About the Box Plot Maker
This box plot maker draws a box-and-whisker plot from your data in seconds. Paste a list of numbers — or several labelled data sets, one per line, such as “Class A: 62, 68, 71 …” — and it sorts each group, finds the quartiles and median, draws the box from Q1 to Q3 with a line at the median, extends the whiskers to the most extreme values inside the 1.5 × IQR fences and marks any outliers as separate dots. You can also show the mean and switch the whiskers to run all the way to the minimum and maximum.
Box plots are the quickest way to compare the centre, spread and skew of several groups side by side, which is why they appear in every introductory statistics and AP Statistics course. Teachers use this generator to compare class results, students use it for homework and projects, and analysts use it to compare response times, prices or measurements across categories. The summary table lists each group’s five-number summary, IQR, mean and outliers so you can quote exact values.
Quartiles follow the method you choose: median of halves (TI-83/84 and most textbooks), Excel QUARTILE.INC (also NumPy and Google Sheets) or Excel QUARTILE.EXC. The plot is drawn in your browser, so your data never leave your device, and it can be saved as an SVG image.
How to use the box plot maker
- 1Paste your numbers, or several data sets each on its own line starting with a label and a colon.
- 2Choose the quartile method your course or software uses.
- 3Pick Tukey whiskers to see outliers, or min-to-max whiskers.
- 4Compare the boxes: the median line shows the centre and the box length shows the spread.
- 5Download the plot as an SVG and copy values from the summary table.
Formula and method
Each data set is sorted and summarised by its quartiles. The box runs from the first quartile Q1 to the third quartile Q3, so its length is the interquartile range and it contains the middle 50% of the values; the line inside the box is the median. In a Tukey box plot the whiskers extend to the smallest and largest observations that lie within 1.5 IQRs of the box, and anything beyond those fences is plotted individually as a possible outlier.
With the minimum-to-maximum option the whiskers simply reach the smallest and largest values and no outliers are shown. The quartile method changes Q1 and Q3 slightly on small samples: median of halves excludes the median from both halves when n is odd, QUARTILE.INC interpolates at position 1 + p(n − 1) and QUARTILE.EXC at p(n + 1).
- Q1, Q3
- First and third quartiles (box edges)
- IQR
- Interquartile range, the length of the box
- 1.5·IQR
- Tukey’s fence distance used to flag outliers
Worked examples
Two classes’ test scores (median of halves)
For Class A (n = 12) the lower half 62–77 has median 72.5 and the upper half 79–95 has median 83.5, so the box spans 72.5–83.5 around a median of 78. In Class B, Q1 = 62 and Q3 = 82.5 give a lower fence of 62 − 1.5 × 20.5 = 31.25, so the score of 31 is drawn as an outlier.
One data set with an outlier
Q1 = 1.7 and Q3 = 2.6, so the upper fence is 2.6 + 1.5 × 0.9 = 3.95. The whisker stops at 3.0, the largest value inside the fence, and 6.8 is plotted as a separate outlier point.
Same data, whiskers to min and max
With min-to-max whiskers the upper whisker stretches all the way to 6.8 and no outliers are drawn — the simpler style used in some introductory courses.
Frequently asked questions
How do you make a box and whisker plot?+
Find the five-number summary (minimum, Q1, median, Q3, maximum). Draw a box from Q1 to Q3 with a line at the median, then draw whiskers out to the smallest and largest values that are not outliers, and mark any outliers as dots.
How are outliers shown on a box plot?+
Values more than 1.5 × IQR below Q1 or above Q3 are plotted as individual points beyond the whiskers. The whiskers stop at the most extreme values that are still inside those fences.
How do I compare two box plots?+
Compare the median lines for the centre, the box lengths (IQRs) for spread, and the whisker lengths and median position inside the box for skew. If one group’s median lies outside the other group’s box, the difference is usually noticeable.
What does it mean if the median is not in the centre of the box?+
It suggests skew. A median close to Q1 with a longer upper part of the box and upper whisker indicates right skew; a median close to Q3 indicates left skew.
Why does my box plot look different from my calculator’s?+
Software uses different quartile definitions and whisker rules. TI-84 uses medians of halves, Excel uses QUARTILE.INC or QUARTILE.EXC, and some plots draw whiskers to the minimum and maximum. Match the options above to your source.