Just because a distribution of data has the same mean and median values, does not mean it can be considered a ‘normal’ distribution.

Recently a number of candidates in our business improvement training lodged assignment work. They were asked to draw conclusions about the normality of a data set and quite a few used an incorrect reference in the way they validated their conclusions.

I want to make sure we clear this up.

Clearing Up Misunderstandings About Normality Assessment

A normal distribution has a number of properties, one of which ends up being this – the mean and median are the same or very close to being the same.

To give an analogy – men wear trousers, but that does not mean that someone who wears trousers is a man.

Same thing applies here …

A normal distribution has a mean and median that are equal. However, a data set with a mean that equals the median is not necessarily normal.

So we need to be very careful about drawing conclusions based on the existence of this characteristic because it can be wrong.

Take a look at the example I’ve provided below.

You’ll notice that the distribution is symmetrical, it has the same mean and median, but it is clearly non-normal.

To draw conclusions about normality, you always run a normality test, the most robust of which (for our purposes) is the Anderson Darling Test and its test P-value.

Hope this clears any misunderstandings up.

George

More Information

This article was written by George Lee Sye, author of Australia’s best selling lean six sigma body of knowledge – Process Mastery with Lean Six Sigma. For more information CLICK HERE where you’ll discover why this is one of the most important text books in the business improvement world today.

If you want to check out the data set used above, CLICK HERE to download.