Question

here are the shopping times (in minutes) for a sample of 6 shoppers at a particular grocery store. 38, 37, 20, 39, 21, 25 send data to calculator find the standard deviation of this sample of shopping times. round your answer to two decimal places. (if necessary, consult a list of formulas.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{38 + 37+20+39+21+25}{6}=\frac{180}{6}=30$.

Step2: Calculate the squared - differences

$(38 - 30)^2=64$, $(37 - 30)^2 = 49$, $(20 - 30)^2=100$, $(39 - 30)^2 = 81$, $(21 - 30)^2=81$, $(25 - 30)^2 = 25$.

Step3: Calculate the sum of squared - differences

$64+49+100+81+81+25 = 400$.

Step4: Calculate the sample variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{400}{6 - 1}=\frac{400}{5}=80$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{80}\approx8.94$.

Answer:

$8.94$