The correct option is C 16
Let 15 observations be x1,x2,x3,…,x15
Mean=Sum of values of all observationsNumber of observations
⇒Sum of values of all observations = Mean x Number of observations
Sum of values of all observations = 15 × 8 = 120.
i.e., x1+x2+x3+…+ x15=120----(1)
Mean of first 8 observations = 7
Hence, the sum of first 8 observation = 7 × 8 = 56
x1+x2+x3+…+ x8=56----(2)
Mean of last 8 observations = 10
Hence, the sum of the last 8 observation = 10 ×8 = 80
x8+x9+x10+…+ x15=80-----(3)
Adding 2 and 3 we get,
(x1+x2+x3+,…,+ x8)+(x8+x9+x10+,…,+ x15)=56+80
⇒x1+x2+x3+…+ x15+x8=136
substituting 1 in the above equation, we get,
120+x8=136
⇒x8=136−120 =16
Hence, the value of x8 is 16