Question

find mean of 100 multiples of 1

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{first}100\mathrm{multiples}\mathrm{of}1\mathrm{are}: \\ 1,2,3,4,5,..............99,100 \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{sum}\mathrm{of}\mathrm{first}\mathrm{n}\mathrm{natural}\mathrm{numbers}\mathrm{is}\mathrm{given}\mathrm{by}: \\ {\mathrm{S}}_{\mathrm{n}}=\frac{\mathrm{n}\left(\mathrm{n}+1\right)}{2} \\ \mathrm{Now},{\mathrm{S}}_{100}=\frac{100\times 101}{2}=50\times 101=5050 \\ \mathrm{now},\mathrm{mean}\mathrm{of}\mathrm{first}100\mathrm{multiples}\mathrm{of}1=\frac{{\mathrm{S}}_{100}}{100}=\frac{5050}{100}=50.5 \end{gathered}$$