Box Plot Maker
Paste or type your numbers below — commas, spaces, newlines or a pasted spreadsheet column all work — and the tool draws a box-and-whisker plot alongside the five-number summary it was built from. Everything runs in your browser; the values never leave your device.
Reading Every Part of the Box
A box plot compresses a whole distribution into five numbers. Each one has a fixed place in the drawing:
| Element | What it marks | How to read it |
|---|---|---|
| Line inside the box | The median (Q2) | Half the values fall below it, half above |
| Lower box edge | Q1, the 25th percentile | A quarter of the values sit below this |
| Upper box edge | Q3, the 75th percentile | A quarter of the values sit above this |
| Box length | The interquartile range (IQR = Q3 − Q1) | The span of the middle 50% of the data |
| Whiskers | The reach of the non-outlying data | They stop at real data points, not at fixed distances |
| Separate points | Values beyond the fences | Candidates for closer inspection |
The single most useful property is that the box always contains exactly half the data. A short box means the middle of your distribution is tightly packed; a long one means it is spread out. Because both edges are percentiles rather than averages, neither is dragged around by an extreme value the way a mean or a standard deviation would be.
Where the Whiskers Stop
The whiskers are the part people most often get wrong. They do not run to the minimum and maximum by default, and they are not a fixed multiple of anything. The rule John Tukey set out in Exploratory Data Analysis (1977) works in two steps:
- Compute the fences: a lower fence at Q1 − 1.5 × IQR and an upper fence at Q3 + 1.5 × IQR.
- Draw each whisker to the most extreme actual data point that still falls inside its fence.
So a whisker always ends on a real observation. The fences themselves are never drawn. Anything past a fence is plotted as an individual point.
Why 1.5? It is a convention chosen for its behaviour on roughly bell-shaped data, where the fences land about 2.7 standard deviations from the centre and flag around 0.7% of observations — about one point in every 143. That rate is deliberately low enough that a flagged point is worth a look, and high enough that flags still appear in clean data. In a sample of 50 values, seeing one point beyond a fence is entirely ordinary. Seeing six is a signal that the distribution has heavy tails, not that you have six bad records.
Working the Quartiles Out by Hand
Take nine support tickets and the hours each took to get a first reply:
14, 61, 17, 12, 30, 19, 38, 15, 24
Sort them: 12, 14, 15, 17, 19, 24, 30, 38, 61. With nine values (n = 9) the interpolation positions all land on whole numbers, counting from position 0:
- Q1 sits at 0.25 × (9 − 1) = position 2 → the third value → 15
- Median sits at 0.5 × 8 = position 4 → the fifth value → 19
- Q3 sits at 0.75 × 8 = position 6 → the seventh value → 30
From there:
- IQR = 30 − 15 = 15
- 1.5 × IQR = 22.5
- Lower fence = 15 − 22.5 = −7.5 — no value is below it, so the lower whisker runs to the minimum, 12
- Upper fence = 30 + 22.5 = 52.5 — the 61 is beyond it, so it is drawn as an outlier and the upper whisker stops at 38
Note what the mean would have told you. It is 230 ÷ 9 = 25.6 hours, well above the median of 19, because that one 61-hour ticket pulls it up. The median barely notices. When one number has to stand for "typical", a skewed distribution like this is exactly the case where the median is the honest choice.
Reading Skew from an Off-Centre Median
In the example above, the median at 19 sits 4 units above Q1 and 11 below Q3. That asymmetry is the chart telling you the data is right-skewed: the upper quarter of the middle 50% is stretched out. The whiskers agree — 3 units below the box, 8 above.
The general reading:
- Median near the centre of the box, whiskers similar in length — roughly symmetric.
- Median pushed toward the lower edge, longer upper whisker — right skew. Typical of durations, incomes, page load times, and anything else bounded below by zero with no ceiling.
- Median pushed toward the upper edge, longer lower whisker — left skew. Less common, but usual for scores near a maximum, like test results with a ceiling of 100.
Ticking Show mean adds a dashed line at the arithmetic mean plus a marker spanning one standard deviation either side. Comparing that line's position to the median line is the fastest visual skew check there is: mean noticeably to the right of the median means right skew, and the size of the gap tells you how much the tail is pulling.
Comparing Groups Is What Box Plots Are For
A single box plot is a modest chart — a histogram tells you more about one dataset. The reason box plots persist is that they stack. Because each group compresses to a single narrow shape on a shared axis, ten or twenty groups fit side by side without overlapping, and differences in centre, spread and skew are all readable at once. Ten histograms in a row are far harder work.
This tool plots one dataset at a time, so to compare groups, generate each in turn and compare their five-number summaries directly — the summary cards below the chart give you the exact figures. What matters when you do compare is what you compare: overlapping boxes mean the groups' middle halves genuinely overlap, and a difference in medians that is small relative to the box lengths is unlikely to be worth acting on.
The Blind Spot: Two Clusters Look Like One Spread
This is the failure worth memorising. Consider these two sets of nine values:
- Set A: 10, 20, 30, 40, 50, 60, 70, 80, 90
- Set B: 10, 27, 30, 33, 50, 67, 70, 73, 90
Run either through the tool. Both give a minimum of 10, Q1 of 30, a median of 50, Q3 of 70 and a maximum of 90 — so both draw exactly the same box plot, right down to the whiskers. But Set A is an even spread, while Set B is two tight clusters near 30 and 70 with almost nothing between them. Those are completely different stories about your data, and the box plot cannot tell them apart.
Bimodality like this usually means two populations have been mixed: two server regions, two customer segments, two versions of a product. It is often the most important thing in the dataset, and a box plot will hide it every time. The defences are cheap:
- Tick Show all points to overlay the raw values on the box. On modest datasets the gap becomes obvious immediately, and Point jitter in Advanced Settings spreads overlapping dots so you can see density.
- Plot the same numbers as a histogram first. Checking the shape before summarising it is the right order of operations.
When to Reach for a Different Chart
- Fewer than about ten values. Plot the points themselves. A box built on five numbers derived from eight observations implies a precision that is not there.
- Categories rather than a distribution. If each label has exactly one value — revenue by region, response time by endpoint — you want a dot plot or a bar chart, not a box plot.
- The audience has never seen one. Box plots are compact but not self-explanatory; the whisker rule in particular has to be learned. For a general audience a histogram usually lands better.
- You need to show the shape. Any time multimodality, gaps or unusual clumping is the point, use a histogram.
Everything else — comparing spread across groups, spotting skew, screening a batch of numbers for extreme values before you model them — is what this chart does better than anything else its size.