Question

The mean of 9 observations is 36. If the mean of the first 5 observations is 32 and that of the last 5 observations is 39, then the fifth observation is ....

(A) 28 

(B) 31 

(C) 43 

(D) 37

Answer 1

The correct option is: (B) 31 

Explanation:

36 x 9 = x₁ + x₂ + x₃ +...+x₉      ...(i) 

5 x 32 = x₁ + x₂ + x₃ + x₄ + x₅    ...(ii)

5 x 39 = x₅ + x₆ + x₇ + x₈ + x₉     ...(iii)

Adding (ii) and (iii), we get 

355 = x₁ + x₂ + x₃ + x₄ + x₅ + ... + x₉ + x₅

Using (i), we get 355 - 36 x 9 = x₅ => x₅ = 31