If the mean and variance of the data 65 , 68 , 58 , 44 , 48 , 45 , 60 , α , β , 60 where α > β are 56 and 66 . 2 respectively, then α 2 + β 2 is equal to

Step-by-step solution

Given: x ¯ = 56 and σ 2 = 66 . 2 We know that, σ 2 = ∑ x i 2 n - x 2 ⇒ 65 2 + 68 2 + 58 2 + 44 2 + 48 2 + 45 2 + 60 2 + α 2 + β 2 + 60 2 10 - 56 2 = 66 . 2 ⇒ α 2 + β 2 + 25678 10 - ( 56 ) 2 = 66 . 2 ⇒ α 2 + β 2 + 25678 10 = 3136 + 66 . 2 ⇒ α 2 + β 2 = 32022 - 25678 ⇒ α 2 + β 2 = 6344