Question

11 8 15 12 11 12 11 14 15 5 6 11

16 14 13 14 13 9 11 19 12 10 13 5

13 7 3 14 13 16 20 15 5 15 15 5

15 7 9 11 17 18 10 14 9 7 4 15

13 12 16 8 12 12

(a)  Find:

i.            Variance

ii. Standard deviation

Answer 1

i. Variance

$var=\frac{\sum(xi-\bar{x})^2}{n-1}$

The table below gives $\sum(xi-\bar{x})^2$

From the table, $var=\frac{830}{53}=15.66$

ii standard deviation

$std=\sqrt{var}$

$=\sqrt{15.66}$

$=3.957$