If the difference between median and mean of a moderately symmetric distribution is $12$ , then find the difference between mode and mean.

36

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24

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12

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16

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Solution

The correct option is B $36$
We know that $m o d e = 3 m e d i a n - 2 m e a n$

$⟹ m o d e = 3 m e d i a n - 3 m e a n + m e a n$

$⟹ m o d e - m e a n = 3 (m e d i a n - m e a n)$

Given that difference between median and mean is $12$

Therefore, $m o d e - m e a n - = 3 (12) = 36$

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