General Question

717richboy's avatar

Can an IQR, mean or median be negative?

Asked by 717richboy (234 points ) September 25th, 2012

Statistics question. Thanks in advance.

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3 Answers

seekingwolf's avatar

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.

PhiNotPi's avatar

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

dxs's avatar

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.

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