Answer
a)
0, 4/16
24.5, 2/16
2, 2/16
50, 2/16
40.5, 2/16
4.5, 2/16
72, 2/16
b) $24.2$
c) Yes
Work Step by Step
a) We know that there are $4$ numbers, so there are $4^2=16$ ways to combine them. Combining the values with the same sample variances, we obtain the following:
Sample variance, probability:
0, 4/16
24.5, 2/16
2, 2/16
50, 2/16
40.5, 2/16
4.5, 2/16
72, 2/16
b) We knowthat sample variance=$σ^2=\frac{Σ(x−\overline{x})^2}{n}$. Using this as well as the population variance, we see that the sample and population variances are both $24.2$. (To verify, it is the easiest to use a program like Microsoft Excel.)
c) The population variance is unbiased, because it is equal to the sample variance.
