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;

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

Find the mean

$mean=\frac{132}{6}=22$

Hence the standard deviation will be;

$\begin{gathered} \sigma=\sqrt{\frac{1446}{6-1}=}17.005881 \\ \sigma\approx17.01\text{ to 2 decimal places} \end{gathered}$

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

$17.01$