Answer :
Given:
7, 7, 6, 10, 10
To find the standard deviation assuming that the scores constitute an entire population, we first note the formula:
[tex]\sigma=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_{i_-\mu})^2}{n}}[/tex]where:
[tex]\begin{gathered} \sigma=standard\text{ deviation} \\ n=count=5 \\ \mu=mean=\frac{7+7+6+10+10}{5}=8 \\ (x_{i_-\mu})^2=sum\text{ of squares} \end{gathered}[/tex]Next,we get the sum of squares as shown below:
Then, we solve for the standard deviation:
[tex]\begin{gathered} \sigma=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_i-\mu)^2}{n}} \\ \sigma=\sqrt{\frac{14}{5}} \\ Calculate \\ \sigma=1.67 \end{gathered}[/tex]Therefore, the answer is: 1.67
