Is cholesterol a continuous or discrete variable?

Answer 1

Depends on how you measure it. If it is a continuously-variable measurement in a statistical study, using percentages for instance, then it would be a continuous variable. (Cool how that works, eh?) But if it is measured in discrete increments, like the common "cholesterol count" or parts-per-million (ppm) or even molecule by molecule (for a nano-scale experiment), then it's a discrete variable.

The difference here is that "discrete" measurements use "whole steps" (a cholesterol count of either 181 or 182, no in-between amount or partial steps), while "continuous" measurements assume that the thing being measured is a degreed quality like time or distance that doesn't proceed by "whole steps" even if the continuous measurement seems to do so.

For instance, direction (on a 2-dimensional plane, to keep it simple) is measured in degrees, 360 of them on a compass. But as you are taking a particular bearing, you know that degrees only approximate the exact direction you are trying to measure. So the gap from one degree to another can be broken down into minutes, and each "minute" can be broken down into "seconds" and so on, hypothetically with infinitely greater precision. The same is true with measuring time, or length, or pressure. The more precisely we are able to measure those things, the more complex our measurement numbers become.

This is not true with cholesterol. Many measurements of cholesterol (in a person's bloodstream, or in a food, or in a test-tube solution, etc) are approximate, and might behave like and be correctly treated as a continuous variable, especially in very large samples (like the entire human population of the Eastern hemisphere).

But there is a final finite step at which you can count precisely, molecule by molecule, a discrete measurement of cholesterol, if your instruments permit you to do so. So, ultimately, it becomes a discrete variable. And if you are able to count it molecule by molecule, you'll have no half-steps or decimal places to deal with: there are either 65 molecules of cholesterol on that microscope slide, or you missed one and there are 66, but you won't ever have 65.328 molecules of cholesterol. (When a cholesterol molecule breaks apart it isn't cholesterol anymore...)