AnswersIntegrated Math II FullComparing Measures of Center and Variability

Comparing Populations Answers

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1
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A business owner collected data on the people working for her company. She determined the average number of minutes each employee spent on breaks during an average workday. The data, broken up by gender, is shown below.Number of Minutes Women Spend on BreaksNumber of Minutes Men Spend on BreaksThe business owner uses the median and IQR to determine the center and variability of the data sets. Which best describes the comparison?

Question illustration
A
The comparison would be more accurate using the mean and MAD because one of the graphs is symmetric.
B
The comparison would be more accurate using the mean and MAD because the median of both data sets is the same.
C
The comparison using median and IQR is best because one of the graphs is not symmetrical.
D
The comparison using median and IQR is best because the median is greater than the IQR for both data sets.
2
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Takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. Her data are shown in the plots below.Which best explains the variability of the sets?

Question illustration
A
The shaded plants set has greater variability because more data is clustered around the median.
B
The sets are equally variable because the ranges of the data sets are equal.
C
The full sun plants set has greater variability because the IQR for full sun plants is greater.
D
The full sun plants set has greater variability because the median for full sun plants is greater.
4

Ayana and Tabitha recorded the amount of time spent on homework on ten school days. Graphs of their data are shown.Ayana’s Time Spent on HomeworkTabitha’s Time Spent on HomeworkWhich best explains who spends more time on homework?

Question illustration
A
Ayana, because she has a higher maximum time spent
B
Ayana, because she has more variability in her time spent
C
Tabitha, because she has a higher median time spent
D
Tabitha, because she has more variability in her time spent
7

Two baseball coaches recorded the number of hits each player had during practice. They displayed the results in the box plots below.Number of Hits by Team 1 PlayersNumber of Hits by Team 2 PlayersThe coaches determined the mean and MAD from the raw data and used that information to compare the two plots. They determined there is more variability in the number of hits per player on Team 2 than on Team 1. Which best describes this conclusion?

Question illustration
A
Inaccurate. The data sets are not symmetrical and the ranges of the two teams’ data are the same.
B
Accurate. The data sets are not symmetrical. There is more variability on Team 2 than on Team 1 because the median of Team 2 is greater than the median of Team 1.
C
Inaccurate. The data sets are not symmetrical. There is less variability on Team 2 than on Team 1 because the IQR of Team 2 is less than the IQR of Team 1.
D
Accurate. The data sets are not symmetrical. The MAD for Team 2 was calculated to be a larger number than the MAD for Team 1.
8

The sets of data below show the heights, in inches, of students in two different preschool classes.Class 1Class 2The teachers of the two classes want to compare the heights of their students. Which statements about the data sets are accurate? Select three options.

Question illustration
A
Because the sets are symmetrical, the mean should be used to compare the data sets.
B
Because the sets do not contain outliers, the MAD should be used to compare the data sets.
C
Because the sets are not symmetrical, the IQR should be used to compare the data sets.
D
Because the sets contain outliers, the median should be used to compare the data sets.
E
The mean and mode cannot be accurately determined based on the type of data display.
10

The monthly energy use, in kilowatt hours, for two neighbors is shown in the box plots below. Neighbor 1Neighbor 2Which statements accurately compare the two data sets? Select three options.

Question illustration
A
Neighbor 1 tends to use fewer kilowatt hours each month.
B
The median value for Neighbor 2 is 75 kilowatt hours greater than the median value for Neighbor 1.
C
Neighbor 1 had greater variability in the number of kilowatt hours used per month.
D
Neighbor 2 had greater variability in the number of kilowatt hours used per month.
E
The median value for Neighbor 2 is 50 kilowatt hours greater than the median value for Neighbor 1.

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