## Elementary Statistics (12th Edition)

a) $2.16$ b) Sample;$σ$ (4,4); 0 (5,5); 0 (9,9); 0 (4,5); 0.71 (4,9); 3.536 (5,4); 0.71 (5,9); 2.828 (9,4); 3.5356 (9,5); 2.828 c) $1.572$ d) No
a) We know that for the standard deviation: $σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}=2.16$ b) There are $9$ possibilities, because there are $3$ numbers that can go into $9$ different pairs of two ($3^2=9$). $σ=\sqrt{\frac{Σ(x−\overline{x})^2}{n}}.$ Each sample has a probability of $1/9$. Hence we find: Sample;$σ$ (4,4); 0 (5,5); 0 (9,9); 0 (4,5); 0.71 (4,9); 3.536 (5,4); 0.71 (5,9); 2.828 (9,4); 3.5356 (9,5); 2.828 c) Since the probabilities are equal, we can use the normal equation for mean. Hence the mean is $1.572$. d) Since the results of part a) and part c) are not equal, we can see that the sampling median is not an unbiased predictor.