Question

Find the variance and standard deviation of 3, 4, 6, 5, 5, 3, 8, 1, 7, 5

Answer 1

xi	3	4	6	5	5	3	8	1	7	5	47
xi2	9	16	36	25	25	9	64	1	49	28	259

 \(\bar x = \frac{\displaystyle\sum_{i=1}^n x_i}{n}\) = \(\frac{47}{10}\) = 4.7

Variance \(\big(\sigma^2\big)\) = \( \frac{\displaystyle\sum_{i=1}^n x_i^2}{n}\) = \((\bar x)^2\)

\(\frac{259}{10} - (4.7)^2\) = 25.9 - 22.09 = 3.8

Standard Deviation (\(\sigma\)) = \(\sqrt{Variance} = \sqrt{3.8} = 1.95\)