Question

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

A. 13/2
B. 5/2
C. 11/2
D. 6

Answer 1

To find the variance of the combined data set, you can use the formula V(combined) = [(n₁ - 1)V₁ + (n₂ - 1)V₂] / (n₁ + n₂ - 2). Plugging in the given values, the variance of the combined data set is 13/2.

Step-by-step explanation:

To find the variance of the combined data set, we can use the formula:

V(combined) = [(n₁ - 1)V₁ + (n₂ - 1)V₂] / (n₁ + n₂ - 2)

Plugging in the given values: V(combined) = [(5 - 1)(4) + (5 - 1)(5)] / (5 + 5 - 2) = 26 / 8 = 13/2

To find the variance of the combined data set, you can use the formula V(combined) = [(n₁ - 1)V₁ + (n₂ - 1)V₂] / (n₁ + n₂ - 2). Plugging in the given values, the variance of the combined data set is 13/2.