Mathematics - Statistics Question with Solution | TestHub

Let the items be ${\mathrm{a}}_1,{\mathrm{a}}_2,\dots \dots ..,{\mathrm{a}}_{\mathrm{n}}$ then $\bar{X}=\frac{a_1+a_2+\dots \dots .+a_n}{n}$ Now, according to the given condition: $\bar{X}=\frac{\left(a_1+1\right)+\left(a_2+2\right)+\dots \dots \dots +\left(a_n+n\right)}{n}$ $=\overline{\mathrm{X}}+\frac{1+2+3+\dots \dots \dots +n}{n}=\bar{X}+\frac{n(n+1)}{2n}$ (using sum of n natural nos.) $=\overline{\mathrm{X}}+\frac{\mathrm{n}+1}{2}$.