$V_1$ = variance of {13, 16, 19, . . . , 103}. $V_2$ = variance of {3, 6, 9, . . . , 93}. Find $\frac{V_1}{V_2}$.
Step-by-Step Solution
Key Concept: Variance is invariant under translation but scales with the square of the scaling factor applied to data
$V_1$ is the variance of the arithmetic sequence {13, 16, 19, . . . , 103} with common difference 3. $V_2$ is the variance of {3, 6, 9, . . . , 93} with common difference 3. Since variance of an AP with common difference $d$ is proportional to $d^2$, and both sequences have the same common difference but $V_1$ is from {13, 16, . . .} starting at 13 and $V_2$ from {3, 6, . . .} starting at 3, the ratio $\frac{V_1}{V_2} = \frac{36 \text{ of } (20,32,...,200)}{9 \text{ of } (1,2,3,...,31)} = 4$.
Correct Answer: 4