What is the difference between discrete and continuous variables?

John Predmore

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A discrete variable can take on a finite, or countable, number of values within a range. In contrast, a continuous variable can take on an infinite number of values in the same range.

I offer a simple example. Highway speed limits are discrete - the sign says either 30 mph or 40 or 45 or 55. Within the range of speeds which automobiles travel, the speed limit is always a whole number. The digital speedometer on the dashboard is also discrete, in the range of speeds your automobile can operate, there is a larger, but still finite, number of possibilities - 30 mph, 31, 32, 33, and so on.

But the actual speed of the automobile is a continuous variable. If I am driving 30 mph and I go a tiny bit faster, the car can speed up to 30.1 mph, 30.15 mph, 30.1575, 30.166666666667 mph, and on forever. The possibilities are not limited by the resolution of my readout, there are in fact an infinite number of real numbers in the range of speeds which automobiles operate. I can choose to limit my view of the speed variable with a digital readout which displays only whole numbers, but in reality, velocity is a continuous variable.
 

Bev D

Heretical Statistician
Leader
Super Moderator
I would add to that as I see the highway speed thing (like the difference between currency and monetary worth) isn't a precise or complete description of a discrete value vs a continuous value.

The idea of speeds being reported or stated as an integer value is (through rounding or instrument resolution) is an example of chunky data which in a small range of values behaves like discrete data (specifically ordinal data).

For me, what has not been articulated is the nature and consequences of 'discrete data'. discrete data is more precisely named nominal or ordinal data (aka categorical, attribute, count or proportional data). "True" discrete data comes from events that can only be assessed and counted. Nominal data is data that has no natural rank order. (such as pass fail, or presence/absence of a defect or characteristic like color (i.e attribute). Ordinal data has a natural rank order. small, medium large, dissatisfied, neutral, satisfied in surveys. note that some categorical data is the result of transformation continuous data into human manageable 'chunks'

The importance of knowing what kind of data you have is that certain mathematical and therefore statistical tests are quite dependent on the data type...

Perhaps this is overkill but I have attached a document I use in my training materials that explains this in greater detail. You might find it useful...
 

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Bev D

Heretical Statistician
Leader
Super Moderator
It seems useful.
well this article is from a statistically pure standpoint (lots of statistical verbiage; using common words that have very different meaning in the statistical context). It also doesn't' speak to the type of data as I explained. Rather it speaks from the frame of the population to be described. two very different uses of the terms discreet and continuous. As the article alludes to briefly, these definitions are related to fixed and random variables. (Miner if I've misinterpreted this let us know) As Deming would say "that is academically interesting, but has little value in the real world." (paraphrased form his comment regarding p values ANOVA studies, etc.)

could you elaborate more on what context you are 'using' the terms discrete and continuous' data?
 
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