A set of four observations has mean 1 and variance 13 . Another set of six observations has mean 2 and variance 1 . Then, the variance of all these 10 observations is equal to:

Step-by-step solution

Given for the first set: n₁ = 4 , x ₁ = 1 , ₁^2 = 13 . ₁^2 = x_i^2 n₁ - ( x ₁)^2 13 = x_i^2 4 - 1^2 x_i^2 = 56 Also, x_i = n₁ x ₁ = 4 1 = 4 Given for the second set: n₂ = 6 , x ₂ = 2 , ₂^2 = 1 . ₂^2 = y_i^2 n₂ - ( x ₂)^2 1 = y_i^2 6 - 2^2 y_i^2 = 30 Also, y_i = n₂ x ₂ = 6 2 = 12 For the combined set of 10 observations: Total sum z_i = x_i + y_i = 4 + 12 = 16 Combined mean z = 16 10 = 1.6 Total sum of squares z_i^2 = x_i^2 + y_i^2 = 56 + 30 = 86 Combined variance ^2 = z_i^2 10 - ( z )^2 ^2 = 86 10 - (1.6)^2 = 8.6 -