How this calculator works
The box extends from Q1 to Q3 with a line at the median. Under the default rule, whiskers end at actual observations within the 1.5 IQR fences; values strictly beyond the fences are listed separately. Linear interpolation and medians of halves can disagree on small samples. The output tables supply drawing coordinates rather than a rendered chart.
Formula
IQR = Q3-Q1; lower fence = Q1-1.5IQR; upper fence = Q3+1.5IQR. Linear quantile index = (n-1)p in zero-based sorted data.
Worked example
For 1, 2, 3, 4, 5, 100, linear Q1 = 2.25 and Q3 = 4.75. Fences are -1.5 and 8.5, whiskers are 1 and 5, and 100 is flagged.
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Frequently asked questions
Are whiskers the fences?
No. Whiskers are observed values inside the fences; the fences are calculated thresholds.
Should flagged values be removed?
Review their context first. A flagged value can be a valid rare observation.
Why is there no drawn box?
The coordinate and flagged-value tables provide the information needed to draw the box using the selected convention.