Box Plot Generator

Quartiles — median-split (Moore & McCabe, exclusive): the data is sorted and split at the median, leaving the median itself out when the count is odd; Q1 and Q3 are the medians of the two halves.

Whiskers — Tukey convention: each whisker extends to the most extreme data point still within 1.5 × IQR of the box, not to a computed fence value and not necessarily to the minimum or maximum.

Outliers: values beyond either fence are plotted as individual dots rather than absorbed into a whisker.

A box plot compresses an entire distribution into one horizontal figure. The box spans the middle 50% of the data, from Q1 to Q3, and the line cutting through it marks the median. The whiskers reach outward to the most extreme observations that still count as ordinary, and anything past them appears as an individual dot demanding an explanation. Reading left to right you see, in order: extreme low values, the ordinary low tail, the crowded middle, the ordinary high tail, and extreme high values.

Note that the whiskers stop at actual data points, not at the fences themselves. The fences are invisible thresholds; the whiskers snap inward to the last real observation on each side. That is why a whisker often ends at an oddly specific value rather than a round number.

Two perfectly correct box plot tools can draw different boxes from the same data, because quartiles have several published definitions. This generator uses the exclusive median-split method of Moore and McCabe, the convention taught in most introductory statistics courses and used consistently across this site — the quartile calculator and the five number summary calculator will always agree with the chart drawn here.

Spreadsheets typically interpolate instead: Excel's QUARTILE.INC can place Q1 and Q3 a fraction away from the values shown here on small data sets. Neither answer is wrong, but a homework grader or a journal reviewer will expect you to name the convention — which is exactly why this page states both the quartile method and the whisker rule up front.

The 1.5 multiplier comes from John Tukey, who invented the box plot in the 1970s. Because the interquartile range measures the spread of the middle half of the data, it cannot be inflated by the very outliers it is screening for — the weakness that makes standard-deviation-based rules unreliable. For roughly bell-shaped data, the zone between the fences covers about 99.3% of observations, so a point outside it is rare enough to plot individually.

A dot beyond the fence is a flag, not a conviction. It may be a typo, a measurement glitch, or a genuine extreme event worth its own paragraph in your report. The outlier calculator applies the same fences numerically when you need the flagged values as a list rather than a picture.

A mean reduces a data set to one number; a box plot keeps its shape. Skew shows up instantly: if the median line sits close to Q1 and the upper whisker stretches far to the right, the data leans toward high values. Spread is the width of the box, robust to whatever the extremes are doing. And unusual observations are physically separated from the body of the data instead of being silently averaged in.

The format really pays off in comparisons. Stacking box plots of the same measurement across groups — test scores by class, response times by server, yields by field — reveals differences in center, spread, and outliers in a single glance, with no distributional assumptions required.

A help desk logs eight ticket resolution times, in minutes: 1, 45, 50, 52, 55, 58, 60, 120 — one auto-closed duplicate, six routine tickets, and one escalation. The generator proceeds like this:

1. Sort: 1, 45, 50, 52, 55, 58, 60, 120.
2. Median: with 8 values, average the 4th and 5th: (52 + 55) ÷ 2 = 53.5.
3. Split into halves: lower half 1, 45, 50, 52 and upper half 55, 58, 60, 120.
4. Quartiles: Q1 = (45 + 50) ÷ 2 = 47.5; Q3 = (58 + 60) ÷ 2 = 59; IQR = 59 − 47.5 = 11.5.
5. Fences: 47.5 − 1.5 × 11.5 = 30.25 and 59 + 1.5 × 11.5 = 76.25.
6. Outliers: 1 and 120 fall outside the fences, so both are drawn as dots.
7. Whiskers: the most extreme values inside the fences are 45 and 60, so the whiskers stop there — not at 1 or 120, and not at the fence values 30.25 and 76.25.

The resulting picture tells the honest story: a tight box from 47.5 to 59 says routine tickets take about an hour, while the two dots expose the auto-closed record and the escalation. A bare average of 55.1 minutes would have hidden both.