Question

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

 2, 4, 5, 6, 8, 17.

Answer 1

2,4,5,6,8,17

\[\text{ Mean } = \bar{ X } = \frac{2 + 4 + 5 + 6 + 8 + 17}{6} = \frac{42}{6} = 7\]

\[x_i\]	\[\left( x_i - X \right) = \left( x_i - 7 \right)\]	\[\left( x_i - 7 \right)^2\]
2	-5	25
4	-3	9
5	-2	4
6	-1	1
8	1	1
17	10	100
		\[\sum^6_{i = 1} \left( x_i - X \right)^2 = 140\]

 

n =6

\[\text{ Variance } (X) = \frac{\sum^6_{i = 1} \left( x_i - X \right)^2}{n}\]

\[ = \frac{140}{6}\]

\[ = 23 . 33\]

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

\[ = \sqrt{23 . 33}\]

\[ = 4 . 83\]