The mean of 5 numbers is 20. If one number is excluded, mean of the remaining numbers becomes 23. Find the excluded number.

Given, mean of 5 numbers = 20.

By formula,

Mean = $\dfrac{\text{Total sum of observations}}{\text{No. of observations}}$

$\therefore 20 = \dfrac{\text{Total sum of observations}}{5} \\[1em] \text{Total sum of observations} = 20 \times 5 = 100.$

Let number excluded be x.

Given, Mean of the remaining numbers becomes 23.

$\therefore 23 = \dfrac{100 - x}{4} \\[1em] \Rightarrow 23 \times 4 = 100 - x \\[1em] \Rightarrow 92 = 100 - x \\[1em] \Rightarrow x = 100 - 92 \\[1em] \Rightarrow x = 8.$

Hence, excluded number = 8.