For two data sets, each with size 5 , the variances are given to be 3 and 4 and the corresponding means are given to be 2 and 4 , respectively. The variance of the combined data set is

Step-by-step solution

σ x 2 = 3 σ y 2 = 4 x ¯ = 2 y ¯ = 4 Σ x i 5 = 2 ⇒ Σ x i = 10 ; Σ y i = 20 ; σ x 2 = 1 5 ∑ x i 2 − x ¯ 2 ⇒ 1 5 ∑ x i 2 − 4 = 3 ∑ x i 2 = 35 ∑ y i 2 = 100 σ z 2 = 1 10 ∑ x i 2 + ∑ y i 2 − x ¯ + y ¯ 2 2 = 1 10 35 + 100 - 9 = 135 - 90 10 = 45 10 = 9 2