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Chapter 2: Q37E (page 94)
Explain how the relationship between the mean and median provides information about the symmetry or skewness of the data鈥檚 distribution.
If the mean is to the right, the distribution is skewed to the right.
If the mean is to the left, the distribution is skewed to the left.
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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?
Nuclear power plants.According to the Nuclear Energy Institute (NEI), 62 nuclear power plants were operating in the United States in 2015. The table at top of the next column lists the 30 states that operate nuclear power
plants, the number of plants in each state, and whether the state has passed legislation supporting nuclear energy expansion (regulated) or not (deregulated).
a.Find the mean, median, and mode of the number of power plants per state. Interpret these values.
b.Repeat part afor the regulated states only.
c.Repeat part afor the deregulated states only.
d.Compare the results, parts band c.What inference can you make about the impact that state regulation has on the number of nuclear power plants?
e.Eliminate the state with the largest number of power plants from the data set and repeat part a.What effect does dropping this measurement have on the measures of central tendency found in part a?
f.Arrange the 30 values in the table from lowest to highest. Next, eliminate the lowest two values and the highest two values from the data set and find the mean of the remaining data values. The result is called a 10% trimmed meanbecause it is calculated after removing the highest 10% and the lowest 10% of the data values. What advantages does a trimmed mean have over the regular arithmetic mean?
State | Status | Number of Power Plants |
Alabama | Regulated | 2 |
Arizona | Regulated | 1 |
Arkansas | Regulated | 1 |
California | Regulated | 1 |
Connecticut | Deregulated | 1 |
Florida | Regulated | 3 |
Georgia | Regulated | 2 |
Illinois | Deregulated | 6 |
Iowa | Deregulated | 1 |
Kansas | Regulated | 1 |
Louisiana | Regulated | 2 |
Maryland | Deregulated | 1 |
Massachusetts | Deregulated | 1 |
Michigan | Deregulated | 3 |
Minnesota | Regulated | 2 |
Mississippi | Regulated | 1 |
Missouri | Regulated | 1 |
Nebraska | Regulated | 2 |
New Hampshire | Deregulated | 1 |
New Jersey | Deregulated | 3 |
New York | Deregulated | 4 |
North Carolina | Regulated | 3 |
Ohio | Deregulated | 2 |
Pennsylvania | Deregulated | 5 |
South Carolina | Regulated | 4 |
Tennessee | Regulated | 2 |
Texas | Deregulated | 2 |
Virginia | Regulated | 2 |
Washington | Regulated | 1 |
Wisconsin | Deregulated | 1 |
Budget lapsing at army hospitals.Accountants use the term budget lapsingto describe the situation that occurs when unspent funds do not carry over from one budgeting period to the next. Due to budget lapsing, U.S. army hospitals tend to stockpile pharmaceuticals and other supplies toward the end of the fiscal year, leading to a spike in expenditures. This phenomenon was investigated in the Journal of Management Accounting Research(Vol. 19, 2007). Data on expenses per full-timeequivalent employees for a sample of 1,751 army hospitalsyielded the following summary statistics: xbar= \(6,563,m= \)6,232, s= \(2,484, QL = \)5,309 and QU = \(7,216.
a.Interpret, practically, the measures of relative standing.
b.Compute the interquartile range, IQR, for the data.
c.What proportion of the 1,751 army hospitals have expenses between \)5,309 and $7,216?
If the range of a set of data is 20, find a rough approximation to the standard deviation of the data set.
Give the percentage of measurements in a data set that are above and below each of the following percentiles:
a. 75th percentile
b. 50th percentile
c. 20th percentile
d. 84th percentile
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