of The test scores of 15 students are...

Question 16

Here are the test scores of 32 students: 35 37 41 44 46 48 53 55
56 57 59 63 65 66 68 69
70 71 74 74 75 77 78 79
80 82 83 86 89 92 95 99
A)35
B)35,99
C)99
D)35,95,99
E)None

Accepted Answer

The answer of Here are the test scores of 32...

Question 17

The boxplots display case prices (in dollars)of white wines produced by three vineyards in south-western Ontario.Describe these wine prices. 
A)Vineyards A and B have about the same average price; the boxplots show similar medians and similar IQRs.Vineyard C has higher prices except for one low outlier,and a more consistent pricing as shown by the smaller IQR.The three distributions are roughly symmetric.
B)Vineyards A and B have different average price,but a similar spread.Vineyard C has lower prices except for one low outlier,and a more consistent pricing as shown by the smaller IQR.
C)Vineyards A and B have about the same average price; the boxplots show similar medians and similar IQRs.Vineyard C has consistently higher prices except for one low outlier,and a more consistent pricing as shown by the larger IQR.
D)Vineyards A and B have about the same average price; the boxplots show similar medians and similar IQRs.Vineyard C has higher prices except for one low outlier,and a less consistent pricing as shown by the larger IQR.
E)Vineyards A and B have about the same average price; the boxplots show similar medians and similar IQRs.Vineyard C has higher prices except for one low outlier,and a more consistent pricing as shown by the smaller IQR.

Accepted Answer

The boxplots show that Vineyards A and B have similar medians and IQRs, indicating they have about the same average prices and a similar spread. Vineyard C has consistently higher prices, except for one low outlier, which suggests that it produces more expensive wines overall. However, the smaller IQR in the Vineyard C boxplot suggests that its pricing is more consistent. Therefore, E is the best choice.

Question 18

The weights (in kilograms)of 27 dogs are listed below. $$\begin{array} { l l l l l l l l l } 
1.2 & 2.0 & 2.2 & 2.2 & 2.4 & 2.5 & 2.5 & 2.5 & 2.6 \
2.6 & 2.6 & 2.6 & 2.6 & 2.7 & 2.8 & 2.8 & 2.8 & 2.9 \
2.9 & 2.9 & 3.0 & 3.0 & 3.1 & 3.1 & 3.3 & 3.6 & 4.2
\end{array}$$
A)1.2,4.2
B)3.6,4.2
C)1.2,2.0
D)1.2,3.6,4.2
E)None

Accepted Answer

The outliers in a dataset are the values that are significantly higher or lower than the majority of the data. In this list, 1.2 and 4.2 are the lowest and highest values, respectively, and they stand out from the rest of the data, which is more closely clustered around the 2.5 to 3.1 range.

Question 19

Use the Olympic gold medal performances in the men's high jump from the years 1960-2012 to construct a timeplot. $$\begin{array} { c c } 
\text { Year } & \text { High Jump } \
&\text { (in.) } \
\hline 1960 & 85.25 \
\hline 1964 & 85.75 \
\hline 1968 & 88.25 \
\hline 1972 & 87.75 \
\hline 1976 & 88.50 \
\hline 1980 & 92.50 \
\hline 1984 & 92.50 \
\hline 1988 & 93.75 \
\hline 1992 & 92.25 \
\hline 1996 & 94.00 \
\hline 2000 & 92.50 \
\hline 2004 & 93.00 \
\hline 2008 & 93.00 \
\hline 2012 & 93.75
\end{array}$$

Accepted Answer

The answer of Use the Olympic gold medal performances in...

Question 20

The boxplots display case prices (in dollars)of white wines produced by three vineyards in south-western Ontario.In which vineyard are the wines generally more expensive? 
A)Vineyards A and B,because they have a similar average price,and roughly the same spread.
B)Vineyard C,because it has the highest average price and the smallest spread.
C)Vineyard C,because it has the smallest range.
D)Vineyard B,because it has the highest case price at about $150.
E)Vineyard A,because it has one outlier at about $145.

Accepted Answer

The boxplot for Vineyard C shows a higher median and a smaller spread, indicating that the prices of wines from this vineyard are generally more expensive than those from the other two vineyards. The fact that Vineyard B has one outlier at a high price does not necessarily mean its wines are generally more expensive.

Quiz 4: Understanding and Comparing Distributions

The times,in minutes,it took for 21 students to finish writing a statistics test are given below. 32.4 30.5 34.6 64.9 22.1 31.8 16.6 27.7 36.2 60.6 24.3 47.2 45.6 9.2 27.1 18.9 14.2 31.4 24.2 12.5 35.4

The boxplots display case prices (in dollars) of white wines produced by three vineyards in south-western Ontario.Which vineyard produces the cheapest wine?

The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700

Here are the heights,in centimetres,of 32 Grade 3 students. 100 100 105 105 106 106 107 107 108 110 110 112 112 112 114 114 114 115 116 117 118 118 118 118 118 119 120 121 122 125 128 142

The ages of the 21 members of a track and field team are listed below. 15 18 18 19 22 23 24 24 24 25 25 26 26 27 28 28 30 32 33 40 42

The boxplots display case prices (in dollars) of white wines produced by three vineyards in south-western Ontario.Which vineyard produces the most expensive wine?

The Ontario Ministry of Education collects data on the number of years of teaching experience of high school teachers.A sample taken this year of 19 high school teachers yielded the following data on number of years of teaching experience. 16 28 1 33 15 6 18 7 20 14 17 19 16 10 21 29 14 39 18

The weekly salaries (in dollars) of sixteen government workers are listed below. 690 578 813 630 728 546 469 614 502 677 685 350 530 787 477 1086

The test scores of 15 students are listed below. 33 60 50 65 66 68 70 73 74 77 78 82 87 90 99

Here are the test scores of 32 students: 35 37 41 44 46 48 53 55 56 57 59 63 65 66 68 69 70 71 74 74 75 77 78 79 80 82 83 86 89 92 95 99

The boxplots display case prices (in dollars) of white wines produced by three vineyards in south-western Ontario.Describe these wine prices.

The weights (in kilograms) of 27 dogs are listed below. $\begin{array} { l l l l l l l l l } 1.2 & 2.0 & 2.2 & 2.2 & 2.4 & 2.5 & 2.5 & 2.5 & 2.6 \\2.6 & 2.6 & 2.6 & 2.6 & 2.7 & 2.8 & 2.8 & 2.8 & 2.9 \\2.9 & 2.9 & 3.0 & 3.0 & 3.1 & 3.1 & 3.3 & 3.6 & 4.2\end{array}$

The boxplots display case prices (in dollars) of white wines produced by three vineyards in south-western Ontario.In which vineyard are the wines generally more expensive?