The variance of given observation is 5. If each observation is multipl

1.	The variance of given observation is 5. If each observation is multiplied by 2 then find new variance.1. 202. 53. 104. None of these
Answer» Correct Answer - Option 1 : 20 Concept: Variance: Let x_i for i = 1, 2, 3, …, n be observations then variance is given as: \(\rm \sigma^2 = \frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n}\) Properties of variance: Var(X + C) = Var(X), where C is a constant. Var(CX) = C² × Var(X), where C is a constant. Calculation: Given: Var(X) = 5 Each observation is multiplied by 2. So, new variance = Var(2X) = 2² × 5 = 20

The variance of given observation is 5. If each observation is multiplied by 2 then find new variance.1. 202. 53. 104. None of these

Answer» Correct Answer - Option 1 : 20

Concept:

Variance: Let x_i for i = 1, 2, 3, …, n be observations then variance is given as:

\(\rm \sigma^2 = \frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n}\)

Properties of variance:

Calculation:

Given: Var(X) = 5

Each observation is multiplied by 2.

So, new variance = Var(2X)

= 2² × 5

= 20