AnswersAZ-Common Core Algebra II BRepresenting Data

Representing Data Answers

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1
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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
2
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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.
3

The graphs below display new car values for cars at the same dealership. The graphs display the same data. Which graph is more likely to show a buyer that it is a good time to buy a car?

Question illustration
A
graph 1 because the x-axis scale makes it look like cars are selling at a lower price
B
graph 1 because the y-axis scale makes it look like cars are selling at a lower price
C
graph 2 because the x-axis scale makes it look like cars are selling at a lower price
D
graph 2 because the y-axis scale makes it look like cars are selling at a lower price
4

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.
5

The stem-and-leaf plot below shows the number of pages each student in the class read the previous evening. According to the plot, 75% of students read less than

Question illustration
A
13 pages.
B
33 pages.
C
35 pages.
D
46 pages.
6

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

Question illustration
A
mean
B
median
C
range
D
mode
7

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.
8

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.
9

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.
10

A representative from plan 1 wants to use the graph below to sell health plans for his company. How might the graph be redrawn to emphasize the difference between the cost per doctor visit for each of the three plans?

Question illustration
A
The scale on the y-axis could be changed to 0–100.
B
The scale on the y-axis could be changed to 25–40.
C
The interval of the y-axis could be changed to count by 5s.
D
The interval of the y-axis could be changed to count by 20s.
11

The stem-and-leaf plot below shows the number of pages each student in the class read the previous evening. According to the plot, 75% of students read less than

Question illustration
A
13 pages.
B
33 pages.
C
35 pages.
D
46 pages.
12

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.
13

The histograms below show the ages of dogs at four different shelters. For which set of data is the mean most likely greater than the median?

A
A bar graph has age on the x-axis and number of dogs on the y-axis. There is 1 dog that is 0 to 1 year of age; 4 dogs that are 2 to 3; 2 dogs that are 4 to 5; 0 dogs that are 6 to 7; 1 dog that is 8 to 9.
Option A
B
A bar graph has age on the x-axis and number of dogs on the y-axis. There are 0 dogs that are 0 to 1 year of age; 3 dogs that are 2 to 3; 4 dogs that are 4 to 5; 3 dogs that are 6 to 7; 0 dogs that are 8 to 9.
Option B
C
A bar graph has age on the x-axis and number of dogs on the y-axis. A bar graph has age on the x-axis and number of dogs on the y-axis. There are 0 dogs that are 0 to 1 year of age; 1 dog that is 2 to 3; 2 dogs that are 4 to 5; 4 dogs that are 6 to 7; 1 dog that is 8 to 9.
Option C
D
A bar graph has age on the x-axis and number of dogs on the y-axis. There are 2 dogs that are 0 to 1 year of age; 1 dog that is 2 to 3; 2 dogs that are 4 to 5; 1 dog that is 6 to 7; 2 dogs that are 8 to 9.
Option D
14

The box-and-whisker plot below shows the age distribution of people at a family reunion.The stem-and-leaf plot below shows the same data.Which of the following best explains why one graph appears skewed and one graph appears symmetrical?

Question illustration
A
The scale of the box-and-whisker plot does not start at zero.
B
The interval of the box-and-whisker plot is too large.
C
The interval of the stem-and-leaf plot is not consistent.
D
The scale of the stem-and-leaf plot is too small for the set of data.
15

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.

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