### Percentage data – is it continuous or discrete?

I received the following email in response to a previous article about discrete and continuous data.  The exchange has been edited slightly for ease of reading.

“Hello Roger.  I enjoyed your posted article regarding discrete and continuous data. I have encountered similar discussions with other Industrial Engineers and Master Black Belts over the years. As an IE and MBB, I solve productivity and capacity utilization issues frequently, and one of the most effective tools is a histogram, which is used with continuous data.

Using your criteria, would you classify an average test grade of 86.54% for students in a math class as discrete or continuous?  Another example is money.  Many MBBs argue that it is always continuous, no ifs, ands, or buts.  However, one can count the coins, or even create a Pareto chart from a bag of coins.

In summary, while we desire black and white choices, in the real world, my rule is that practicality should always be a consideration when selecting or using a tool, or teaching a class.   I would appreciate any thoughts you might have.”

I replied as follows:

“Percentage or proportion data is an interesting case.  Let’s talk about test grades as an example.  The underlying data that the percentage of correct answers is calculated from is discrete – each individual question is either correct or it is not correct.  The percentage of correct questions is therefore calculated based on discrete data and technically speaking is discrete.  In practice, percentage data is almost always treated as continuous.   The percentage does exist on a continuum and a fraction of a percent does makes sense, both of which are common sense tests for continuous data.

Money is also almost always treated as continuous data.  Again, from a technical standpoint, it is based on count data which is discrete.  Currency exists in discrete quantities – one dollar, two dollars, etc. if we are counting dollar bills.  One quarter, two quarters, etc. if we are counting quarters.  And so on.  But, money does exist on a continuum and fractions of a dollar or even fractions of a penny makes sense, and so it is typically treated in practice as continuous.

You are quite correct that Pareto charts can be constructed from discrete (i.e. count) data.  But, Pareto charts do not demand continuous data like the histogram.  Pareto charts can be constructed from either continuous or discrete data.

Hope this helps!  Regards, Roger”