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 

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

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

 

\[\therefore n = 8\]

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

\[ = \frac{310}{8}\]

\[ = 38 . 75\]

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

\[ = \sqrt{38 . 75} \]

\[ = 6 . 22\]