StatReason

Quartile and IQR Calculator

Find the boundaries of the middle half of your data, and the potential-outlier fences built from them.

What this answers

This calculator answers "where does the middle half of my data sit, and how spread out is it?" Q1 marks the boundary below which a quarter of your data falls; Q3 marks the boundary below which three-quarters falls. The interquartile range, the distance between them, is a measure of spread that ignores the most extreme quarter on each end, making it more resistant to extreme values than the full range.

How it is calculated

Q1 and Q3 use the Hyndman-Fan Type 7 interpolation method, the site-wide convention. The interquartile range (IQR) is Q3 minus Q1. The lower and upper fences use the standard Tukey convention: 1.5 times the IQR below Q1 and above Q3, marking the range outside which a value is flagged as a potential outlier.

Worked example

For the values 1 through 5: Q1 is 2 and Q3 is 4, giving an IQR of 2. The lower fence sits at 2 minus 3 (negative 1) and the upper fence at 4 plus 3 (7), meaning any value below negative 1 or above 7 in this dataset would be flagged as a potential outlier, though none of the actual values here reach that far.

Assumption audit

Calculated from your data: Q1, Q3, the IQR, and the resulting fences computed directly from your entered values.
Evidence to review: fences are computed here as a reference; check the Box Plot Maker to see exactly which of your values, if any, actually fall outside them.
You must verify: that a value falling outside the fences is investigated, not automatically deleted; the fence rule is a heuristic convention, not proof of a data error.

Common mistakes

Treating every value beyond the fences as automatically wrong is a frequent misinterpretation: the 1.5 times IQR rule is a convention for flagging candidates worth a closer look, not a formal statistical test for errors. A genuinely unusual but entirely correct observation, such as one exceptional sale in an otherwise ordinary batch of transactions, will trigger the same flag as a data-entry mistake, and only investigating the actual value can tell them apart.

Limitations

With a small dataset, quartiles and the fences built from them can shift noticeably from adding or removing just one value, so treat fence-based outlier flags on small samples as suggestive, not definitive.