## Elementary Statistics (12th Edition)

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
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.