The variance of the numbers 2 , 3 , 11 and x is 49 4 , then the values of x are

Step-by-step solution

From the given data, we make the following table x x 2 2 4 3 9 11 121 x x 2 ∑ x = 16 + x ∑ x 2 = 134 + x 2 But we know that, variance = ∑ x 2 n - ∑ x n 2 ⇒ 134 + x 2 4 - 16 + x 4 2 = 49 4 (given) ⇒ 134 + x 2 4 - 256 + x 2 + 32 x 16 = 49 4 ⇒ 3 x 2 - 32 x + 280 16 = 49 4 ⇒ 3 x 2 - 32 x + 280 = 196 ⇒ 3 x 2 - 32 x + 84 = 0 ⇒ x - 6 3 x - 14 = 0 ⇒ x = 6 , x = 14 3 Therefore, the values of x are 6 or 14 3