Question

The mean and mode of a frequency distribution are 28 and 16 respectively. The median is
(a) 22
(b) 23.5
(c) 24
(d) 24.5

Answer 1

(c) 24
$$\begin{gathered} \mathrm{Mode}=\left(3\times \mathrm{median}\right)-\left(2\times \mathrm{mean}\right) \\ \Rightarrow \left(3\times \mathrm{Median}\right)=\left(\mathrm{mode}+2\mathrm{mean}\right) \\ \Rightarrow \left(3\times \mathrm{Median}\right)=16+56 \\ \Rightarrow \left(3\times \mathrm{Median}\right)=72 \\ \Rightarrow \mathrm{Median}=\frac{72}{3} \\ \therefore \mathrm{Median}=24 \end{gathered}$$