Q 85. - The Practice of Statistics for AP

Question

Suppose that a Major League Baseball team’s mean yearly salary for its players is $1.2 million and that the team has 25 players on its active roster. What is the team’s total annual payroll?

If you knew only the median salary, would you be able to answer this question? Why or why not?

Step-by-Step Solution

Answer

The total annual payoff cannot be calculated using the median. The total annual salary is $\$ 30,000,000$

Step 1: Given Information

The Mean yearly salary of players $\overline{x}= \$1.2 million$

Number of players, $n=25$

Step 2: Concept

 The total of all observations divided by the number of observations is the observation means. The median of a distribution organized in ascending order is the midway.

Step 3: Calculation

The mean is calculated by dividing the total number of values by the sample size.

As a result, the mean annual salary is calculated by dividing the total annual compensation by the number of players: $\overline{x}=\frac{Total annual payoff}{n}$

Multiply each side by n, then swap the left and right sides:

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

Fill in the known values and evaluate:

The total annual payroll is $\$1, 200, 000 \times 25 = \$30, 000, 000$

Because the median is the middle value of the sorted data set, it does not contain information about each player's reward and so cannot be used to calculate the total annual payoff. As a result, calculating the whole annual payment from the median is impossible. The total annual payroll is $\$30, 000, 000$