Multiple choice

Kate selected a series of random numbers. The difference of median and mean of the series is 36. What would be the difference of mode and mean?

  1. 86

  2. 108

  3. 142

  4. 184

  5. 190
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B Correct answer
Explanation

Empirical relationship: Mode = 3*Median - 2*Mean. Mode - Mean = 3*Median - 3*Mean = 3*(Median - Mean). Given Median - Mean = 36, so Mode - Mean = 3 * 36 = 108.

AI explanation

Using the empirical relationship between mean, median and mode, the formula is Mode equals 3 times Median minus 2 times Mean. This can be rearranged to Mean minus Mode equals 2 times Mean minus 3 times Median, which further factors as 2 times Mean minus Median. Since the difference between Median and Mean is given as 36, the difference between Mean and Mode is 2 times 36, giving 108.

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