Question

The median and mode of a frequency distribution are 26 and 29 respectively. Then, the mean is
(a) 27.5
(b) 24.5
(c) 28.4
(d) 25.8

Answer 1

(b) 24.5
$$\begin{gathered} \mathrm{Mode}=\left(3\times \mathrm{median}\right)-\left(2\times \mathrm{mean}\right) \\ \Rightarrow \left(2\times \mathrm{Mean}\right)=\left(3\times \mathrm{median}\right)-\mathrm{mode} \\ \Rightarrow \left(2\times \mathrm{Mean}\right)=3\times 26-29 \\ \Rightarrow \left(2\times \mathrm{Mean}\right)=49 \\ \Rightarrow \mathrm{Mean}=\frac{49}{2} \\ \therefore \mathrm{Mean}=24.5 \end{gathered}$$