Question

For a certain distribution, mode and median were found to be 1000 and 1250 respectively. Find mean for this distribution using an empirical relation. [CBSE 2014]

Answer 1

There is an empirical relationship between the three measures of central tendency:

3Median = Mode + 2Mean

$$\begin{gathered} \Rightarrow \mathrm{Mean}=\frac{3\mathrm{Median}-\mathrm{Mode}}{2} \\ =\frac{3\left(1250\right)-1000}{2} \\ =1375 \end{gathered}$$

Thus, the mean is 1375.