A box plot condenses an entire dataset into five numbers and a picture: where the middle of the data sits, how spread out it is, and which points are unusual enough to call out individually. This calculator builds that chart from your data — and, unlike a single-dataset box plot, lets you plot up to four labeled groups on one chart so you can compare their medians and spread directly.
How the five-number summary and IQR are calculated
The calculation starts by sorting each group's data from smallest to largest. The minimum and maximum are simply the first and last values. The median (Q2) splits the sorted list into a lower half and an upper half; Q1 is the median of the lower half and Q3 is the median of the upper half. When a group has an odd number of values, this calculator excludes the overall median from both halves before taking their medians — Tukey's original 'hinges' convention, the same one used by the site's Quartile Calculator.
The interquartile range, IQR = Q3 minus Q1, measures the spread of the middle 50% of the data. Because it ignores the top and bottom quarters entirely, it's far less sensitive to a single extreme value than the full range (max minus min) would be — which is exactly why it's the basis for the outlier rule below.
Whiskers, fences, and what counts as an outlier
The whiskers aren't drawn to the true minimum and maximum. Instead, each whisker extends to the most extreme data point that still falls within 1.5 times the IQR of the nearest box edge — the fences. Any value beyond a fence is drawn as an individual dot and flagged as an outlier rather than stretching the whisker out to meet it. This convention (chosen by John Tukey) flags roughly 0.7% of values as outliers for a normal distribution — a useful balance that neither buries real anomalies nor flags routine variation.
A box plot with no outliers has whiskers reaching all the way to that group's true minimum and maximum. Skew shows up as an off-center median line inside the box, or as one whisker noticeably longer than the other.
Comparing groups on one chart
Entering data into Group 2, 3, or 4 stacks additional box plots on the same axis as Group 1, each in its own color, with a comparison table below showing median, IQR, and outlier count side by side. This is the fastest way to answer questions a single box plot can't: is one class's typical score higher than another's? Is a process more variable in one quarter than the next? Each group only needs 4 or more values to be included — a group with fewer is skipped with an inline note so it never silently distorts the shared axis scale.
Because every group shares the same x-axis, comparing box widths (spread) and positions (center) is direct and visual — no need to memorize four separate sets of numbers.