Question

The mean of $6$ numbers is $22$. If one number is excluded the mean becomes $23$. what is the excluded number?

Answer 1

Finding the excluded number

Given mean of $6$ numbers is$22.$

$$\begin{gathered} \frac{x_1+x_2+x_3+x_4+x_5+x_6}{6}=22----\overline{)1} \\ byexcludingonevalue,meanbecomes23 \\ \frac{x_1+x_2+x_3+x_4+x_5}{5}=23 \\ {x}_1+x_2+x_3+x_4+x_5=23\times 5 \\ {x}_1+x_2+x_3+x_4+x_5=115---\overline{)2} \\ Use\overline{)2}in\overline{)1} \\ \frac{115+x_6}{6}=22 \\ 115+x_6=22\times 6 \\ {x}_6=132-115 \\ {x}_6=17. \end{gathered}$$

Hence, the excluded number is$17$.