AnswersMathematics for College Liberal Arts Sem 1 1207350 BCPS 2025-26Comparing Data Sets

Comparing Data Sets Answers

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1
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The box plots show the distributions of the numbers of words per line in an essay printed in two different fonts. Which measure of center would be best to compare the data sets?

Question illustration
A
The median is the best measure because both distributions are left-skewed.
B
The mean is the best measure because both distributions are left-skewed.
C
The median is the best measure because both distributions are symmetric.
D
The mean is the best measure because both distributions are symmetric.
2
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The box plots represent the distributions of typing speeds of students before and after a computer-programming course. Which statement is true about the variability of the distributions?

Question illustration
A
The interquartile range of the typing speeds after the course is greater than the interquartile range of the speeds before the course.
B
The interquartile ranges of the two distributions are the same.
C
The range of the speeds after the course is smaller than the range of the speeds before the course.
D
The ranges of the two distributions are the same.
3

The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale.

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0
2
2
4
4
7
7
4

The histogram shows the distributions of prices for packs of adult socks and packs of kid socks at a store. Which measure of center is the best to use to compare the prices of kid socks and adult socks?

Question illustration
A
range
B
mean
C
median
D
standard deviation
5

A research study was conducted to measure the time students focus on a task before being distracted. The box plots show the distributions of attention spans of high school and college students.Which statements are true regarding the data sets? Select two options.The median attention span of college students is greater than the median attention span of high school students. The range of attention span of college students is greater than the range of attention spans of high school students.The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students.All of the college students in the study had greater attention spans than the high school students.The minimum attention span of high school students is greater than the minimum attention span of college students.

Question illustration
A
The median attention span of college students is greater than the median attention span of high school students.
B
The range of attention span of college students is greater than the range of attention spans of high school students.
C
The interquartile range of attention spans of college students is greater than the interquartile range of attention spans of high school students.
D
All of the college students in the study had greater attention spans than the high school students.
E
The minimum attention span of high school students is greater than the minimum attention span of college students.
6

The table shows the battery lives, in hours, of ten Brand A batteries and ten Brand B batteries. Which would be the best measure of variability to use to compare the data?

Question illustration
A
Only Brand A data is symmetric, so standard deviation is the best measure to compare variability.
B
Only Brand B data is symmetric, so the median is the best measure to compare variability.
C
Both distributions are symmetric, so the mean is the best measure to compare variability.
D
Both distributions are skewed left, so the interquartile range is the best measure to compare variability.
7

The histogram shows the distributions of essay scores for high school sophomores and juniors in a contest. Which comparison of the distributions is true?

Question illustration
A
Both distributions are nearly symmetric.
B
Both distributions are right-skewed.
C
The distribution of sophomores’ scores is right-skewed, and the distribution of juniors’ scores is left-skewed.
D
The distribution of sophomores’ scores is left-skewed, and the distribution of juniors’ scores is right-skewed.
8

The table shows the test scores of students who studied for a test as a group (Group A) and students who studied individually (Group B).

Question illustration
T
The scores of Group B are skewed right, so the mean and range are the best measures for comparison.
B
Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.
B
Both distributions are nearly symmetric, so the median and the interquartile range are the best measures for comparison.
T
The scores of both groups are skewed, so the median and standard deviation are the best measures for comparison.
9

The box plots represent the ages of pennies in two 50-cent rolls.

Question illustration
A
She is correct because the medians are 10 years apart, which means the means are half of that, or 5 years apart.
B
She is correct because the maximum ages of the pennies in each set are 5 years apart.
C
She is not correct because the means are both equal to 12.
D
She may not be correct because means cannot be determined from the box plots.
10

Two histograms showing the number of pets owned by boys and girls in a science class are each skewed left. Which measure of variability should be used to describe the data?

A
mean
B
median
C
standard deviation
D
interquartile range
11

The histogram represents the distributions of boiling temperatures, in degrees Celsius, of tap water and a mixture of salt water.

Question illustration
A
The two distributions are each nearly symmetric.
B
The distributions do not overlap on the same range of temperatures.
C
The distribution of salt water boiling temperatures is left-skewed.
D
The distribution of tap water boiling temperatures is right-skewed.
12

The histogram shows the distributions of essay scores for high school sophomores and juniors in a contest. Which comparison of the distributions is true?

Question illustration
A
Both distributions are nearly symmetric.
B
Both distributions are right-skewed.
C
The distribution of sophomores’ scores is right-skewed, and the distribution of juniors’ scores is left-skewed.
D
The distribution of sophomores’ scores is left-skewed, and the distribution of juniors’ scores is right-skewed.
13

The table shows the daily time, in minutes, Maggie spent at swim practice and band practice over the last ten days. Which statement is true about the measures of center of the practice times?

Question illustration
A
Maggie’s daily time at band practice tends to be greater than her time at swim practice.
B
Maggie’s daily time at band practice has less variation than her daily time at swim practice.
C
Maggie’s daily time at swim practice tends to be greater than her time at band practice.
D
Maggie’s daily time at swim practice tends to have more variation than her daily time at band practice.
14

The box plots represent the ages of pennies in two 50-cent rolls.

Question illustration
A
She is correct because the medians are 10 years apart, which means the means are half of that, or 5 years apart.
B
She is correct because the maximum ages of the pennies in each set are 5 years apart.
C
She is not correct because the means are both equal to 12.
D
She may not be correct because means cannot be determined from the box plots.
15

The box plots show the data distributions for the number of customers who used a coupon each hour for two days of a store sale.

Question illustration
A
0
B
2
C
4
D
7
16

The box plots represent the distributions of typing speeds of students before and after a computer-programming course. Which statement is true about the variability of the distributions?

Question illustration
A
The interquartile range of the typing speeds after the course is greater than the interquartile range of the speeds before the course.
B
The interquartile ranges of the two distributions are the same.
C
The range of the speeds after the course is smaller than the range of the speeds before the course.
D
The ranges of the two distributions are the same.
17

The box plots show the data distributions for the number of laps two students run around a track each day.

Question illustration
A
The difference between the medians of both data sets is 2.
B
The difference between the medians of both data sets is 4.
C
The difference between the ranges of both data sets is 2.
D
The difference between the ranges of both data sets is 4.
18

The table shows the test scores of students who studied for a test as a group (Group A) and students who studied individually (Group B).

Question illustration
A
The scores of Group B are skewed right, so the mean and range are the best measures for comparison.
B
Both distributions are nearly symmetric, so the mean and the standard deviation are the best measures for comparison.
C
Both distributions are nearly symmetric, so the median and the interquartile range are the best measures for comparison.
D
The scores of both groups are skewed, so the median and standard deviation are the best measures for comparison.
19

The histogram shows the prices for six-packs of adult socks and six-packs of kid socks at a store. What is true about the variability of the prices of socks in kid sizes or adult sizes?

Question illustration
A
There is more variability in the prices of kid socks because they have a greater range.
B
There is more variability in the prices of kid socks because the median is lower.
C
There is more variability in the prices of adult socks because there are two bars of equal height.
D
There is more variability in the prices of adult socks because the median is greater.
20

The box plots show the distributions of the numbers of words per line in an essay printed in two different fonts. Which measure of center would be best to compare the data sets?

Question illustration
A
The median is the best measure because both distributions are left-skewed.
B
The mean is the best measure because both distributions are left-skewed.
C
The median is the best measure because both distributions are symmetric.
D
The mean is the best measure because both distributions are symmetric.

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