Question

The mean of 4 numbers is 5. Find the new mean , if each number is increased by 2.

Answer 1

$$\begin{gathered} \mathrm{Let}{\mathrm{x}}_1,{\mathrm{x}}_2,{\mathrm{x}}_3\mathrm{and}{\mathrm{x}}_4\mathrm{are}\mathrm{the}4\mathrm{numbers}. \\ \mathrm{Mean}\mathrm{of}4\mathrm{numbers}=\frac{{\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3+{\mathrm{x}}_4}{4} \\ \Rightarrow 5=\frac{{\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3+{\mathrm{x}}_4}{4} \\ \Rightarrow {\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3+{\mathrm{x}}_4=20....\left(1\right) \\ \mathrm{When}\mathrm{each}\mathrm{number}\mathrm{is}\mathrm{increased}\mathrm{by}2,\mathrm{then} \\ \mathrm{new}\mathrm{mean}\mathrm{of}4\mathrm{numbers}=\frac{\left({\mathrm{x}}_1+2\right)+\left({\mathrm{x}}_2+2\right)+\left({\mathrm{x}}_3+2\right)+\left({\mathrm{x}}_4+2\right)}{4} \\ =\frac{8+\left({\mathrm{x}}_1+{\mathrm{x}}_2+{\mathrm{x}}_3+{\mathrm{x}}_4\right)}{4} \\ =\frac{8+20}{4}\left[\mathrm{Using}\left(1\right)\right] \\ =\frac{28}{4} \\ =7 \end{gathered}$$