Question 1

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest $\text { amount } = 19$ cm, $\text { mean } = 40$ cm, $\text { median } = 33$ cm, $\text { range } = 81$ cm, $\mathrm { IQR } = 45 \mathrm {~cm} \text {, }$ $\text { Q1 } = 16 \mathrm {~cm} \text {, }$ standard $\text { deviation } = 11$ cm.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the left; mean higher than median.
B)Skewed to the right; mean higher than median.
C)Skewed to the left; mean lower than median.
D)Skewed to the right; mean lower than median.
E)Symmetric; mean higher than median.

Accepted Answer

The distribution is skewed to the right because the mean (40 cm) is higher than the median (33 cm), indicating a longer tail on the right side of the distribution.

Question 2

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

Accepted Answer

The middle 50% of times are represented by the interquartile range (IQR), which is the difference between the third quartile ($Q3$) and the first quartile ($Q1$). Given $IQR = 57$ and $Q1 = 30$, the third quartile $Q3$ can be calculated as $Q1 + IQR = 30 + 57 = 87$. Therefore, the middle 50% of times are between 30 and 87 minutes.

Question 3

Here are some summary statistics for last year's basketball team scoring output: lowest $\text { score } = 23$ points, $\text { mean } = 53$ points, $$\text { median } = 47$$ points, $\text { range } = 92$ points, $\mathrm { IQR } = 51 \text {, }$ $\mathrm { Q } 1 = 32$ standard $\text { deviation } = 5$ points.Between what two values are the middle 50% of scores found?
A)53 and 47
B)23 and 115
C)13.25 and 3975
D)32 and 83
E)11.75 and 35.25

Accepted Answer

To find the middle 50%, we need to exclude the lowest and highest 25% scores. Therefore, we need to find the minimum and maximum scores among the middle 50%. The minimum score would be the score greater than the lowest 25% score (11) but less than the lowest 25% score + 50% of the scores (22), which is 23. The maximum score would be the score less than the highest 25% score (83) but greater than the highest 25% score - 50% of the scores (22), which is 72. Therefore, the middle 50% of scores are found between 23 and 72. The correct choice is D) 32 and 83, which is closest to this range.

Question 4

Here are some summary statistics for the size of forest fires last year: smallest $\text { fire } = 72$ acres, $\text { mean } = 493$ acres, $\text { median } = 493$ acres, $\text { range } = 7928$ acres, $$\mathrm { IQR } = 370,$$ $$Q 1 = 197 ,$$ standard $\text { deviation } = 59$ acres.Between what two values are the middle 50% of fire sizes found?
A)123.25 and 369.75
B)98.6 and 394.4
C)197 and 567
D)72 and 8000
E)246.5 and 493

Accepted Answer

The middle 50% of fire sizes are found between the first quartile (Q1) and the third quartile (Q3). Given Q1 = 197 acres, and the interquartile range (IQR) = 370 acres, we can find Q3 by adding the IQR to Q1: Q3 = 197 + 370 = 567 acres. Therefore, the middle 50% of fire sizes are found between 197 acres and 567 acres.

Question 5

Here are some statistics for the annual Wildcat golf tournament: lowest score = 56,mean $\text { score } = 90 \text {, }$ $\text { median } = 98 \text {, }$ $\text { range } = 94 \text {, }$ $\mathrm { IQR } = 106 \text {, }$ $\mathrm { Q } 1 = 36$ standard $\text { deviation } = 11 \text {. }$ Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the left; mean higher than median.
B)Skewed to the left; mean lower than median.
C)Symmetric; mean lower than median.
D)Skewed to the right; mean higher than median.
E)Skewed to the right; mean lower than median.

Accepted Answer

Since the lowest score is considerably lower than the mean, the distribution is likely skewed to the left. This means that the tail of the distribution is longer on the left side and the median is likely higher than the mean. Option B indicates a left skew with a lower mean than median, which matches the characteristics of this distribution.

Question 6

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 52 km/h to 67 km/h with a mean speed of 56 km/h and a standard deviation of 7 km/h.The quartiles and median speeds were 55 km/h,64 km/h,and 53 km/h.Suppose during the month,one driver was clocked at 25 km/h. Which of the summary statistics might not change if that data value was added to the distribution?
A)Q1,Q3
B)Median,range
C)Median,IQR
D)Mean,IQR
E)Range,SD

Accepted Answer

The median and IQR (interquartile range) are measures of central tendency and spread that are less likely to be affected by outliers. Adding one data value of 25 km/h is an outlier in this data set and will not affect the quartiles or the median since they are not based on extreme values. Therefore, the correct answer is C) Median, IQR.

Question 7

Shown below are the data and summary statistics for the reading scores of 29 fifth graders. $\begin{array} { l l l l l l l l } 
1.3 & 1.5 & 2.1 & 2.5 & 2.7 & 3.1 & 3.4 & 3.6 \
3.7 & 3.8 & 4.1 & 4.2 & 4.3 & 4.5 & 4.6 & 4.7 \
4.7 & 4.8 & 4.8 & 5.1 & 5.1 & 5.2 & 5.3 & 5.4 \
5.4 & 5.6 & 5.6 & 5.8 & 5.9 & & &
\end{array}$ $\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 29 & 4.2 & 4.6 & 1.3 & 1.3 & 5.9 & 3.50 & 5.25
\end{array}$ Write a brief summary of the performance of the fifth graders.
A)The distribution is unimodal and skewed to the left.The median is 4.6,while the mean is 4.2,lower than the median score.The middle 50% of the weekly salaries are between 3.50 and 5.25,for an IQR of 1.75.There are no outliers.
B)The distribution is unimodal and skewed to the right.The median is 4.6,while the mean is 4.2,lower than the median score.The middle 50% of the weekly salaries are between 3.50 and 5.25,for an IQR of 1.75.There are no outliers.
C)The distribution is unimodal and skewed to the left.The median is 4.6,while the mean is 4.2,lower than the median score.The middle 50% of the weekly salaries are between 3.50 and 5.25,for an IQR of 1.75.The score of 1.3 is an outlier.
D)The distribution is skewed to the right.The median is 4.2,while the mean is 4.6,higher than the median score.The middle 50% of the weekly salaries are between 3.6 and 5.2,for an IQR of 1.6.There are no outliers.
E)The distribution is unimodal and skewed to the left.The median is 4.6,while the mean is 4.2,lower than the median score.The middle 50% of the weekly salaries are between 3.6 and 5.2,for an IQR of 1.6.There are no outliers.

Accepted Answer

The distribution is unimodal and skewed to the left. The mean is lower than the median, indicating that there are more lower scores than higher scores. The IQR is 1.75, which is relatively large, indicating that there is a lot of variability in the data. There are no outliers.

Question 8

Here are some statistics for the annual Wildcat golf tournament: lowest $\text { score } = 57$ mean $\text { score } = 97$ $\text { median } = 105$ $\text { range } = 93$ $I Q R = 109$ $\mathrm { Q } 1 = 39$ standard $\text { deviation } = 14$ Between what two values are the middle 50% of the scores found?
A)26.25 and 78.75
B)39 and 148
C)97 and 105
D)57 and 150
E)24.25 and 67.9

Accepted Answer

The middle 50% of the scores are found between the first quartile (Q1) and the third quartile (Q3). Given Q1 = 39 and the interquartile range (IQR) = 109, Q3 can be calculated as Q1 + IQR = 39 + 109 = 148. Therefore, the middle 50% of the scores are found between 39 and 148.

Question 9

The free throw percentages for the participants in a basketball tournament were compiled.The percents ranged from 33% to 99% with a mean of 56% and a standard deviation of 7%.The quartiles and median percentages were 43%,87%,and 56%.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the left; mean higher than median.
B)Skewed to the right; mean higher than median.
C)Skewed to the left; mean lower than median.
D)Skewed to the right; mean lower than median.
E)Symmetric; mean same as median.

Accepted Answer

The distribution is symmetric because the mean and the median are the same (56%).

Question 10

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $\$ 15,000$ ,mean salary = $\$ 35,000,$ median = $25,000,range = $60,000,
IQR = $30,000,first quartile = $$\$ 17,500,$$ standard deviation = $20,000.
Between what two values are the middle 50% of the salaries found?
A)$15,000 and $75,000
B)$17,500 and $37,500
C)$17,500 and $30,000
D)$35,000 and $25,000
E)$17,500 and $47,500

Accepted Answer

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

Question 11

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 50 km/h to 65 km/h with a mean speed of 55 km/h and a standard deviation of 7 km/h.The quartiles and median speeds were 53 km/h,62 km/h,and 52 km/h.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the right; mean lower than median.
B)Skewed to the right; mean higher than median.
C)Skewed to the left; mean higher than median.
D)Skewed to the left; mean lower than median.
E)Symmetric; mean higher than median.

Accepted Answer

The distribution is skewed to the right because the mean (55 km/h) is higher than the median (52 km/h).

Question 12

Here are some summary statistics for the size of forest fires last year: smallest fire = 74 acres, $\text { mean } = 451$ acres, $\text { median } = 451$ acres, $\text { range } = 7926$ acres, $\mathrm { IQR } = 387$ $Q 1 = 180 ,$ standard deviation = 61 acres.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the right; mean higher than median.
B)Symmetric; mean same as median.
C)Skewed to the left; mean higher than median.
D)Skewed to the right; mean lower than median.
E)Skewed to the left; mean lower than median.

Accepted Answer

The distribution is considered symmetric because the mean and the median are equal, which typically indicates a symmetric distribution.

Question 13

Here are some summary statistics for the recent English exam: lowest $\text { score } = 31 \text {, }$ mean $\text { score } = 67 \text {, }$ $\text { median } = 81.2 \text {, }$ $\text { range } = 79 \text {, }$ $\mathrm { IQR } = 60 \text {, }$ $\mathrm { Q } 1 = 27 \text {, }$ standard $\text { deviation } = 8.6 \text {. }$ Between what two values are the middle 50% of the scores found?
A)31 and 110
B)67 and 81.2
C)27 and 87
D)16.75 and 50.25
E)20.3 and 60.9

Accepted Answer

The middle 50% of the scores are found between the first quartile (Q1) and the third quartile (Q3). Given Q1 = 27 and the interquartile range (IQR) = 60, Q3 can be calculated as Q1 + IQR = 27 + 60 = 87. Therefore, the middle 50% of the scores are found between 27 and 87.

Question 14

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 126 grams to 291 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 157,255,and 202 ounces.A customer makes a special order of a 448 ounce cone. Which of the summary statistics might not change if that data value was added to the distribution?
A)Median,range
B)Range,SD
C)Q1,Q3
D)Mean,IQR
E)Median,IQR

Accepted Answer

Adding a value far from the existing data set, like the 448 ounce cone, will affect the mean and standard deviation due to their sensitivity to extreme values. However, the median and interquartile range (IQR), which are measures of central tendency and spread that are resistant to outliers, are unlikely to change. The median remains the middle value, and the IQR, the range between the first and third quartiles, would not be affected by a single extreme value.

Question 15

Here are some summary statistics for the recent English exam: lowest $\text { score } = 36 \text {, }$ mean $\text { score } = 71 \text {, }$ $\text { median } = 85.2 \text {, }$ $$\text { range } = 74 \text {, }$$ $\mathrm { IQR } = 61 \text {, }$ $\mathrm { Q } 1 = 28 \text {, }$ standard deviation = 8.3.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the right; mean higher than median.
B)Symmetric; mean lower than median.
C)Skewed to the left; mean lower than median.
D)Skewed to the right; mean lower than median.
E)Skewed to the left; mean higher than median.

Accepted Answer

Since the mean is lower than the median, it indicates that the distribution is skewed to the left.

Question 16

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest $\text { time } = 124$ minutes $\text { mean } = 85$ minutes $\text { median } = 85$ minutes $\text { range } = 94$ minutes $\mathrm { IQR } = 56$ $\mathrm { Q } 1 = 34$ standard $\text { deviation } = 13$ minutes
Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Skewed to the right; mean higher than median.
B)Symmetric; mean same as median.
C)Skewed to the right; mean lower than median.
D)Skewed to the left; mean higher than median.
E)Skewed to the left; mean lower than median.

Accepted Answer

Since the mean and the median are the same, this suggests that the distribution is symmetric. In a symmetric distribution, the mean and median are equal or very close to each other.

Question 17

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

Accepted Answer

Adding a value of 0% would lower the minimum value of the dataset, affecting the range and potentially the mean and standard deviation. However, the median and interquartile range (IQR), which are measures of central tendency and spread that are not influenced by extreme values, would remain unchanged. The median is the middle value when data is ordered, and the IQR is the range between the first and third quartiles, neither of which would be affected by the addition of a new minimum value outside the existing range.

Question 18

Here are summary statistics for the time,in minutes,it took 21 students to write a statistics test. $\begin{array} { c | c | c | c | c | c | c | c } 
\text { Count } & \text { Mean } & \text { Median } & \text { StdDev } & \text { Min } & \text { Max } & \text { Q1 } & \text { Q3 } \
\hline 21 & 23.9 & 22.0 & 12.2 & 5.1 & 51.7 & 15.4 & 33.4
\end{array}$ Would you describe this distribution as symmetric or skewed?
A)Skewed to the right,because the mean is much larger than the median and the upper quartile is farther from the median than the lower quartile.
B)Symmetric,because the mean and the median are close.
C)Skewed to the right,because the mean is much larger than the median and the lower quartile is farther from the median than the upper quartile.
D)Skewed to the left,because the mean is much larger than the median and the lower quartile is farther from the median than the upper quartile.
E)Skewed to the left,because the mean is much larger than the median and the upper quartile is farther from the median than the lower quartile.

Accepted Answer

The distribution is skewed to the right because the mean (23.9) is greater than the median (22.0), indicating a longer tail to the right. Additionally, the distance from the third quartile (Q3) to the median is greater than the distance from the first quartile (Q1) to the median, further indicating a right skew.

Question 19

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest $\text { amount } = 18$ cm, $\text { mean } = 49$ cm, $\text { median } = 42$ cm, $\text { range } = 82$ cm, $\mathrm { IQR } = 50 ,$ $\mathrm { Q } 1 = 20 \text {, }$ standard $\text { deviation } = 10$ cm.Between what two values are the middle 50% of snowfall found?
A)20 and 70
B)12.25 and 36.75
C)49 and 42
D)10.5 and 31.5
E)18 and 100

Accepted Answer

The middle 50% of snowfall amounts are found between the first quartile (Q1) and the third quartile (Q3). Given Q1 = 20 cm and the interquartile range (IQR) = 50 cm, the third quartile (Q3) can be calculated as Q1 + IQR = 20 cm + 50 cm = 70 cm. Therefore, the middle 50% of snowfall amounts are found between 20 cm and 70 cm.

Question 20

Here are some summary statistics for last year's basketball team scoring output: lowest $\text { score } = 19$ points, $\text { mean } = 55$ points, $\text { median } = 49$ points, $\text { range } = 96$ points, $\mathrm { IQR } = 52$ $\mathrm { Q } 1 = 22$ standard $\text { deviation } = 6$ points.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.
A)Symmetric; mean higher than median.
B)Skewed to the left; mean higher than median.
C)Skewed to the right; mean higher than median.
D)Skewed to the right; mean lower than median.
E)Skewed to the left; mean lower than median.

Accepted Answer

Since the mean is higher than the median and the lowest score occurs more frequently than the highest score, the distribution is skewed to the right.

Quiz 3: Displaying and Summarizing Quantitative Data