I'm trying to find outliers using 1.5 x interquartile range but I'm getting a negative value for the lower bound. I found Q3 and Q1 which are 13.30 & 3.00 respectively but for the lower bound i get -12.45 which seem odd. Is there something I'm doing wrong?

There are 43 numbers in this chart so I just get (75/100)*43 to find Q3 and (25/100)*43 to find Q1

enter image description here

  • $\begingroup$ What's odd about having a negative lower IQR bound? $\endgroup$
    – John
    Sep 15 '14 at 1:15

The correct answer should be similar, so that's probably correct; by my reckoning the box plot's lower inner-fence is -12.45 so your quartiles are probably fine (sample quartile definitions vary, but are generally close to Tukey's hinges, and - for some quartile definitions at least - sometimes hinges and quartiles do coincide).

Since all your observations are positive, there are no "outliers" (by the present definition) on the low side.

If your data are necessarily positive but sufficiently right-skew and with some values close to zero, negative values for the inner fence are quite common.

The rule has no way to know that negative values are impossible for your data; the rule isn't necessarily entirely appropriate for this kind of data, but it looks to me like you have correctly carried the calculation out on the data you have.

Incidentally, for the boxplot, here's an illustration of essentially the same "outlier" bound calculation:

enter image description here


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