Answer:
[tex]\begin{equation*} SD=1.55 \end{equation*}[/tex]
Step-by-step explanation:
The standard deviation of a data set is represented by the following equation:
[tex]\begin{gathered} SD=\sqrt{\frac{\sum_^\lvert{x_i-\bar{x}}\rvert^2}{n}} \\ where, \\ x_i=\text{ represent each number in the data set} \\ \bar{x}=\text{ mean} \\ n=\text{ number of elements in the data set} \end{gathered}[/tex]
Therefore, for the given sample:
[tex]\begin{gathered} 6,10,6,6,7 \\ \text{ mean=}\frac{6+10+6+6+7}{5} \\ \text{ mean=7} \end{gathered}[/tex]
For each data point, find the square of its distance to the mean.
[tex]\begin{gathered} \sum_^\lvert x_i-\bar{x}\lvert{}^2=(6-7)^2+(10-7)^2+(6-7)^2+(6-7)^2+(7-7)^2 \\ \sum_^\lvert x_i-\bar{x}\lvert{}^2=12 \end{gathered}[/tex]
Now, solving for the standard deviation:
[tex]\begin{gathered} SD=\sqrt{\frac{12}{5}} \\ SD=1.55 \end{gathered}[/tex]
