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suppose a major league baseball team’s mean yearly salary for a player is $1.2 million, and that the has 25 players on its active roster. what is the team’s annual payroll for players? if u knew only the median salary, would u be able to answer the question? why or why not?
Since it is an average within the 25 players (the sample size average, not the population size), then you would say that the annual payroll for the players is 1.2*25 = $30 million.
You can give an approximation if you knew only the median, but it would not be 100% certain. The median, by chance, could be the average value as well, but by definition the median is only a measure of the midpoint of the data…
So lets say that out of 25 players, 12 players made exactly $1.1 million, 12 players made exactly $1.3 million, and the last player made $1.2 million. The average would be $1.2 million and since the midpoint of the data if you arranged each value from smallest to largest, would also be $1.2 million.
However, if the data is dispersed more erratically, the median and the mean would differ, and therefore you could not accurately answer the question with the data given. For example, if 12 players made $900,000, 11 made $1.1 million, 1 made $1 million and the last player made $2 million, then the median would be $1 million, but the average would be $1.036 million. So the annual salary would be $1.036*25 = $2.59 million based off the mean (which is consistent with adding each of the salaries) but the annual salary based on the median would be $1*25 = $1 million.
In short, the median does not take into consideration the sample size of the data, whereas the mean does. So the median is not a good statistic for determining cumulative values of the sample size.
MLB TTC- 2010 MLB Team Salaries- ESPN List