Question

The following data reflect the number of customers who return merchandise for a refund on Monday. Note these data reflect the population of all 10 Mondays for which data are available. 40 12 17 25 9 46 13 22 16 7Based on these data, what is the standard deviation?

Answer 1

Answer:

The standard deviation of given data is 12.36  

Step-by-step explanation:

We are given the following data in the question:

40, 12, 17, 25, 9, 46, 13, 22, 16,7

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$  

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.  

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{207}{10} = 20.7$

Sum of squares of differences =

372.49 + 75.69 + 13.69 + 18.49 + 136.89 + 640.09 + 59.29 + 1.69 + 22.09 + 187.69 = 1528.1

$\sigma = \sqrt{\dfrac{1528.1}{10}} = 12.36$

Thus, the standard deviation of given data is 12.36