Statistics
Change of Scale and Origin
Premium Question
Grade 11
Question:
The mean and variance of 6 observations are 8 and 16 respectively. If each observation is multiplied by 3, the new mean and new variance are:
(1) mean 24, variance 48
(2) mean 24, variance 144
(3) mean 11, variance 144
(4) mean 24, variance 16
Step-by-Step Solution
Key Concept: The mean scales by the same factor as the observations, while the variance — having squared units — scales by the square of that factor.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)