Question

Calculate standard deviation of the following marks obtained by 5 students in a tutorial group
Marks: 8, 12, 13, 15, 22

Answer 1

Solution:

To calculate Standard deviation ,we fist calculate Variance

$SD = \sqrt{Variance}$
$Variance = \frac{\Sigma {(x_{i} - \bar x)}^{2} }{n} \\ \\ here \: \bar x \: is \: mean \:$
$\bar x = \frac{8 + 12 + 13 + 15 + 22}{5} \\ \\ = \frac{70}{5} \\ \\ \bar x = 14$

For variance , calculate ${(x_{i} - \bar x)}$,for each value of xi

$8 - 14 = - 6 \\ \\ 12 - 14 = - 2 \\ \\ 13 - 14 = - 1 \\ \\ 15 - 14 = 1 \\ \\ 22 - 14 = 8$
$variance = \frac{\Sigma {(x_{i} - \bar x)}^{2} }{n} \\ \\ = \frac{36 +4 + 1 + 1 + 64 }{5} \\ \\ = \frac{106}{5} \\ \\ variance= 21.2 \\ \\ SD = \sqrt{21.2} \\ \\ SD= 4.60$

Hope it helps you