Question

Comparing Standard Deviations
The standard deviation of batting averages of all teams in the American League is 0.008. The standard deviation of all players in the American League is 0.02154. Why is there less variability in team batting averages?


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Answer 1

Explanation:

There may be a couple of reasons for this:

1. Each team represents a sample of the players in the league. The averages of (random) samples can be expected to have a standard deviation that is smaller than the population standard deviation by a factor related to sample size.

2. A team average will result from the players who are played the most. Each team can be expected to field players more often whose averages are among the highest. The standard deviation of a set of the top tier of players will necessarily be smaller than the standard deviation of the set of all players.