Categorical, Discrete, and Continuous Variables

The test for whether a variable is quantitative isn't whether it looks like a number. It's whether arithmetic on those values means something. Zip code 90210 and zip code 10001 are both five-digit numbers, but averaging them gives you a meaningless number that points to no real place. Zip codes are just labels, so the variable is categorical even though it's written in digits. Height in centimeters, by contrast, can be averaged, subtracted, compared, and every result still means something physical. That's what makes it quantitative.

Once you've confirmed a variable is quantitative, ask a second question: can you count the possible values one by one, or does it slide continuously along a scale? Number of siblings is discrete, you can only have 0, 1, 2, 3 siblings, never 2.4 of them. Weight is continuous, because a fish could weigh 2.0 kg, 2.03 kg, or 2.0317 kg depending on how precisely you measure. The discrete/continuous split only applies after you've established the variable is quantitative in the first place; it never applies to categorical variables.

This distinction sets up everything else in the unit. The type of variable determines which graphs and summary statistics make sense later: categorical data gets bar charts and proportions, quantitative data gets histograms, means, and standard deviations. Mixing them up, like averaging zip codes or eye colors, is the kind of error that makes an entire analysis meaningless before it starts.