A data set is a crowd, and there are only three useful things to ask about a crowd. Where is it? — that is a measure of CENTRE, and the mean $\mu$ (say mu) is the headline one: every observation added and shared out evenly. How far does it wander? — that is SPREAD, and this chapter carries four dialects of it. Where does one member stand inside it? — that is POSITION, and the z-score owns that job.

The spread dialects differ in what they consult. The range $R = x_{\max} - x_{\min}$ asks only the two extremes. The interquartile range $IQR = Q_3 - Q_1$ asks the quartiles — $Q_1$ is the value a quarter of the data sits below, $Q_3$ the value three quarters sit below — so it reports the width of the middle half and shrugs at the tails. The standard deviation $\sigma$ (say sigma) asks EVERY observation how far it strays and reports the typical answer. Three tools, three appetites.

Read the recipe, not the number. Two numbers subtracted at the ends is a range; two quartiles subtracted is an IQR; a value rescaled against a mean and a spread is a z-score, and it comes out naked — no marks, no minutes, no millilitres — because it is already counted in standard deviations.