A data consists of n observations: x 1 , x 2 , … , x n . If ∑ i = 1 n x i + 1 2 = 9 n and ∑ i = 1 n x i - 1 2 = 5 n , then the standard deviation of this data is

Step-by-step solution

Given: ∑ i = 1 n x i + 1 2 = 9 n ⇒ ∑ i = 1 n x i 2 + 2 x i + 1 = 9 n     . . . 1 And, ∑ i = 1 n x i - 1 2 = 5 n ⇒ ∑ i = 1 n x i 2 - 2 x i + 1 = 5 n     . . . 2 Form 1 + 2 , we get ∑ i = 1 n 2 x i 2 + 2 = 14 n ⇒ ∑ i = 1 n x i 2 = 6 n     . . . 3   From 1 - 2 , we get ⇒ ∑ i = 1 n x i = n     . . . 4 ∴ Variance, σ 2 = E x 2 - E x 2 ⇒ σ 2 = ∑ x 2 n - ∑ x n   ⇒ &#963