Question

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.

Answer 1

Let $x_1,x_2,x_3,x_4\&x_5$ be five numbers whose mean is 18. Then,
18 = Sum of five numbers $÷$ 5
∴ Sum of five numbers = 18 $\times$ 5 = 90.

Now, if one number is excluded, then their mean is 16.
So,
​16= Sum of four numbers ​$÷$ 4
∴ Sum of four numbers = 16 $\times$ 4 = 64.

The excluded number = Sum of the five observations - Sum of the four observations

∴ The excluded number = 90 - 64
∴ The excluded number = 26.