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Chapter 2: Q55E (page 98)

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?

b.To refute the argument, which measure of central tendency should the owners apply to the players鈥� salaries? Why?

Short Answer

Expert verified
  1. Median
  2. Mean

Step by step solution

01

Identifying the best measure of central tendency to support the argument

Suppose the players鈥� association wants to support its argument for a higher average salary. They should use the median because the median gives you the centermost value and would therefore give us the appropriate average.

Lower median as the average will prompt the owners to increase the median and thus increase the average.

02

Finding the best measure of central tendency to refute the argument 

The owners will use the mean because there are very high chances that the data might be skewed to the right and would pull the mean to the right and make it larger than the median value.

By using the mean in skewed data, the owners can refute the argument by showing the already higher average.

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Most popular questions from this chapter

Calculate the range, variance, and standard deviation for the following samples:

a.4, 2, 1, 0, 1

b.1, 6, 2, 2, 3, 0, 3

c.8, -2, 1, 3, 5, 4, 4, 1, 3, 3

d.0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3,-2, -1, 0, 1

Museum management. Refer to the Museum Management and Curatorship (June 2010) study of how museums evaluate their performance, Exercise 2.14 (p. 74). Recall that managers of 30 contemporary art museums identified the performance measure used most often. A summary of the results is reproduced in the table. Consider the bar graph shown. Identify two ways the bar graph might mislead the viewer by overemphasizing the importance of one of the performance measures.

Is honey a cough remedy?Refer to the Archives of Pediatrics and Adolescent Medicine(December 2007) study of honeyas a remedy for coughing, Exercise 2.31 (p. 86). The coughingimprovement scores (as determined by the children鈥檚 parents)for the patients in the over-the-counter cough medicinedosage (DM) group, honey dosage group, and control groupare reproduced in the accompanying table.

Honey Dosage

12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12

DM Dosage

4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10

No Dosage
(Control)

13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3

a.Find the standard deviation of the improvement scores for the honey dosage group.

b.Find the standard deviation of the improvement scores for the DM dosage group.

c.Find the standard deviation of the improvement scores for the control group.

d.Based on the results, parts a鈥揷, which group appears to have the most variability in coughing improvement scores? The least variability?

Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.

a.The salaries of all persons employed by a large university

b.The grades on an easy test

c.The grades on a difficult test

d.The amounts of time students in your class studied last week

e.The ages of automobiles on a used-car lot

f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)

Question: Color and clarity of diamonds.Diamonds are categorized according to the 鈥渇our C鈥檚鈥�: carats, clarity, color, and cut. Each diamond stone that is sold on the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted from Singapore鈥檚 Business Times (Journal of Statistics Education, Vol. 9, No. 1, 2001). Color is classified as D, E, F, G, H, or I, while clarity is classified as IF, VVS1, VVS2, VS1, or VS2. In addition to color and clarity, the independent certification group (GIA, HRD, or IGI), the number of carats, and the asking price were recorded.

a.Use a graphical technique to summarize the color and clarity of the 308 diamond stones. What is the color and clarity that occurs most often? Least often?

b.Use a graphical method to describe the carat distribution of all 308 diamonds.

c.Use a graphical method to describe the carat distribution of diamonds certified by the GIA group.

d.Repeat part cfor the HRD and IGI certification groups.

e.Compare the three-carat distributions, parts cand d.Is there one particular certification group that appears to be assessing diamonds with higher carats than the others?

f.Find and interpret the mean of the data set.

g.Find and interpret the median of the data set.

h.Find and interpret the mode of the data set.

i.Which measures of central tendency best describe the 308-carat values? Explain.

j.Use the mean and standard deviation to form an interval that will contain at least 75% of the carat values in the data set.

k.Construct a scatter plot for the data, with a number of carats on the horizontal axis and price on the vertical axis. What type of trend do you detect?
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