Question

the mean of 25 observations is 36, out f these observation, the mean of the first 13 observations is 32 and that of the last 13 observations is 40. find the 13 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 + x3 .., x25)/25
36×25 = ( x1 + x2 ....x13) +(x13 +x14 ...,.x25) -x13

900 =13× 32 + 13 × 40 -x13

900= 416 + 520 - x13

900 = 936 - x13

x13 = 36