Question

If in a moderately skewed distribution the values of mode and mean are $6\lambda$ and $9\lambda$ respectively, then the value of median is

Answer 1

Find the median

Given: mode$=6\lambda$ , mean$=9\lambda$

Empirical relation: $\mathrm{mode}=3\left(\mathrm{median}\right)-2\left(\mathrm{mean}\right)$

$$\begin{gathered} \Rightarrow 6\mathrm{\lambda }=3\left(\mathrm{median}\right)-2\left(9\mathrm{\lambda }\right) \\ \Rightarrow 6\mathrm{\lambda }+18\mathrm{\lambda }=3\left(\mathrm{median}\right) \\ \Rightarrow \frac{24\mathrm{\lambda }}{3}=\mathrm{median} \\ \Rightarrow \mathrm{median}=8\mathrm{\lambda } \end{gathered}$$

Hence, median$=8\lambda$.