Question

A sample was done, collecting the data below. Calculate the standard deviation, to one decimalplace.х24726573

Answer 1

We have the following data

`24,7,26,5,13`

The standard deviation is given by

`\sigma=\sqrt[]{(\sum(x_i-\mu)^2)/(N)}`

Where μ is the mean and N is the number of data points

Let us first find the mean of the data.

`\mu=\frac{\text{sum}}{number\text{ of data points}}=(24+7+26+5+13)/(5)=(75)/(5)=15`

Finally, the standard deviation is

`\begin{gathered} \sigma=\sqrt[]{((24-15)^2+(7-15)^2+(26-15)^2+(5-15)^2+(13-15)^2)/(5)} \\ \sigma=\sqrt[]{((9)^2+(-8)^2+(11)^2+(-10)^2+(-2)^2)/(5)} \\ \sigma=\sqrt[]{\frac{81^{}+64^{}+110^{}+100^{}+4^{}}{5}} \\ \sigma=\sqrt[]{(359)/(5)} \\ \sigma=\sqrt[]{71.8} \\ \sigma=8.5 \end{gathered}`

Therefore, the standard deviation of the data set is 8.5