Question

Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12.

Answer 1

6, 7, 10, 12, 13, 4, 8, 12

Mean $\bar{x}=\frac{\sum_{i=1}^{8}}{n}=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}=9$

The following table is obtained

$x_i$	$(x_i-\bar{x})$	$(x_i-\bar{x})^2$
6	3	9
7	2	4
10	1	1
12	3	9
13	4	16
4	5	25
8	1	1
12	3	9
	74

$Variance(σ^2)=\frac{1}{n}\sum_{i=1}^{8}(x_i-\bar{x})^2=\frac{1}{8}×74=9.25$