Question

The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.
6,6, 5, 8, 10
Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.

Answer 1

Answer:

2

Step-by-step explanation:

Given: 5 quiz scores of a student in a statistics course are 6,6, 5, 8, 10

To find:  standard deviation of the population

Solution:

Mean (M) = $\frac{\sum_{i=1}^{n}x_i}{n}$

here, $x_i$ denotes number of observations and n denotes number of observations.

Variance = $\frac{\sum_{i=1}^{n}(x_i-M)^2}{n-1}$

Standard deviation = $\sqrt{variance}$

$M=\frac{6+6+5+8+10}{5}=\frac{35}{5}=7$

Variance = $\frac{\sum_{i=1}^{n}(x_i-7)^2}{n-1}$

$=\frac{\left [ (6-7)^2+(6-7)^2+(5-7)^2+(8-7)^2+(10-7)^2 \right ]}{5-1}\\=\frac{1+1+4+1+9}{4}\\=\frac{16}{4}\\=4$

Standard deviation = $\sqrt{4}=2$