Question

The following are distances (in miles) traveled to the work place by 6 employees of a certain brokerage firm. Find the standard deviation of this sample distances. ROund your answer to two decimal places

Answer 1

Step 1

Arrange the data from smallest to biggest

`2,5,14,34,37,40`

Step 2

The formula for standard deviation for sample is given as;

`\begin{gathered} \sigma=\sqrt{(\sum(x-\mu)^2)/(n-1)} \\ \mu=mean \\ n=number\text{ of data} \end{gathered}`

Find the mean

`mean=(132)/(6)=22`

Hence the standard deviation will be;

`\begin{gathered} \sigma=\sqrt{(1446)/(6-1)=}17.005881 \\ \sigma\approx17.01\text{ to 2 decimal places} \end{gathered}`

Answer; The standard deviation for the sample to two decimal places is;

`17.01`