Question

Find the mean, variance and standard deviation for the data 15, 22, 27, 11, 9, 21, 14, 9.

 

Answer 1

 15,22,27,11,9,21,14,9 

$$\text{ Mean }=\frac{15+22+27+11+9+21+14+9}{8}=\frac{128}{8}=16$$

$$x_i$$	$$(x_i-X)=(x_i-16)$$	$${(x_i-\overline{X})}^2$$
15	−1	1
22	6	36
27	11	121
11	5	25
9	−7	49
21	5	25
14	−2	4
9	−7	49
		$$\sum _{i=1}^8{(x_i-\overline{X})}^2=310$$

 

$$\therefore n=8$$

$$\text{ Variance }\left(X\right)=\frac{\sum _{i=1}^8{(x_i-x)}^2}{n}$$

$$=\frac{310}{8}$$

$$=38.75$$

$$\text{ Standard deviation }=\sqrt{\text{ Variance }\left(X\right)}$$

$$=\sqrt{38.75}$$

$$=6.22$$