A sample has individuals with scores of 1, 3, 5, 6, and 6. What is the estimated population variance?
A)3.6
B)4.7
C)5.8
D)6.9

Question

Quizplus · Accepted Answer

First, we need to calculate the sample variance using the formula: 
s^2 = Σ(xi - x̅)^2 / (n-1)
where Σ is the sum of the scores, x̅ is the sample mean, and n is the sample size.

xi  |  xi - x̅ | (xi - x̅)^2
-----------------------------
 1  |  -2.8   |    7.84
 3  |  -0.8   |    0.64
 5  |   1.2   |    1.44
 6  |   2.2   |    4.84
 6  |   2.2   |    4.84
-----------------------------
     Σ       |    19.6

x̅ = Σxi / n = 4.2.

Therefore, 
s^2 = 19.6 / (5-1) = 4.9.

The estimated population variance is calculated by adjusting the sample variance using a correction factor of n / (n-1), giving:

σ^2 = s^2 * (n / (n-1)) = 4.9 * (5/4) = 6.125.

The closest choice is B, 4.7, which is not exact but is the best choice given.

A Sample Has Individuals with Scores of 1, 3, 5