Discrete or Continuous? A Subtle Problem with Ogives.

We sometimes receive reports that FX Stat is “doing something wrong”. Often the problems are actually a symptom of a deeper issue – when is data discrete and when is it continuous?

Sometimes data is CLEARLY discrete in nature. Those cases are simple and we will not look at them.

Sometimes data is CLEARLY continuous and needs to be graphed appropriately. Again, this is easy.

Sometimes things are not so clear. For example here is some data that is not clearly discrete or continuous. Unfortunately, it is almost identical to the first data set! Certainly the histogram will be the same.

Is this data discrete? Should we graph it using a dot plot? Or is it “sort” of continuous so a histogram is fine?

Often the answer to these questions depends on the context of the data, but our products (obviously) have problems with context. On the whole, we do not get involved. If you decide to graph it as a dot plot or a histogram, our products will do as they are told.

The real problem comes with ogives. If you are thinking of this data as “discrete”, the ogive should look like this (we have put in the histogram so you can see what we mean.)

Many of you are probably saying “but that is wrong – it should look like the first graph”.

Well … it depends.

If you are intending the data to be discrete, then this ogive makes perfect sense – by the time you get to 16 (as opposed to 16.5), your cumulative frequency is 8. If you are thinking of this data as continuous then you need the first graph.

Unfortunately, we cannot tell what you are thinking or, sometimes more importantly, which school system you are teaching in. Different school systems have different “standards”.

We have taken the decision to make our products treat the data as entered. If you enter discrete values with a frequency we will always draw the second, offset ogive. If you really mean your data to be continuous and want to draw the ogive, you will need to enter your data as groups.

 

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