Question

Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 12. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 12. Listed below are the nine different samples.
2,2 2,4 2,12 4,2 4,4 4,12, 12,2 12,4 12,12
Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values

Answer 1

Ok So you need to find the variances of all the pairs of points right? The variance is
\[ s^2=\frac{1}{n-1}\sum_{i=1}^n(x_i-\bar{x})^2\]

Answer 2

So for example, for 2,4:

\[\bar{x}=\frac{2+4}{2}=3 \]
\[ s^2=\frac{1}{2-1}\left( (2-3)^2+(4-3)^2\right)\]