Question

3. Recently, ESPN reported that the average salary of an NFL place-kicker is $1.9 million, while the average salary for an NFL running back is only $1.7 million. This statistic was cited as evidence that, in the current NFL, running backs are considered less valuable than place-kickers. The claim being made based on this statistic is misleading. In what way?   (Hint: Teams have 1 place-kicker and, usually, 5 or 6 running backs, one of whom is their lead back.)

Answer 1

As per the information is given in the last line of the question that a team has one place-licker, 5-6 running-backs, with one lead.

So, for a placekicker, in one single team, the data will be only one representative data which is the average value. I shall proceed to the broader picture later in this answer. But first, start with the single team. In one team, there are 5-6 running-backs, of which one is the lead. Naturally, the lead will have greater salary than the other ones. If not, then also we can safely assume that all the 5-6 running-backs will NOT have the same salary. There will be variations. So, in this case, the average value will not give a clear picture of the salary structure of the players. So, variation measurement is necessary to compare the salaries when we are considering different players with different responsibilities.

Now, coming to the second part of the answer, here as I told earlier, I shall now consider more than one teams. Now, for each team, the salary structure may be different and they will follow a different salary distribution with different expected values and different deviations. So, inter-team variation should be a necessary measure in this case.

So keeping all in mind, there should be a proper structure of measurement of expectations and variations (both intra-team and inter-team variation) to get the clear picture of the salary structure. But just with the average values, when the study is being conducted over the different sample with different sample sizes, it will not make proper sense.

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