Question

The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that the last 13 observations is 40, the 13^th observations is

(a) 23
(b) 36
(c) 38
(d) 40

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 25 observations = 36 (Given)

∴ Sum of 25 observations = 36 × 25 = 900

Mean of first 13 observations = 32 (Given)

∴ Sum of first 13 observations = 32 × 13 = 416

Mean of last 13 observations = 40 (Given)

∴ Sum of last 13 observations = 40 × 13 = 520

Now,

13^th observation

= Sum of first 13 observations + Sum of last 13 observations − Sum of 25 observations

= 416 + 520 − 900

= 36

Thus, the 13^th observation is 36.

Hence, the correct answer is option (b).