What would you expect to see if you were calculating the sample STANDARD DEVIATION of sales from a convenient store

Question

What units would you expect to see if you were calculating the sample STANDARD DEVIATION of sales from a convenient store? 

Answer 1

Hi Diann,

 

The standard deviation is

 

σ = √[(1/N) ∑(x_i - μ)²]

 

where the x_i are your data points, μ is the mean of your data and there are N data points in all. The ∑ is a capital Greek sigma (which is a Greek S) and it stands for a sum over index i running from 1 to N.

 

Basically, this formula tells you to first calculate the mean μ. Then calculate the difference x_i - μ for each data point. Then add up all of the squares of these differences, and then divide that sum by N, the total number of data points. Finally, you take the square root of your answer.

 

Now, the units you are dealing in are dollars, since it represents sales. The mean μ is also in dollars. When you add all of the squares, you are adding $². But, when you take the final square root, that takes the $² back to $. So, the standard deviation for sales data should be dollars, provided you are working un U.S. currency.