Question

Here are the shopping times in minutes) for a sample of 5 shoppers at a particular grocery store.38, 36, 28, 35, 43Find the standard deviation of this sample of shopping times. Round your answer to two decimal places.

Answer 1

`\begin{gathered} \text{Solve for the mean }\bar{x}\text{ first} \\ \bar{x}=(\Sigma x_i)/(n)=(38+36+28+35+43)/(5) \\ \bar{x}=36 \\ \text{Then solve for the variance }s^2 \\ s^2=\frac{\Sigma(x_i-\bar{x})^2}{n-1} \\ s^2=((38-36)^2+(36-36)^2+(28-36)^2+(35-36)^2+(43-36)^2)/(5-1) \\ s^2=((2)^2+(0)^2+(-8)^2+(-1)^2+(7)^2)/(5-1) \\ s^2=(118)/(4) \\ s^2=29.5 \\ \text{The square root of the variance is the standard deviation} \\ s=\sqrt[]{29.5} \\ s=5.4313902456001 \\ \text{round off to two decimal place and we have} \\ s=5.43 \end{gathered}`