Representing Data Answers

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Thirty adults were asked how many pets they have had over their lifetime. The results are shown in the histogram below. Which of the following is most likely true?

Question illustration
A
The mean and median are both in the interval 1–5.
B
The mean and median are both in the interval 6–10.
C
The mean is in the interval 6–10, and the median is in the interval 1–5.
D
The mean is in the interval 1–5, and the median is in the interval 6–10.
2
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A histogram shows data that is skewed to the right. Which most likely describes the relationship between the mean and the median?

A
The mean is greater than the median. The rightmost values in the data set raise the mean more than the median.
B
The median is greater than the mean. The rightmost values in the data set raise the median more than the mean.
C
The mean is greater than the median. The leftmost values in the data set lower the median more than the mean.
D
The median is greater than the mean. The leftmost values in the data set lower the mean more than the median.
3

Indira makes a box-and-whisker plot of her data. She finds that the distance from the minimum value to the first quartile is greater than the distance between the third quartile and the maximum value. Which is most likely true?

A
The mean is greater than the median because the data is skewed to the right.
B
The mean is greater than the median because the data is skewed to the left.
C
The mean is less than the median because the data is skewed to the right.
D
The mean is less than the median because the data is skewed to the left.
4

Gemma is creating a histogram based on the table below. Salary RangeNumber of People0 - $19,99940$20,000 - $39,99930$40,000 - $59,99935Which scale can she use for the vertical axis such that the difference in the heights of the bars is maximized?

A
0–50
B
0–40
C
10–50
D
25–40
5

The stem-and-leaf plot below shows the amount of tips received by the servers in a restaurant in one night. Why is the plot misleading?

Question illustration
A
The plot shows that the data is skewed.
B
There is not an equal number of data points for each stem.
C
The plot shows duplicate data points.
D
The stem does not clearly show the outlier.
6

The histogram below shows the age distribution of Elizabeth’s grandchildren. The box-and-whisker plot below shows the same data. Which of the following best explains why one graph appears skewed and one graph appears symmetric?

Question illustration
A
The intervals on the x-axis of the histogram are too large.
B
The interval on the y-axis of the histogram is too small.
C
The interval on the x-axis of the histogram is inconsistent.
D
The interval on the box-and-whisker plot is too small.
7

Charles owns a catering business. The amount his 10 most recent clients spent is shown in the histogram below. Why is the graph misleading?

Question illustration
A
The x-axis scale shows the data is more clustered than it actually is.
B
The y-axis scale shows the data is more skewed than it actually is.
C
The scales are different on the x-axis and the y-axis.
D
The data is not distributed equally across the x-axis intervals.
8

Which measure would be the most appropriate to describe the center of the data in the histogram below?

Question illustration
A
mean
B
range
C
median
D
interquartile range
9

Which measure is most appropriate to describe the center of the data in the stem-and-leaf plot below?

Question illustration
A
interquartile range
B
median
C
mean
D
range
10

Which best represents the center of the data set below? Average Monthly Grocery Bill

Question illustration
A
mean
B
median
C
range
D
mode

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