Question

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

Answer 1

Given date is, $6,7,10,12,13,4,8,12$
Mean $\overline{x}=\frac{{\sum }_{i=1}^8{x}_i}{n}=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}=9$
Now,

$x_i$	$(x_i-\overline{x})$	${(x_i-\overline{x})}^2$
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

$\therefore$ Variance $\left({\sigma }^2\right)=\frac{1}{n}\sum _{i=l}^8(x_i-\overline{x}{)}^2=\frac{1}{8}\times 74=9.25$