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Chapter 12: Problem 70

You read an article that states, "Of the 411 players in the National Basketball Association, only 138 make more than the average salary of \(\$ 3.12\) million." Is \(\$ 3.12\) million the mean or the median salary? Explain your answer.

Short Answer

Expert verified
The \$3.12 million is the mean salary, not the median.

Step by step solution

01

Understanding Mean vs Median

Begin by identifying what distinguishes mean and median. The mean is the sum of all values divided by the number of values. It is affected by extreme values. The median is the middle value in a sorted list. It isn't affected by extremes.
02

Analyzing the problem

In this case, we know that 'only 138 players make more than the average salary'. From this, we can conclude that the average provided is larger than most individual player's salaries since only 138 out of 411 salaries exceed this average. This is a characteristic of the mean, which incorporates the influence of extreme values. The median, however, represents the middle most figure and wouldn't be as affected by the high values.
03

Conclusion

Ultimately, based on this observation, we can conclude that the \$3.12 million figure given is likely the mean salary, not the median. The mean value is representative of all salaries (including the high earners), whereas the median value would be less than or equal to the salaries of half of the players.

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Most popular questions from this chapter

The data sets give the ages of the first six U.S. presidents and the last six U.S. presidents (through Barack Obama). AGE OF FIRST SIX U.S. PRESIDENTS AT INAUGURATION $$ \begin{array}{|l|c|} \hline \text { President } & \text { Age } \\ \hline \text { Washington } & 57 \\ \hline \text { J. Adams } & 61 \\ \hline \text { Jefferson } & 57 \\ \hline \text { Madison } & 57 \\ \hline \text { Monroe } & 58 \\ \hline \text { J. Q. Adams } & 57 \\ \hline \end{array} $$ AGE OF LAST SIX U.S. PRESIDENTS AT INAUGURATION $$ \begin{array}{|l|c|} \hline \text { President } & \text { Age } \\ \hline \text { Carter } & 52 \\ \hline \text { Reagan } & 69 \\ \hline \text { G. H. W. Bush } & 64 \\ \hline \text { Clinton } & 46 \\ \hline \text { G. W. Bush } & 54 \\ \hline \text { Obama } & 47 \\ \hline \end{array} $$ a. Without calculating, which set has the greater standard deviation? Explain your answer. b. Verify your conjecture from part (b) by calculating the standard deviation for each data set. Round answers to two decimal places.

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