Sample vs Population Data

The one idea: Every number you compute is either a parameter (a true fact about the whole population, which you almost never have) or a statistic (an estimate from a sample, which is what you almost always have). They use different symbols, different formulas, and — critically — the sample versions are built to correct for the fact that a sample understates the messiness of the full population.

⚠️ The trap: Treating a sample statistic as if it were the population parameter — reporting "average order value is $50.90" with no acknowledgment that a different sample of the same customers would have produced $49.80 or $52.10. The number you computed is one draw from a process that produces a different number every time you re-sample. Confusing the draw for the truth is the single most common error in applied statistics.

Every dataset an analyst touches sits somewhere on a spectrum between two poles: the population — every unit that exists, full stop — and a sample — the subset you actually got your hands on. Statistics Canada surveying every household is a population study (a census). A/B testing 2,000 of your 4 million users is a sample. The distinction sounds academic until you notice that it changes which Greek letter you're allowed to write, which formula you're required to use, and how much you're allowed to trust the number in front of you.

Parameters describe the population, statistics describe the sample

A parameter is a characteristic of a population: the true mean order value across every customer you have ever had or ever will have. A statistic is a characteristic of a sample: the mean order value…