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Best Suited Measure of Central Tendency in Different Cases and the Empirical Relationship between Them

If mode of a ...

Question

If mode of a data exceeds its mean by $12$ , the mode exceeds the median by

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Solution

The correct option is C $8$
We have,
$M o d e - M e a n = 12$
$∴ M o d e = 3 M e d i a n - 2 M e a n$
$\Rightarrow M o d e - M e a n = 3 (M e d i a n - M e a n)$
$\Rightarrow 12 = 3 (M e d i a n - M e a n)$
$\Rightarrow M e d i a n - M e a n = 4$
Again, $M o d e = 3 M e d i a n - 2 M e a n$
$\Rightarrow M o d e - M e d i a n = 2 (M e d i a n - M e a n) = 2 \times 4 = 8$

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