Chapter 1.3, Problem 85E

To determine

To find: team’s total annual payroll and explain whether the given question is answerable

Answer to Problem 85E

It is not possible todetermine the total annual payoff from the median.

Total annual payroll is $\$30,000,000$

Explanation of Solution

Given:

  $\begin{array}{l}\overline{x}=\$1.2\text{million}=\$1,200,000\\ n=25\end{array}$

Calculation:

The mean is the sum of all values divided by the sample size.

Thus the mean yearly salary is the total annual payoff divided by the number of players:

  $\overline{x}=\frac{\text{Total annual payoff}}{n}$

Multiply each side by n and interchange the left/right side:

  $\text{Total annual payoff}=\overline{x}\times n$

Fill in the known values and evaluate:

Total annual payroll is

  $\$1,200,000\times 25=\$30,000,000$

The median is the middle value of the sorted data set, thus the median does notcontain information about the payoff for each player and it is not possible todetermine the total annual payoff from the median.

Conclusion:

Therefore, it is not possible todetermine the total annual payoff from the median.

Total annual payroll is $\$30,000,000$