A set X consists of 10 elements with a variance of 15 . Another set Y consists of 20 elements with a variance of 24 . If the combined variance of all 30 elements from both sets is 39 , then the absolute difference between the means of set X and set Y is

Step-by-step solution

Let the mean of set X be ₁ and the mean of set Y be ₂ . Let the absolute difference between the means be = | ₁ - ₂| . The combined mean _c of the 30 elements is: _c = 10 ₁ + 20 ₂ 30 = ₁ + 2 ₂ 3 The deviations of the individual means from the combined mean are: d₁ = ₁ - _c = ₁ - ₁ + 2 ₂ 3 = 2( ₁ - ₂) 3 d₂ = ₂ - _c = ₂ - ₁ + 2 ₂ 3 = ₂ - ₁ 3 Squaring these deviations gives: d₁^2 = 4 9 ( ₁ - ₂)^2 = 4 9 ^2 d₂^2 = 1 9 ( ₂ - ₁)^2 = 1 9 ^2 The formula for combined variance is: _c^2 = n₁( ₁^2 + d₁^2) + n₂( ₂^2 + d₂^2) n₁ +