If 2 data sets having 10 and 20 observations have coefficients of variation 50 and 60 respectively and arithmetic means 30 and 25 respectively, then the combined variance of those 30 observations is

Step-by-step solution

Given, n 1 = 10 ,   x ¯ 1 = 30 ,   C V 1 = 5 0 n 2 = 20 ,   x ¯ 1 = 25 ,   C V 2 = 6 0 C V 1 = σ 1 x ¯ 1 × 100 ⇒ 50 = σ 1 30 × 100 ⇒ σ 1 = 1 5 C V 2 = σ 2 x ¯ 2 × 100 ⇒ 60 = σ 1 25 × 100 ⇒ σ 2 = 1 5 Combined mean = 10 × 30 + 20 × 25 30 = 80 3 d 1 = x ¯ 1 - x ¯ = 10 3 ,   d 2 = x ¯ - x ¯ 2 = 5 3 Combined variance = n 1 σ 1 2 + n 2 σ 2 2 + n 1 d 1 2 + n 2 d 2 2