Perhaps one of the simplest but toughest questions for my intro (and graduate) stats students seems to be those asking to classify a variable as discrete or continuous.
My quick rule of thumb (heuristic) is to think about whether the variable is countable or whether it must be measured. I tried to come up with a mnemonic like “population-parameter; sample: statistic” but the best I could do is “finger : digit: discrete” since you have to count your fingers.
Dogs, cats, people, houses, touchdowns, are countable, so they are discrete variables. And we do not often think of dividing a dog or house into parts, e.g. 1.6 dogs, so again that sounds like they are discrete.
Things we measure are Continuous
A person’s weight, gallons of water, the length of a football field, the speed of a car, the temperature of the ocean, price of gas, all must be measured, so they are continuous variables. Another clue is that continuous variables are often stated as fractions or decimals, as in 2.5 gallons of gas.
But then there are some things that are not so obvious. Take the height of buildings. Most commonly, we in America tend to think of buildings in terms of the number of floors. I can remember when the Empire State Building was the tallest building in the world and us kids could quickly tell you it had 102 floors. Floors are countable, so that would make the height of a building discrete, right?
Well, in many other places, buildings are measured. In fact, if you Google the height of the Empire State Building, you would find it is 443.2 meters tall if you include the antenna, which most building owners do so they can brag a bit more. Well, that sounds like someone had to actually measure the height, doesn’t it, so that means building height is really a continuous variable. And, of course, we all have to measure our own height as well.
Time is Continuous
Another confusing variable is time. We tend to think of time as the number of years we have lived, or the days until Christmas, which we can count. But when I was a little kid, I always answered “six and a half” when asked how old I was. So, that was a clue that time could be divided into smaller pieces, which would mean time is not really a discrete variable.
And today, we no longer count the number of moons that have passed. We measure time using very accurate devices. If you want a bit of distraction, check out this page showing a timeline of our universe.
I do hope your statistics instructors do not put purposefully confusing questions on quizzes and exams about time. But if they do, you are now armed to be able to persuade them your answer that time is a continuous variable is correct.
Unless your instructor is also a particle physicist. Then, they are likely to tell you time is both discrete and continuous.
