Question

Question 20
The mean of 25 observation is 36. Out of these observations, if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the ${13}^{th}$ observation is:

A) 23
B) 36
C) 38
D) ​​​​​​​40

Answer 1

The answer is B.
Given, mean of 25 observations = 36
$\therefore$ Sum of 25 observations $=36\times 25=900$
Now, the mean of first 13 observations = 32
$\therefore$ Sum of first 13 observations $=13\times 32=416$
And the mean of last 13 observations = 40
$\therefore$ Sum of last 13 observations $=40\times 13=520$
So, ${13}^{th}$ observation = (Sum of last 13 observations + Sum of first 13 observations) - (Sum of 25 observations)
=(520 + 416) - 900 = 936 - 900 = 36
Hence, the ${13}^{th}$ observations is 36.