Question

the mean of 5 numbers is 20 .if one number is excluded,mean of the remaining numbers becomes 23 find the excluded number​.

Answer 1

→ The excluded number is 8

Explanation :-

${ \tt{ \red{Average = \frac{\text{Sum of observations}}{\text{No. of observations}}}}}</strong></p><p><strong>[tex]{ \tt{ \red{Average = \frac{\text{Sum of observations}}{\text{No. of observations}}}}}$

We are given that The mean of 5 numbers is 20.

${\tt{\purple{\begin{gathered}20 = \frac{\text{Sum of 5 numbers}}{5}\\20 \times 5 = \text{Sum of 5 numbers}\\100=\text{Sum of 5 numbers}\end{gathered}}}}$

Let the excluded number be x

Let the excluded number be xIf one number is excluded, mean of the remaining numbers becomes 23.

Let the excluded number be xIf one number is excluded, mean of the remaining numbers becomes 23.So, no. of observations = 5-1 = 4

Let the excluded number be xIf one number is excluded, mean of the remaining numbers becomes 23.So, no. of observations = 5-1 = 4Sum of 4 observations = 100-x

${ \tt{ \orange{So, \begin{gathered}23 = \frac{100-x}{4} \\23 \times 4 = 100-x \\92=100-x \\x=8\end{gathered}}}}$

Hence The excluded number is 8

Answer 2

→ The excluded number is 8

Explanation :-

${ \tt{ \red{Average = \frac{\text{Sum of observations}}{\text{No. of observations}}}}}</strong></p><p><strong>[tex]{ \tt{ \red{Average = \frac{\text{Sum of observations}}{\text{No. of observations}}}}}$

We are given that The mean of 5 numbers is 20.

${\tt{\purple{\begin{gathered}20 = \frac{\text{Sum of 5 numbers}}{5}\\20 \times 5 = \text{Sum of 5 numbers}\\100=\text{Sum of 5 numbers}\end{gathered}}}}$

Let the excluded number be x

Let the excluded number be xIf one number is excluded, mean of the remaining numbers becomes 23.

Let the excluded number be xIf one number is excluded, mean of the remaining numbers becomes 23.So, no. of observations = 5-1 = 4

Let the excluded number be xIf one number is excluded, mean of the remaining numbers becomes 23.So, no. of observations = 5-1 = 4Sum of 4 observations = 100-x

${ \tt{ \orange{So, \begin{gathered}23 = \frac{100-x}{4} \\23 \times 4 = 100-x \\92=100-x \\x=8\end{gathered}}}}$

Hence The excluded number is 8