Box Plot Builder

Generate box-and-whisker plots showing median, quartiles, and outliers for data sets.

Tested tool guide Tested browser tools Checked August 16, 2026

What Box Plot Builder does, with a checked example

Paste a numeric data set to turn its distribution into a box-and-whisker plot. The chart locates the median inside a box spanning the first and third quartiles, extends whiskers across the non-outlying range, and marks observations treated as outliers. It helps reveal center, spread, skew, and isolated values without inspecting every observation. The common surprise is that quartile and whisker conventions are not universal, so another statistics tool can classify borderline values differently.

Worked example

A concrete input and expected output from the current implementation.

Input

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3

Expected output

A box spanning Q1 = 1 to Q3 = 3, with the median at 2, whiskers ending at 1 and 3, and no outlier points.

The two middle observations are both 2. The middle of the lower half is 1, and the middle of the upper half is 3, giving an interquartile range of 2; every observation lies within the plotted non-outlying range.

How the result is produced

Quartile construction

For each data set, values are ordered before the median and quartiles are located. The box covers the interval from Q1 to Q3, so its length represents the interquartile range, and the internal line marks the median. Repeated values can make a quartile, median, and whisker share the same position.

Whiskers and outliers

The whiskers show the range retained as non-outlying, while observations classified outside that range appear as separate marks. Whisker endpoints therefore need not equal the overall minimum and maximum. A distant point can expand the apparent scale without changing the box much because the box is determined by the middle portion of the ordered data.

Good uses

Compare the medians and score spreads of several classes or test groups.
Check a batch of sensor measurements for isolated readings before deeper analysis.
Summarize response-time samples whose long tails are difficult to judge from raw lists.

Limits and checks

An outlier mark is a rule-based statistical flag, not proof that the observation is erroneous.
A box plot can conceal clusters, gaps, and sample size, so different data sets may produce nearly identical boxes.
Quartile and whisker conventions vary; borderline values may be plotted differently by another application.

Common questions

Does the median line show the average?

No. The median is the middle of the ordered observations, or the midpoint of the two middle observations when the count is even. The arithmetic mean uses every value and is not ordinarily encoded by the median line. Calculate the mean separately if the question depends on total magnitude rather than rank.

Why does another box plot mark different outliers?

Different tools may use different definitions for sample quartiles, especially when the data set is small or a percentile falls between observations. Whisker and outlier conventions can also differ. Compare the reported Q1, median, Q3, and whisker endpoints before assuming either chart is wrong, and check that both tools parsed the same values.

References and verification

The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.