Question

The following are all five quiz scores of a student in a statistics course. Each quiz was graded on a 10 point scale.7, 7, 6, 10, 10Assuming that the scores constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.answer =

Answer 1

Given:

7, 7, 6, 10, 10

To find the standard deviation assuming that the scores constitute an entire population, we first note the formula:

`\sigma=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_(i_-\mu))^2}{n}}`

where:

`\begin{gathered} \sigma=standard\text{ deviation} \\ n=count=5 \\ \mu=mean=(7+7+6+10+10)/(5)=8 \\ (x_(i_-\mu))^2=sum\text{ of squares} \end{gathered}`

Next,we get the sum of squares as shown below:

Then, we solve for the standard deviation:

`\begin{gathered} \sigma=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_i-\mu)^2}{n}} \\ \sigma=\sqrt{(14)/(5)} \\ Calculate \\ \sigma=1.67 \end{gathered}`

Therefore, the answer is: 1.67