Question

The variance of 25 observations is 6. If each observation is multiplied by 3, then the new variance of the resulting observations is

• A. 56
• B. 50
• C. 54
• D. 36

Hint:

Adding or subtracting a constant does not change variance. Multiplying by \(k\) changes variance by a factor of \(k^2\).

Answer 1

The Correct Option is C

Concept: If every observation is multiplied by a constant \(k\), then \[ \text{New Variance} = k^2\times\text{Old Variance}. \] This is because variance depends on squared deviations from the mean.

Step 1: Identify the given values. \[ \text{Old Variance}=6, \qquad k=3. \]

Step 2: Apply the variance transformation formula. \[ \text{New Variance} = 3^2\times6. \] \[ = 9\times6. \] \[ = 54. \] Conclusion: \[ \boxed{54} \]