Question

Finding the standard deviation round answer two decimal places when necessary

Answer 1

`\begin{equation*} SD=1.55 \end{equation*}`

Explanation:

The standard deviation of a data set is represented by the following equation:

`\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}`

Therefore, for the given sample:

`\begin{gathered} 6,10,6,6,7 \\ \text{ mean=}(6+10+6+6+7)/(5) \\ \text{ mean=7} \end{gathered}`

For each data point, find the square of its distance to the mean.

`\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}`

Now, solving for the standard deviation:

`\begin{gathered} SD=\sqrt{(12)/(5)} \\ SD=1.55 \end{gathered}`