# The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 40, find the 13th observation.

(a) 36

(b) 35

(c) 40

(d) none of these

Solution:

The mean of 25 observations = 36

Sum of 25 observations = 25×36 = 900

Mean of the first 13 observations = 32

Sum of first 13 observations = 32×13 = 416

Mean of the last 13 observations = 40

Sum of last 13 observations = 40×13 = 520

Sum of first 13 observations + sum of last 13 observations – 13th observation = sum of 25 observations

=> 416 + 520 – 13th observation = 900

13th observation = 936 – 900

= 36

Hence option a is the answer.