One sample has a variance of s² = 10 and a second sample has a variance of s² = 6.Which of the following most accurately describes the pooled variance for the two samples? A)Closer to 6 than to 10 B)Closer to 10 than to 6 C)Somewhere between 6 and 10 D)Around 16

Question

Quizplus · Accepted Answer

The pooled variance is calculated as the weighted average of the variances of the individual samples, where the weights are proportional to the degrees of freedom of each sample. Since both samples have equal size and are assumed to have equal variance, the degrees of freedom for each sample are n-1. The pooled variance is therefore: 
(s1^2)*(n1-1) + (s2^2)*(n2-1) / (n1+n2-2) 
= (10*9 + 6*9) / 16 
= 54 / 16 
≈ 3.375 
This value is between 6 and 10, so the answer is C.

One Sample Has a Variance of S2 = 10 and a Second

One Sample Has a Variance of S² = 10 and a Second