Box Plot Maker

A box plot (box and whisker plot) is a chart that shows how a set of numbers is spread out using five values, the five-number summary: the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. The box runs from Q1 to Q3 and holds the middle 50% of the data, the line inside it is the median, and the whiskers reach out to the smallest and largest values that are not outliers.

John Tukey introduced it in Exploratory Data Analysis (1977). Box plot, box and whisker plot, box-and-whisker diagram and box chart all mean the same thing. It is the standard way to compare several groups at a glance, from class test scores to measurements in a lab report.

Read one box plot from the middle out:

• The line in the box is the median: half the values are below it, half above.
• The box spans Q1 to Q3, the middle 50% of the data. Its length is the interquartile range (IQR), a measure of spread that ignores extreme values.
• The whiskers show the rest of the range, up to the most extreme values that are not outliers.
• Separate dots are outliers: values more than 1.5 × IQR below Q1 or above Q3.
• Skew: if the median sits near one end of the box, or one whisker is much longer, the data are skewed toward the longer side. Turn on Mark the mean: a mean (◇) above the median points to right skew, below it to left skew.

To compare groups, look at the medians first (which group is typically higher), then the box lengths (which group is more spread out), then the whiskers and outliers. If the boxes barely overlap, the groups clearly differ; if they overlap a lot, the difference in medians may be small compared with the spread. A box plot does not show how many values each group has or whether the data have two peaks, so report n, and switch to the violin plot maker when the shape of the distribution matters.

Raw values, one observation per cell, in any of these layouts:

Tabs (what spreadsheets copy), commas, semicolons and spaces all work, columns can have different lengths, and cells such as NA are skipped and counted under the box.

A five-number summary, when that is all you have: switch to the 5-number summary tab and type one group per line, for example Class A: 52, 64, 71, 80, 95 in the order min, Q1, median, Q3, max. A table copied with the header group, min, q1, median, q3, max works too. With only five numbers the tool cannot know the outliers, the mean or n, so it draws whiskers to the min and max.

• Excel (2016 and later) has a built-in Box and Whisker chart: select the data, then Insert › Insert Statistic Chart › Box and Whisker. Its quartile calculation is a format setting on the series (inclusive or exclusive median), so check that it matches the method your course uses.
• Google Sheets has no box plot chart type. The closest is a candlestick chart built from a min, Q1, Q3, max table, which is why many people paste their columns into a tool like this one instead.
• R: boxplot(value ~ group, data = df) uses Tukey's hinges; ggplot(df, aes(group, value)) + geom_boxplot() uses quantile() type 7.
• Python: matplotlib.pyplot.boxplot and seaborn.boxplot use NumPy's linear percentiles, the same as Excel INC / R / Python here.

If you already work in R or Python, code is the reproducible route. Use this page when you need the figure now, want the five-number summary checked against your own working, or need a box plot from a five-number summary that spreadsheets cannot plot directly.

A notch narrows the box around the median. Its height is the median ± 1.58 × IQR / √n (McGill, Tukey and Larsen, 1978), the same formula as R's boxplot(notch = TRUE). If the notches of two boxes do not overlap, that is rough evidence that their medians differ. It is a visual guide, not a significance test, and the notch is only meaningful with a reasonable number of values per group: for small groups it can stick out past the box, so the tool clips it at Q1 and Q3.

Whoever reads your figure, a teacher, a lab supervisor or a reviewer, will look for the same things:

1. n per group, under each box (on by default) or in the caption.
2. What the whiskers show: 1.5 × IQR or min to max. Readers cannot tell from the picture alone.
3. The quartile method, if your numbers will be checked by hand or against other software.
4. Units on the value axis: Commute time (minutes), not Time.
5. The data points for small groups (under about 20 values), so readers see how few there are.

A caption you can adapt: “Box plots of commute time by mode of transport. Boxes show the median and interquartile range; whiskers extend to the most extreme values within 1.5 × IQR; open circles are outliers. n = 30 per group.”