StatReason

Box Plot Maker

Compare the spread and center of one or more groups at a glance, with potential outliers flagged using the standard 1.5 times IQR fence rule.

One group per line, as "label: value, value, value". Label is optional.

What this answers

A box plot answers "where does this group's data center, how spread out is the middle half of it, and are there any values far enough from the rest to be worth a closer look?" It packs five numbers (minimum, first quartile, median, third quartile, maximum) into one compact picture, and does it for multiple groups side by side so their spreads can be compared directly.

How it is calculated

Quartiles use the same Hyndman-Fan Type 7 convention used throughout this site. The interquartile range (IQR) is the third quartile minus the first. A value is flagged as a potential outlier if it falls more than 1.5 times the IQR below Q1 or above Q3, the standard convention from Tukey's original box plot definition, applied here identically to the Outlier Calculator's default rule.

Worked example

For the values 1, 2, 3, 4, and 100: Q1 is 2, Q3 is 4, so the IQR is 2, and the fences sit at 2 minus 3 (below 0) and 4 plus 3 (7). Since 100 is far above the upper fence of 7, it is flagged as a potential outlier, exactly the kind of value a box plot is built to surface at a glance rather than bury inside a single summary number.

Reading the chart

A potential-outlier flag from this fence rule is evidence to investigate, not proof of an error. Compare the flagged group against the Median Calculator for that group's exact quartile values, and never remove a flagged point automatically without understanding why it is unusual.

Assumption audit

Calculated from your data: the five-number summary and IQR-based fences for each group, and exactly which values (if any) fall outside those fences.
Evidence to review: whether a flagged value looks like a genuine extreme observation or a data-entry mistake, and whether groups being compared are measured on comparable scales.
You must verify: that a flagged potential outlier is not simply removed without investigation; the fence rule is a heuristic convention, not an error-detection algorithm.

Limitations

With a very small number of values per group, quartiles and fences can be unstable and sensitive to exactly which values you have. The 1.5 times IQR fence is a widely used convention, not a universal statistical law, and different fields sometimes use a wider or narrower multiplier.