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Chapter 2: Q107E (page 125)

Suppose a data set consisting of exam scores has a lower quartile QL = 60, a median QM = 75, and an upper quartile QU = 85. The scores on the exam range from 18 to 100. Without having the actual scores available to you, construct as much of the box plot as possible.

Short Answer

Expert verified

IQR = QU 鈥� QL

= 85 鈥� 60

= 25

Lower Inner Fence = QL - 1.5(IQR)

= 60 鈥� 1.5(25)

= 60 鈥� 37.5

= 22.5

Upper Inner Fence = QU + 1.5(IQR)

= 60 + 1.5(25)

= 60 + 37.5

= 122.5

Step by step solution

01

Finding the fences

IQR = QU 鈥� QL

= 85 鈥� 60

= 25

Lower Inner Fence = QL - 1.5(IQR)

= 60 鈥� 1.5(25)

= 60 鈥� 37.5

= 22.5

Upper Inner Fence = QU + 1.5(IQR)

= 60 + 1.5(25)

= 60 + 37.5

= 122.5

02

Creating the box plot

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Most popular questions from this chapter

Question: For any set of data, what can be said about the percentage of the measurements contained in each of the following intervals?

a.xbar- sto xbar+ s

b.xbar- 2sto xbar+ 2s

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99 92 94 95 97 91 91 92 92 89 84 85 100 87 83 83 89 79 94 79 79 87 76 67 76 76 76 70 74 64 74 69 66 72 65 76 64 65 61 69 62 69 52 64 64 47 60 57 63 62

a.Find the median, lower quartile, and upper quartile for the data.

b.Find IQR for the data.

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Question: Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability

behaviors of CPA corporations, Exercise 2.48 (p. 96). Numerical measures of variation for level of support for the 992 senior managers are shown in the accompanying Minitab printout.

Descriptive Statistics: Support

Variable

N

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StDev.

Variance

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Maximum

Range

Support

992

67.755

26.871

722.036

0.000

155.000

155.000

a.Locate the range on the printout. Comment on the accuracy of the statement: 鈥淭he difference between the largest and smallest values of level of support for the 992 senior managers is 155 points.鈥�

b.Locate the variance on the printout. Comment on the accuracy of the statement: 鈥淥n average, the level of support for corporate sustainability for the 992 senior managers is 722 points.鈥�

c.Locate the standard deviation on the printout. Does the distribution of support levels for the 992 senior managers have more or less variation than another distribution with a standard deviation of 50? Explain.

d.Which measure of variation best describes the distribution of 992 support levels? Explain.

Professional athletes鈥� salaries.The salaries of superstar professional athletes receive much attention in the media. The multimillion-dollar long-term contract is now commonplace among this elite group. Nevertheless, rarely does a season pass without negotiations between one or more of the players鈥� associations and team owners for additional salary and fringe benefits for allplayers in their particular sports.

a.If a players鈥� association wanted to support its argument for higher 鈥渁verage鈥� salaries, which measure of central tendency do you think it should use? Why?

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(9.0, -.1, -1.6, 14.6, 16.0, 7.7, 19.9, 9.8, 3.2, 24.8, 17.6, 10.7, 9.1)

a.Find the range of the data for the 13 stock screeners. Give the units of measurement for the range.

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