Posters · Glossary
What is a box plot?
A box plot, or box and whisker plot, summarises a set of numbers with five values: the minimum, the lower quartile, the median, the upper quartile and the maximum. The box spans the middle half of the data, a line marks the median, whiskers reach the furthest values within a set range, and points beyond them are drawn as outliers.
A box plot shows in one glance what a bar chart of means hides: how spread out the data are, whether they lean one way, and which values sit far from the rest.
Indunil Asanka · Co-founder
4 min read · Published
| Part of the box plot | Value | How it is found |
|---|---|---|
| Median | 13 | The middle value, the 6th of 11 |
| Lower quartile, Q1 | 8 | Median of the lower five values |
| Upper quartile, Q3 | 21 | Median of the upper five values |
| Interquartile range | 13 | Q3 minus Q1, the length of the box |
| Whiskers | 4 to 26 | Furthest values within 1.5 IQR of the box, here up to 40.5 |
| Outlier | 58 | Beyond 1.5 IQR above Q3, drawn as a point |
How to read one
Start with the line inside the box: half the values are below it, half above. The box itself holds the middle 50 percent, so a tall box means widely spread data and a short one means tightly clustered data. If the median sits off centre, or one whisker is much longer, the data are skewed. Points beyond the whiskers are outliers worth a second look, either real extreme values or errors.
How it is built
Sort the data, find the median, then the quartiles that split each half again. The interquartile range is the distance between them. Under the common Tukey convention, whiskers extend to the most extreme values within 1.5 times the IQR from the box, and anything further is plotted individually. The NIST Engineering Statistics Handbook describes this construction. Different software calculates quartiles in slightly different ways, so state the method on a poster when exact quartiles matter.
When to use it instead of a bar chart
Use a box plot when the spread or skew of the data matters, when comparing distributions across groups, and when there are outliers a mean would hide. Waiting times, lengths of stay, costs and reaction times are classic cases, because they are usually skewed with a long upper tail. A Nature Methods column on visualising samples recommends box plots over bars with error bars for exactly this reason. For very small samples, show the individual points as well, since five numbers summarise little when there are only six values.
Common mistakes
Not saying what the whiskers represent, since some charts draw them to the minimum and maximum. Comparing boxes from groups of very different sizes without giving the numbers. Treating outliers as errors and deleting them without explanation. Drawing a box plot of a few values where a dot plot would be more honest. And using a box plot for data that are not continuous, such as a five point rating, where most of the box collapses onto one value.
Showing it on a poster board
The poster tab's chart figures offer ten kinds, vertical and horizontal bar, stacked column, line, area, pie, donut, radar, waterfall and waffle, and none of them is a box plot. A five number summary can still be shown: in a table on one of the three boards that carry a table slot, or as key numbers in stat blocks, which 26 of the 40 boards have. State the median and IQR in the text, and if a box plot is essential, the poster may be better built where you can draw one.
Questions people ask
What is the difference between a box plot and a histogram?
A histogram shows the full shape of a distribution as bars over value ranges, including several peaks if there are any. A box plot compresses it to five numbers and outliers, which makes it easier to compare many groups side by side but hides features such as two separate clusters. Use a histogram for one detailed distribution and box plots for comparisons.
Do box plots show the mean?
Not by default. The line in the box is the median. Some software adds a marker, often a small cross or diamond, for the mean. When the mean and median differ noticeably, the data are skewed, which is one reason analysts like to see both. If you add the mean, say so in the caption.
What does a long whisker mean?
That values stretch further in that direction, so the data are spread more on that side. A long upper whisker with a median near the bottom of the box is the typical pattern of right skewed data, such as incomes or waiting times, where most values are low and a few are much higher.
How many data points do you need for a box plot?
There is no strict minimum, but with fewer than about ten values the quartiles are unstable and the plot can mislead. For small groups, plot the individual values, perhaps with the median marked, so readers see the actual data rather than a summary of very little.
What are notches on a box plot?
Some box plots draw a notch around the median showing a rough confidence interval for it. If the notches of two boxes do not overlap, that is informal evidence the medians differ. Notches are a visual guide, not a formal test, and should be explained in the caption.
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