Free tool
Box plot maker
A box plot shows a group of measurements as five numbers: the smallest, the first quartile, the median, the third quartile and the largest, with points far from the box marked as outliers. Paste one or more groups below to draw it.
IQRequalsQ3 − Q1
FencesequalsQ1 − 1.5 × IQR and Q3 + 1.5 × IQR
Outlierequalsany value outside the fences
3 groups, 34 values read. Start each line with a name and a colon, then the numbers. Use a point for decimals.
What the numbers are, with units
Pre-filled with the worked example. Your data stays in your browser.
Outliers
1
Points beyond 1.5 × IQR from the box, across 3 groups.
Groups
3
Values
34
Quartiles use the inclusive method, the same as Excel's QUARTILE.INC.
| Group | n | Min | Q1 | Median | Q3 | Max | IQR | Mean | Outliers |
|---|---|---|---|---|---|---|---|---|---|
| Shift A | 11 | 41 | 44 | 46 | 47.5 | 51 | 3.5 | 45.8182 | none |
| Shift B | 12 | 40 | 44.5 | 46.5 | 48.5 | 63 | 4 | 47.3333 | 63 |
| Shift C | 11 | 38 | 40.5 | 42 | 43.5 | 45 | 3 | 41.8182 | none |
Next step
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How to use it
Compare groups on one scale
Type one group per line. Start with a name and a colon, then the readings, for example Line 1: 12 14 15 13. Separate values with spaces, commas or semicolons. Use up to 12 groups.
Read the box. The line inside is the median. Half of the readings sit inside the box, so a tall box means a wide spread. A median off-centre in its box means the data are skewed. The red diamond is the mean; when it sits far from the median, a few large values are pulling it.
Check the outliers. Go and look at each marked reading: a mistyped value, a different lot or a real event. For the shape of one group, draw it with the histogram maker, and for whether a stable process fits its limits use Cp and Cpk.
Worked example
Illustrative numbers, not a benchmarkCycle times in seconds for the same operation on three shifts, 11 or 12 readings each.
- 1Shift A: Q1 = 44, median = 46, Q3 = 47.5, so IQR = 3.5 and there are no outliers.
- 2Shift B: Q1 = 44.5, median = 46.5, Q3 = 48.5, so IQR = 4 and the upper fence is 48.5 + 6 = 54.5.
- 3Shift B has a reading of 63, above the fence, so it is plotted as an outlier. The upper whisker stops at 52.
- 4Shift C: Q1 = 40.5, median = 42, Q3 = 43.5, IQR = 3, no outliers.
Embed this tool
Teaching this, or writing about it? Paste this code into your site, course page or intranet and the tool works right there. It is free, with no sign-up.
<iframe src="https://www.theleansuite.com/tools/box-plot-maker/embed" title="Box plot maker by LeanSuite" width="100%" height="2400" style="border:0;max-width:1000px" loading="lazy" allow="clipboard-write"></iframe>
<p style="font:13px/1.4 sans-serif"><a href="https://www.theleansuite.com/tools/box-plot-maker">Box plot maker</a> by LeanSuite</p>How LeanSuite helps
LeanSuite's AI Root Cause Analysis helps teams work from a difference like this one to its cause, and its corrective action tracking follows the fix through to closure.
See Quality ImprovementRead more
- Free template: Histogram template
- Free template: X-bar and R control chart template
- Statistical process control in the lean glossary
- Seven basic quality tools in the lean glossary
- Lean Six Sigma Tools: 13 Common Tools and When to Use Them
- Problem-solving methods: which one to use and when
- Histogram guide: a different view of the same spread
- Control chart guide: spread over time
- Histogram maker: the shape of one sample
FAQ
Box plot maker: common questions
A box plot, also called a box and whisker plot, summarises a group of measurements with five numbers: the smallest, the first quartile, the median, the third quartile and the largest. The box runs from the first to the third quartile with a line at the median. Whiskers reach the furthest points inside the fences, and points beyond them are drawn individually as outliers.
Find the interquartile range, IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is plotted as an outlier. The whiskers stop at the most extreme values still inside those fences. This is Tukey's rule, the usual default. An outlier is a prompt to look at that reading, not permission to delete it.
This tool sorts the values and interpolates between neighbouring ones, which is the method behind Excel's QUARTILE.INC and PERCENTILE.INC. Other software uses slightly different rules, so a small data set can give a slightly different Q1 and Q3 elsewhere. With 30 or more values the difference is negligible.
When you are comparing groups, such as shifts, machines, suppliers or lots. Several boxes side by side on one scale show differences in centre and spread at a glance, where several histograms would be hard to compare. A histogram is better for the shape of one group, and it can show two peaks that a box plot hides.
Five is the least that makes the quartiles meaningful, and 10 or more per group is better. The tool draws a group with fewer than five but tells you the quartiles are rough. If you have a group of only two or three readings, show the points themselves.
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