Question

If empirical relationship between mean,median and mode is expressed as mean$=k(3median-mode)$ then find the value of $k$.

Answer 1

We know that Relation between Mean, Median, Mode is

$Mean-Mode=3(Mean–Median)$

$⟹Mean–Mode=3Mean–3Median$

$⟹2Mean=3Median–Mode$

Or $Mean=\frac{1}{2}(3Median–Mode)$

Comparing with

$Mean=k(3Median–Mode)$

$k=\frac{1}{2}$