Sampling data and using averages to get normal data (CL Theorem) - Is this valid?

I am analyzing the number of order lines as a weekly average for Six Sigma and the data is non normal. I can't assume that 30 plus data points are sufficient to ignore normality tests. However, I found that sampling data points over time and taking those averages results in normal data* which can then be used for parametric tests. Is this a valid approach and how would I validate it?


TS Contributor
It depends on the type of statistical test that you plan to use. The variance of the averages is much smaller than the variance of individual values, so you cannot treat them the same way. What you describe is the basis for Shewhart control charts used in industrial statistics to monitor the stability of a process over time.