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Quantile and quantize scales have very similar names, confusingly so. Here’s how to remember their meanings:

Quantiles are defined, in statistics, as separating a population into intervals of similar sizes (the 10% poorest, the 50% tallest, the 1% richest…); a quantile scale is essentially defined by its domain, a fixed set of values — when applied to a new value, it will then compute its ranking with respect to the initial distribution, and map that ranking to the output range.

To Quantize means to group values with discrete increments — like expressing a list of floating point numbers with 1 decimal digit, or rounding time to the closest minute. It is the output range that is discretized, and such a scale allows to transform an initial continuous range into a discrete set of classes.

Threshold scales allow us to directly specify the cut values that separate the classes.