Variables

Who was measured, and what

Every data set starts with two questions. Who or what did the data come from, and what was recorded about each one?

The individuals that data are collected from are the observational units. They can be people, but they can also be dogs, cities, days, phones or tweets. A variable is a characteristic recorded for each unit that can change from one unit to the next.

Suppose a gym records, for each member: membership type, number of visits last month, age, and how far the member lives from the gym. The members are the observational units. Membership type, visits, age and distance are four variables.

Data does not have to be a number typed into a spreadsheet. Photos, sound clips, videos and text can all be recorded for each unit and carry real information.

Categorical or quantitative

A categorical variable puts each unit into a group: blood type, favorite streaming service, whether a patient improved. A quantitative variable is a measured or counted amount, and it usually has units: dollars, minutes, siblings.

The quick test is to ask whether an average would make sense. The average number of siblings means something. The average zip code does not, because a zip code is a label that happens to be written with digits. Numbers that name things, like jersey numbers and area codes, are categorical.

Discrete or continuous

Quantitative variables come in two kinds. A discrete variable takes values you can count off one by one, like the number of goals in a game or the number of apps on a phone. A continuous variable can take any value in an interval, like time, height or weight.

Rounding does not change the kind of variable. A mile time recorded to the nearest second is still continuous: the time itself could be 7 minutes 31.4 seconds, and only the measurement was rounded.

Parameter or statistic

A parameter describes a whole population, and it is usually unknown. A statistic describes a sample, and you can calculate it from your data. One way to remember: parameter goes with population, statistic goes with sample.

The notation keeps them apart too. A population proportion is $p$ and a sample proportion is $\hat{p}$. A population mean is $\mu$ and a sample mean is $\bar{x}$. A statistic from one sample will usually miss the parameter by a little, and a different sample would give a different value. Measuring that wobble is what Units 2 through 4 are for.