PRACTICE & PROBLEM SOLVING

UNDERSTAND PRACTICE

Additional Exercises Available Online

Practice Tutorial

For each pair of data sets, compare the means and the MADs, and then the medians and the IQRs. Decide which measures are better for comparing the data sets. Explain your reasoning. SEE EXAMPLES 1–4

15.

5

5

4

6

Data Set A

6

4

5

5

5

5

6

4

4

6

5

5

5

6

5

3

Data Set B

9

1

7

5

2

5

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5

5

8

6

4

16.

3.0

3.4

4.8

2.8

3.3

3.1

3.2

2.9

3.2

3.3

3.0

4.9

3.2

4.5

3.1

Data Set A

1.9

3.4

3.2

3.3

3.0

3.6

1.5

3.2

3.5

3.2

3.4

3.1

3.1

1.6

3.3

Data Set B

17. Data Set A

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Data Set B

70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

18. A researcher claims that students tend to have more apps on their smart phones than adults. Do the data support the researcher’s claim? Explain. SEE EXAMPLE 2

10 15 20 25 30 35 40

Number of Apps

Students’ phones

Adults’ phones

10. Reason The mean of the data set represented by the histogram is 12. What is a reasonable estimate for the median? Explain your reasoning.

Freq

uen

cy

6

5

4

3

2

1

0

11. Construct Arguments The means of two data sets are the same, but the median of one data set is much smaller than the median of the other data set. What conclusions can you make about the sets from this information?

12. Error Analysis Describe and correct the errors a student made when making a statement based on the data set represented by the dot plot.

The mean of the data set is

about the same as the median.

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13. Communicate Precisely How are the IQR and the range of a data set similar in terms of comparing data sets? How are they different?

14. Higher Order Thinking Two data sets each have a median of 10. The first data set has an IQR of 22 and the second data set has an IQR of 8.

a. What conclusions can you make about the data sets? Explain.

b. Is it possible to also make a prediction about the MADs from the information given? Explain.

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Practice Tutorial

19. Model With Mathematics The mean score on last year’s math final exam was 82, with MAD of 3.5 points. Scores for this year’s exam are shown in the table. How do the scores for the two years compare?

85

84

88

86

99

82

86

71

85

75

88

70

85

91

84

84

95

92

82

78

85

86

79

85

100

Math Final Exam Scores

20. Make Sense and Persevere The points of each player on Parker’s basketball team for the season are shown in the table. The points of an opposing team are represented by the box plot. How does Parker’s team compare?

35

90

100

32

45

120

60

76

60

80

96

38

36

92

75

Points per Player

70 71 72 73 74 75 76 77

21. Use Structure The label on the cereal box says the weight is 12 ounces. The dot plots show weights of two random samples of 16 boxes packaged on two different machines. How can you compare the data sets to see if there is a problem with one of the machines?

Machine A

11.5 11.6 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5

Machine B

11.5 11.6 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5

22. The table shows the number of minutes Dylan and Kyle spent on their homework each night over the past 5 nights.

Based on this data, which of the following statements are true? Select all that apply.

Ⓐ The median of Kyle’s data is greater than the median of Dylan’s data.

Ⓑ On average, Dylan spends more time on homework than Kyle.

Ⓒ The mean is greater than the median in both groups.

Ⓓ The IQR of the data is greater for Kyle.

23. SAT/ACT The histograms that correspond to two data sets look identical. What conclusion can you make about the data sets.

Ⓐ The data points in each set are the same.

Ⓑ The mean of each of the data sets is the same.

Ⓒ The median of each of the data sets is the same.

Ⓓ none of these

24. Performance Task A consumer group tested battery life times for two different smart phones. Results are shown in the tables below.

10.014.014.213.0

14.20.9

15.015.0

12.014.29.5

14.2

15.19.5

12.511.0

16.015.014.2

9.0

Phone A

12.514.012.814.0

13.014.015.013.6

14.012.013.0 14.2

13.515.015.213.8

15.012.816.015.1

Phone B

Part A Find the mean and MAD for each data set.

Part B Find the median and IQR for each data set.

Part C Create data displays that will allow you to compare the two data sets.

Part D Which cell phone battery is likely to last longer? Explain your reasoning.

45

40

80

60

20

30

35

50

70

30

Dylan Kyle

LESSON 11-2 Comparing Data Sets 479