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.

Things we count are discrete.

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.