If your data set consists of negative numbers, I don’t see why not. Average of – 2, – 2, and -3 is -2.333. See? Negative average. Same goes for the median and IQR too.

The IQR and Standard Deviation cannot be negative, but the mean, median, mode, and the location of the quartiles themselves can be negative.

Original Message:
@PhiNotPi why can’t IQR be negative? You’re just taking the difference of the two quartiles, which can contain negative numbers because it is at the interval level.
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The IQR cannot be negative because you subtract the larger quartile from the smaller one, always resulting positive, even with negative numbers.
I.E.: Data Set: -20, -19, -19, -18, -16, -14 -12, -9, -5, -2, -1
Smaller Quartile: -20, -19, -19, -18, -16
Larger Quartile: -12, -9, -5, -2, -1
-5 — -19=14
It is a range, so it has to be positive.