Multiple choice

If the median of a moderately skewed distribution is 20 and the mode is 16, the mean is approximately:

  1. 18

  2. 19

  3. 21

  4. 22
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D Correct answer
Explanation

For a moderately skewed distribution, the empirical relationship is Mode = 3*Median - 2*Mean. Substituting the values: 16 = 3(20) - 2*Mean. 16 = 60 - 2*Mean. 2*Mean = 44. Mean = 22.

AI explanation

We apply the empirical relationship for a moderately skewed distribution, which states that Mode equals 3 multiplied by Median, minus 2 multiplied by Mean. Substituting the given values gives 16 equals 3 multiplied by 20, minus 2 multiplied by Mean. Solving for the mean, we get 2 multiplied by Mean equals 44, which results in a mean of 22.

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