Box Plot Maker

About the Box Plot Maker

Paste numbers — one column per group, or a column of group names beside a column of values — and get a box-and-whisker plot of every group: the box from the first to the third quartile, a line at the median, whiskers to the furthest values inside the 1.5 × IQR fences and every outlier marked. Add a violin to show the shape of each distribution, jittered points to show every value, and the mean.

Choose how the quartiles are worked out — Tukey’s hinges, Excel’s QUARTILE.INC or QUARTILE.EXC, or the medians of the halves — and read the five-number summary of each group (n, minimum, Q1, median, Q3, maximum) with the IQR, fences, outliers, mean and standard deviation. Your data is read and drawn in your browser; nothing is uploaded.

Common uses

• Comparing test scores, delivery times, prices or measurements across classes, couriers, shops or batches.
• Spotting outliers before averaging or reporting data.
• Showing the spread of survey ratings or response times in a report or slide.
• Checking homework on quartiles, the interquartile range and the five-number summary.
• Seeing whether one group is skewed, has two peaks (a violin shows it) or overlaps the others.

The four quartile methods

Statistics packages disagree on quartiles because there are several reasonable definitions (Hyndman and Fan list nine in Sample Quantiles in Statistical Packages). This tool offers four:

• Tukey’s hinges — the medians of the lower and upper halves of the sorted values, with the median counted in both halves when the count is odd (Tukey, Exploratory Data Analysis).
• Excel QUARTILE.INC — Hyndman–Fan type 7: the value at position (n − 1)·p + 1 of the sorted values, interpolated between neighbours.
• Excel QUARTILE.EXC — Hyndman–Fan type 6: the value at position (n + 1)·p. It needs at least 3 values; Excel shows #NUM! for fewer, and so does this tool (the group is drawn without a box).
• Medians of the halves, median left out — like Tukey’s hinges, but the median is left out of both halves when the count is odd.

All four give the same median, and they differ more for small groups than for large ones. For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 Tukey’s hinges and QUARTILE.INC give Q1 = 25.5 and Q3 = 42.5, while QUARTILE.EXC and the halves without the median give 15 and 43.

Whiskers, fences and outliers

The interquartile range is IQR = Q3 − Q1. Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are outliers; each whisker ends at the furthest value still inside these fences, and outliers are drawn as circles — larger ones beyond 3 × IQR, as in the NIST/SEMATECH e-Handbook of Statistical Methods. A value exactly on a fence counts as inside it.

Choose 3 × IQR to mark only the extreme values, or whiskers to the minimum and maximum to draw no outliers at all (the box and median stay the same).

Violins and points

A violin is a mirrored density curve, wide where values are common and thin where they are rare, so it shows two peaks that a box hides. It is a Gaussian kernel density estimate with Silverman’s rule-of-thumb bandwidth, 0.9 × min(s, IQR / 1.34) × n^−1/5, drawn only between each group’s smallest and largest value (Hintze and Nelson introduced the violin plot in The American Statistician). All violins share one width scale, so a slimmer violin means its values are more spread out.

Points are moved sideways by a small random amount that is the same every time, so equal values do not hide one another and a download matches the screen. Above 5,000 values, every k-th value of each group is drawn; the boxes and the table always use every value.

Reading a box plot

• The box holds the middle half of the values; a taller box means more spread.
• A median line off-centre in the box, or one whisker much longer than the other, means the values are skewed.
• Boxes that do not overlap at all suggest the groups really differ; to test it, use a t-test.
• Small groups give rough quartiles: show the points as well when a group has fewer than about ten values.

Limitations

• Up to 10,000 rows of data and 40 groups; more rows or groups are left out with a note.
• Numbers only: dates and times are not plotted; turn them into numbers (for example days or minutes) first.
• No notches, confidence intervals or significance tests; the violin’s bandwidth follows Silverman’s rule and cannot be changed.
• Files are read in your browser; formulas in Excel files count as their last saved values.

Privacy

Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.