Question

Find the mean, variance and standard deviation for the data:

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

Answer 1

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

\[\text{ Mean } = \frac{6 + 7 + 10 + 12 + 13 + 4 + 8 + 12}{8}\]

\[ = \frac{72}{8}\]

\[ = 9\]

\[x_i\]	\[\left( x_i - X \right) = \left( x_i - 9 \right)\]	\[\left( x_i - X \right)^2\]
6	-3	9
7	-2	4
10	1	1
12	3	9
13	4	16
4	- 5	25
8	-1	1
12	3	9
		\[\sum^8_{i = 1} \left( x_i - X \right)^2 = 74\]

n = 8

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

\[ = \frac{74}{8} \]

\[ = 9 . 25\]

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

\[ = \sqrt{9 . 25} \]

\[ = 3 . 04\]