Question

The variance of 20 observations is 5. If each one of the observations is multiplied by 2, then the variance of the resulting observations is:

• A. \( 40 \)
• B. \( 80 \)
• C. \( 20 \)
• D. \( 10 \)

Hint:

When multiplying each observation by a constant, the variance is multiplied by the square of that constant.

Answer 1

The Correct Option is C

We are given the variance of 20 observations as 5, i.e., \( \sigma^2 = 5 \). If each observation is multiplied by a constant factor \( k = 2 \), the new variance becomes: \[ \sigma'^2 = k^2 \times \sigma^2 \] Substituting the values: \[ \sigma'^2 = 2^2 \times 5 = 4 \times 5 = 20 \] Thus, the variance of the resulting observations is \( 20 \).