Question

The mean of 25 observations is 36. Out of these observations, the mean of first 13 observations is 32 and those of the last 13 observations is 40. Find the 13th observation

Answer 1

mean of 25 observations = 36
⇒sum of observations = 36 × 25 = 900
⇒sum of observations = 36 × 25 = 900
⇒sum of first 13 observations = 32 × 13 = 416
⇒mean of last 13 observations = 40
⇒sum of last 13 observations = 40 × 13 = 520
∴13th observation =(sum of 1st three observation+sum of last 13 observations)-sum of all observation
==== (416 + 520) – 900
==== 936 – 900
==== 36 is the required answer

Answer 2

mean = ( x1 + x2 + . ........x25)/25

36 = {( x1 + x2 + .....x13) + (x13+x14......x25)-x13}/25


given ,

x1 + x2 +....x13 = 13 × 32 = 416
x13 + x14 .....x14 = 13×40 = 520

so,

25× 36 = 416 + 520 - x13

900 = 936 - x13

x13 = 36