Question:
The mean of 25 observations 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 13th observation is
(a) 23
(b) 36
(c) 38
(d) 40
Solution:
(b) Given, mean of 25 observations = 36
∴ Sum of 25 observations = 36 x 25 = 900 Now, the mean of first 13 observations = 32
∴ Sum of first 13 observations = 13 x 32 = 416 and the mean of last 13 observations = 40
∴ Sum of last 13 observations = 40 x 13 = 520
So, 13th observation = (Sum of last 13 observations + Sum of first 13 observations) – (Sum of 25 observations)
=(520 + 416)-900 = 936 – 900 = 36
Hence, the 13th observation is 36.