Question

salaries of professional athletes receive much attention in the media. the multimillion - dollar long - term contract is now commonplace among this elite. nevertheless, rarely does a season pass without negotiations between one or more of the players associations and team owners for additional salary and fringe benefits for all players in their particular sports. complete parts a and b below.
a. the players association would want to use the median to support its argument for higher \average\ salaries, which measure of central tendency do you think it should use? why?
the players association would want to use the median to support its argument for higher \average\ salaries because the median is the value at which half of the data values are higher than it. this is the preferred measure of center because it most accurately depicts the players salaries and would be most likely to result in a higher pay increase.
b. the players association would want to use the mean to support its argument for higher \average\ salaries because the mean is the average value of all the players salaries. the mean is affected by extreme values, so using the mean would most likely result in a lower pay increase.
to refute the argument, which measure of central tendency should the owners apply to the players salaries? why?
a. to refute the argument, the owners should use the mean because the mean is the average value of all the players salaries. the mean is affected by extreme values, so using the mean would most likely result in a lower pay increase.
b. the players association would want to use the mode to support its argument for higher \average\ salaries because the mode is the value that occurs most often. this is the preferred measure of center because it most accurately depicts the players salaries and would be most likely to result in a higher pay increase.
c. the players association would want to use the mode to support its argument for higher \average\ salaries because the mode is the value that occurs most often. this is the preferred measure of center because it most accurately depicts the players salaries and would be most likely to result in a higher pay increase.

Explanation:

The median is often a better measure of central - tendency when there are extreme values in a data set. In the case of player salaries, there are likely some very high - earning elite players (extreme values). The mean is affected by these extreme values and can be pulled upwards, making it seem like the "average" player earns more than is typical. The median represents the middle value when the data is ordered, so it is less affected by outliers and gives a more representative value of what a typical player earns. The players' association would want a higher - seeming "average" to support their argument for higher pay, so they might prefer the mean as it could be inflated by the high salaries of a few players. The owners, on the other hand, would want to use a measure that shows lower "average" pay, so they might prefer the median as it is less influenced by the high - earning outliers.

Answer:

The players' association might want to use the mean because the mean is the average value of all the players' salaries and is likely to be higher due to the presence of high - earning elite players, which would support their argument for higher pay. The owners might want to use the median because the median is the value at which half of the data values are higher and half are lower, and it is less affected by extreme values (the high salaries of elite players), so it is likely to result in a lower "average" pay figure to refute the players' argument for higher pay.