What is the empirical relation between mean, mode and median?

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Mode - Mean = 3 (Median - Mean)

Mode - Mean = 5 (Median - Mean)

Mode - Mean = 3 (Median + Mean)

Mode - Mean = 2 (Median - Mean)

answer is A.

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Detailed Solution

Given the relationship between mean, median and mode.
The empirical relation between mean median and mode is

Mode = 3 Median - 2 Mean

.
Subtracting and adding the value of mean in the above formula of relationship to find the empirical relationship, we get,
Mode - Mean = 3 Median - 2 Mean – Mean.

\Rightarrow

Mode - Mean = 3 Median - 3 Mean.
Taking 3 as the common from the right side of the equation

Mode - Mean = 3 (Median - Mean)

Thus, the relationship between mean, median and mode is

Mode - Mean = 3 (Median - Mean) .

Hence, option 1 is correct.

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