Question

sum of deviation of a set of n values from 24 is 40 and from 26 is -40. then the mean is ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{mean}\mathrm{of}n\mathrm{values}=a \\ \mathrm{Then}\mathrm{the}\mathrm{sum}\mathrm{of}n\mathrm{values}=na \\ \mathrm{Sum}\mathrm{of}\mathrm{deviation}\mathrm{of}\mathrm{a}\mathrm{set}\mathrm{of}n\mathrm{values}\mathrm{from}24=40 \\ \Rightarrow n\left(a-24\right)=40 \\ \Rightarrow na-24n=40.....\left(1\right) \\ \mathrm{Sum}\mathrm{of}\mathrm{deviation}\mathrm{of}\mathrm{a}\mathrm{set}\mathrm{of}n\mathrm{values}\mathrm{from}26=-40 \\ \Rightarrow n\left(a-26\right)=-40 \\ \Rightarrow na-26n=-40.....\left(2\right) \\ \mathrm{From}\left(1\right)-\left(2\right),\mathrm{we}\mathrm{get} \\ na-24n=40 \\ na-26n=-40 \\ \underline{-++} \\ 2n=80 \\ \Rightarrow n=40 \\ \mathrm{Putting}n=40\mathrm{in}n\left(a-24\right)=40,\mathrm{we}\mathrm{get} \\ 40\left(a-24\right)=40 \\ \Rightarrow a-24=1 \\ \Rightarrow a=25 \\ \mathrm{Hence},\mathrm{required}\mathrm{mean}=25 \end{gathered}$$