It is commonly said that the interquartile range (IQR) is suitable to describe ordinal-, interval- and ratio-level data (one of many examples found on the Internet). But calculating the IQR includes finding the difference between two values, and that requires the interval level of measurement. Likewise for the range. I could understand if the IQR and range were to be reported as "from x to y", but I have not seen that as a definition.

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#### Best Answer

That is a good observation, so to use interquartile range for ordinal data it certainly must be redefined. If $Q_1, Q_3$ are respectively first and third quartile, so the usual interquartile range is $R=Q_3 – Q_1$, for ordinal data I would define it as the *interval* $$ R^* = [Q_1, Q_3] $$ (for ordinal data where there are often few unique values, it is important to use the closed interval, including the endpoints, there for $[]$)

(I do not have any references for this definition, but I cannot see some other way to make meaning).

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