Answer to Question #173272 in Statistics and Probability for Denisse Bisuña

Question

The following are data obtained from rolling a die several times. Compute the mean and variance of the frequency distribution.

Outcome Number of Occurrences

1 4

2 8

3 6

4 12

5 3

6 7

Answer 1

$\bar{X} = \frac{\sum x_if(x_i)}{\sum f(x_i)} = \frac{(1\times 4) + (2 \times 8) + (3 \times 6) + (4 \times 12) + (5 \times 3) + (6 \times 7)}{40} \\ = \frac{4+16+18+48+15+42}{40} \\ = 3.575 \\ S^2 = \frac{\sum (X- \bar{X})^2f}{n}\\ = \frac{((1-3.575)^2 \times 4) + ((2-3.575)^2 \times 8) + ((3-3.575)^2 \times 6) + ((4-3.575)^2 \times 12) + ((5-3.575)^2 \times 3) + ((6-3.575)^2 \times 7)}{40} \\ = \frac{26.522+4.961+1.983+4.961+19.891+89.464}{40} \\ = \frac{147.782}{40} \\ = 3.69$