Observational Units, Variables, Parameters, and Statistics

Before you can trust any number, you need to know what it's counting. Every data set is built from observational units: the individual people, cars, schools, or transactions that each row represents. Once you know the unit, the columns next to it are the variables, the characteristics recorded about each unit, like weight, mpg, or country of origin for a car. Mixing these up is easy to do but costly: if you don't know what one row stands for, you can't know what an average of that column actually means.

That distinction feeds directly into parameter versus statistic. A parameter is a fixed, usually unknown number describing the entire population, like the true proportion of all adults who own a pet. A statistic is a number calculated from a sample, the proportion you actually observed among the 250 adults you asked. Statistics vary from sample to sample because different samples catch different people; parameters don't move, they're just hard to see directly.

This sets up the rest of the unit. Once you can name the observational unit and separate variables from each other, you can classify those variables as categorical or quantitative, and once you can separate statistic from parameter, you're ready for the idea that sampling introduces variability, which is the seed of everything inference-related later on.