AnswersMathematics for College Liberal Arts Sem 1 1207350 BCPS 2025-26Measures of Variability

Measures of Variability Answers

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Some teenagers collected trash for a beach clean-up. The data for the number of pounds of trash collected by each teenager are shown below.26, 26, 21, 22, 20, 25, 35

A
4.5 pounds
B
5.033 pounds
C
9 pounds
D
15 pounds
2
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People at a library were asked how many states they had visited. Below is a stemplot of all of the data except for one value.

Question illustration
A
If the missing data value were 32, the IQR would change substantially.
B
If the missing data value were 32, the range would change substantially.
C
If the missing data value were 50, the IQR of the data would change substantially.
D
If the missing data value were 50, the range of the data would change substantially.
3

A tutor kept track of how many students she had helped every week for a year. The range of the number of tutored students was 10 students. Which of the following is the best interpretation of this value?

A
Fifty percent of the tutored students’ data is below 10 students.
B
The middle half of the tutored students’ data has a range that is 10 students wide.
C
The number of students helped within a week typically varies by about 10 students from the mean.
D
The difference between the smallest and largest values in the tutored students’ data was 10 students.
4

As an introduction to probability, a student is asked to roll a fair, six-sided number cube seven times. The results of those seven rolls are shown below.1, 4, 4, 4, 4, 6, 5

A
1.41
B
1.53
C
2.33
D
5
5

Shoppers were surveyed about their spending for holiday shopping. The standard deviation of the amount shoppers spent was $125. Which of the following is the best interpretation of this value?

A
Fifty percent of the amount shoppers spent is above $125.
B
The middle half of the amount shoppers spent has a range that is $125 wide.
C
The amount shoppers spent typically varies by about $125 from the mean.
D
The difference between the largest and smallest amounts shoppers spent was $125.
6

In a recent survey, students were asked how long they play video games in one sitting. The interquartile range of the length of play times was 43 minutes. Which of the following is the best interpretation of this value?

A
Fifty percent of the video game data is below 43 minutes.
B
The middle half of the video game data has a range that is 43 minutes wide.
C
The number of minutes played by students typically varies by about 43 minutes from the mean.
D
The difference between the smallest and largest values in the video game data was 43 minutes.
7

Without making any calculations, which distribution of data has the smallest standard deviation?

A
1, 1, 1, 2, 2, 2
B
1, 1, 1, 1, 2, 2
C
1, 1, 1, 1, 1, 2
D
1, 1, 1, 1, 1, 1
8

Which of the following statements is true about the IQR, range, and standard deviation?

A
The IQR is the least resistant to extreme values.
B
The IQR is the most resistant to extreme values.
C
The range is the most resistant to extreme values.
D
The standard deviation is the most resistant to extreme values.
9

Some teenagers collected trash for a beach clean-up. The data for the number of pounds of trash collected by each teenager are shown below.26, 26, 21, 22, 20, 25, 35

A
1 pounds
B
5 pounds
C
5.033 pounds
D
15 pounds
10

A statistics student gave a survey to students which asked how many first cousins they have. The data from the first nine responses are shown below.6, 2, 7, 8, 8, 8, 5, 10, 10

A
2.52 first cousins
B
3.5 first cousins
C
4 first cousins
D
8 first cousins
11

A statistics student gave a survey to students which asked how many first cousins they have. The data from the first nine responses are shown below.6, 2, 7, 8, 8, 8, 5, 10, 10

A
2.52 first cousins
B
3 first cousins
C
3.5 first cousins
D
8 first cousins
12

A box of LED light bulbs was tested to see how long the light bulbs last. The standard deviation of the light bulb lifetime data was five years. Which of the following is the best interpretation of this value?

A
Fifty percent of the light bulb lifetime data is below five years.
B
The difference between the longest and shortest light bulb lifetime was five years.
C
The lifetime of the light bulbs typically varies by about five years from the mean.
D
The middle half of the light bulb lifetime data has a range that is five years wide.
13

Some teenagers collected trash for a beach cleanup. The data for the number of pounds of trash collected by each teenager are shown below.26, 26, 21, 22, 20, 25, 35

A
0 pounds
B
4.66 pounds
C
5.03 pounds
D
25.33 pounds
14

Some teenagers collected trash for a beach clean-up. The data for the number of pounds of trash collected by each teenager are shown below.26, 26, 21, 22, 20, 25, 35

A
4.5 pounds
B
5.033 pounds
C
9 pounds
D
15 pounds
15

The parallel dotplots below display the girths (belly circumference) of some male and female pigs.

Question illustration
A
The IQR for the distribution of girths is larger in female pigs.
B
The range for the distribution of girths is larger in male pigs.
C
The standard deviation for the distribution of girths is smaller in female pigs.
D
The standard deviation for the distribution of girths is about the same for both male and female pigs.
16

The parallel dotplots below display the number of scholarship applications submitted by students for each of two schools: A and B.

Question illustration
A
The range for the number of submitted scholarships is larger for school A.
B
The range for the number of submitted scholarships is larger for school B.
C
There is a smaller standard deviation for the number of submitted scholarships for school A.
D
The standard deviation in the number of submitted scholarships is the same for both classes.
17

A tutor kept track of how many students she had helped every week for a year. The range of the number of tutored students was 10 students. Which of the following is the best interpretation of this value?

A
Fifty percent of the tutored students’ data is below 10 students.
B
The middle half of the tutored students’ data has a range that is 10 students wide.
C
The number of students helped within a week typically varies by about 10 students from the mean.
D
The difference between the smallest and largest values in the tutored students’ data was 10 students.
18

Which of the following statements is true about the IQR, range, and standard deviation?

A
The IQR is the least resistant to extreme values.
B
The IQR is the most resistant to extreme values.
C
The range is the most resistant to extreme values.
D
The standard deviation is the most resistant to extreme values.
19

Some teenagers collected trash for a beach clean-up. The data for the number of pounds of trash collected by each teenager are shown below.26, 26, 21, 22, 20, 25, 35

A
1 pounds
B
5 pounds
C
5.033 pounds
D
15 pounds

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