Variables

Every data set is built from observational units (the items or individuals measured) and variables (the characteristics recorded about each one, which may change from unit to unit). A variable is categorical when its values are category names or group labels, and quantitative when its values are measured or counted quantities, generally with units. Quantitative variables are discrete when their possible values are countable, like the whole numbers, and continuous when they can take any value in an interval. A summary of a variable for a whole population is a parameter; the same summary for a sample is a statistic, written with its own symbols, such as $p$ and $\hat{p}$.

The classification fails in one predictable way: judging by digits instead of by meaning. Zip codes, jersey numbers, and member IDs get called quantitative because they look numeric, and someone computes an average that names no place, no player, no account. The same reflex runs backwards - coding categories as 1, 2, 3 and then doing arithmetic on the codes, or calling a count categorical because its values are whole numbers. The repair is a single question asked every time: would the mean of these values tell you anything real?