Question

The mean of five number is 30. If one number is excluded, their mean becomes 28. The excluded number is

(a) 28
(b) 30
(c) 35
(d) 38

Answer 1

We know

Mean = $\frac{\mathrm{Sum}\mathrm{of}\mathrm{observations}}{\mathrm{Number}\mathrm{of}\mathrm{observations}}$

⇒ Sum of observations = Mean × Number of observations

Mean of five numbers = 30 (Given)

∴ Sum of five numbers = 30 × 5 = 150 .....(1)

If one number is excluded, their mean is 28.

∴ Mean of four numbers = 28

⇒ Sum of four numbers = 28 × 4 = 112 .....(2)

Now,

Excluded number

= Sum of five numbers − Sum of four numbers

= 150 − 112 [From (1) and (2)]

= 38

Thus, the excluded number is 38.

Hence, the correct answer is option (d).