Question

Scores of ten students in a spelling test.

11, 8, 12, 7, 5, 3, 4, 15, 9, 6. Find the variance and standard deviation of ungrouped data.

Answers:

1. Variance =

2. Standard Deviation =

Answer 1

1.

Variance:

$\sigma^2=\frac{\sum (x_i-\overline{x})^2}{n}=13.00$

where

mean:

$\overline{x}=\frac{\sum x_i}{n}=8$

$n=10$

2.

standard deviation:

$\sigma=\sqrt{13}=3.60$