AnswersHCISD-Mathematical Models with Applications B-CR SUMMERSampling Methods

Comparing Measures of Center and Variability Answers

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1
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What does mean absolute deviation (MAD) measure? Explain how to find the MAD for a set of data.

Answer:

The MAD measures the average distance from a data point from the mean. To find the MAD for a set of data, first find the mean of the data set. Then, find the distance from the mean for each data value. Finally, find the mean of those distances.

2
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What information did you include in your response? Check all that apply.

A
The MAD is a measure of variability.
B
Find the mean of the data set.
C
Find the distance from the mean for each data value.
D
Find the means of the distances.
3

A student found the MAD of the data shown. What was the student’s error?

A
When calculating the mean, the student divided the sum by the wrong number.
B
When calculating the MAD, the student divided the sum by the wrong number.
C
When calculating the distances to the mean, the student forgot to take the absolute values.
D
When calculating the MAD, the student forgot to take the absolute value of the result.
4

Find the mean of the data set shown below. Round to the nearest tenth, if necessary.This Week’s High Temperatures (°F)29, 38, 45, 31, 50, 58, 62

Answer:

44.7

5

The mean of the data is 44.7. Complete the chart to find the distances from the mean.

Answers:
The mean of the data is 44.7. Complete the chart to find the distances from the mean.:0.3
The mean of the data is 44.7. Complete the chart to find the distances from the mean.:5.3
The mean of the data is 44.7. Complete the chart to find the distances from the mean.:17.3
6

y = -2.72.7✔ 5.313.3

A
-2.7
B
2.7
C
✔ 5.3
D
13.3
7

z = 0.36.313.3✔ 17.3

A
0.3
B
6.3
C
13.3
D
✔ 17.3
17

Question text not available

Answer:

10.3

18

Which measures of center and variability for the temperatures were lower this week than last week? Check all that apply.

A
mean
B
median
C
mode
D
range
E
mean absolute deviation
19

Heights of Basketball Players (inches)

Answers:
Heights of Basketball Players (inches) 75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84:78.83
Heights of Basketball Players (inches) 75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84:2.4
20

What is the MAD of the data set? 1.42✔ 2.43

A
1.4
B
2
C
✔ 2.4
D
3
25

What can you infer from the given data? Choose all that apply.

A
Basketball players are generally taller.
B
Soccer players are generally taller.
C
Soccer players and basketball players are generally the same height.
D
Basketball player heights vary slightly more.
E
Soccer player heights vary slightly more.
26

Which statement is true?

A
The difference between the mean heights is approximately equal to the MAD of the data sets.
B
The difference between the mean heights is approximately 2 times the MAD of the data sets.
C
The difference between the mean heights is approximately 3 times the MAD of the data sets.
D
The difference between the mean heights is approximately 4 times the MAD of the data sets.
27

Heights of Basketball Players (inches)

Answers:
Heights of Basketball Players (inches) 75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84:78.83
Heights of Basketball Players (inches) 75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84:2.4

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