A box plot, also called a box-and-whisker plot, is a chart that summarizes the distribution of a numeric variable through five values: the minimum and maximum within a defined range, the first and third quartiles, and the median. In data visualization, it is the standard compact way to show center, spread, skew and outliers at once and to compare these properties across several groups.
The box plot was popularized by the statistician John Tukey in the 1970s as part of exploratory data analysis. Its strength is density of information: a single narrow shape replaces a full histogram, so dozens of groups can be placed side by side on one axis.
Anatomy of a box plot
A box plot consists of a box spanning the interquartile range, a line for the median, whiskers that extend toward the extremes, and individual points for outliers. Each element answers a specific question about the data, so reading a box plot means reading these elements one at a time.
The interquartile range (IQR) is the distance between the first quartile, below which 25% of values fall, and the third quartile, below which 75% fall. The box therefore always contains the middle half of the observations, regardless of how the data are distributed.
The table below lists the elements of a standard Tukey box plot.
| Element | Definition | What it reveals |
|---|---|---|
| Median line | 50th percentile | Typical value, robust to outliers |
| Box edges | First and third quartiles | Spread of the middle 50% |
| Box length | Interquartile range | Variability without extreme values |
| Whiskers | Furthest points within 1.5 IQR of the box | Range of ordinary values |
| Outlier points | Values beyond the whiskers | Unusual observations to investigate |
| Optional mean marker | Arithmetic mean | Skew when it differs from the median |
Whisker conventions and variants
Box plots do not share one universal rule for whiskers, and this is the most common source of misread charts. The Tukey convention extends each whisker to the most extreme data point within 1.5 times the IQR from the box and plots anything beyond as an outlier, but other conventions are also in use.
| Convention | Whisker end | Consequence |
|---|---|---|
| Tukey 1.5 IQR | Last point within 1.5 IQR | Outliers shown individually |
| Minimum and maximum | Smallest and largest values | No outliers shown, extremes dominate |
| Percentile whiskers | For example 5th and 95th percentile | Fixed share of points beyond whiskers |
| Standard deviation | Mean plus or minus one or two SD | Assumes roughly symmetric data |
Several variants extend the basic design. Notched box plots add a notch around the median whose width approximates a confidence interval, so non-overlapping notches suggest that medians differ. Variable-width box plots scale the box width to the square root of the group size, and violin plots replace the box with a mirrored density curve that shows the full shape of the distribution.
Box plot compared with other distribution charts
The box plot is one of several charts for showing distributions, and the right choice depends on how many groups must be compared and how much shape detail matters. Its main weakness is that it hides the shape between the quartiles.
| Chart | Shows | Best suited for |
|---|---|---|
| Box plot | Quartiles, median, outliers | Comparing many groups compactly |
| Histogram | Frequency per value bin | Detailed shape of one distribution |
| Violin plot | Smoothed density and quartiles | Shape comparison across a few groups |
| Strip or dot plot | Every individual value | Small samples, under about 50 points |
| Scatter plot | Relationship of two variables | Correlation, not single distributions |
A bimodal distribution, with two separate peaks, can produce a box plot that looks identical to a unimodal one. When shape matters, a histogram or violin plot should accompany the box plot, or individual points can be overlaid as a jittered strip on top of the boxes.
Reading and designing box plots
Reading a box plot starts with the median position, then the box length, then the symmetry of the box and whiskers, and finally the outliers. Each step corresponds to a property of the distribution.
| Pattern | Interpretation | Follow-up |
|---|---|---|
| Median near the lower box edge | Right-skewed data | Consider a log scale |
| Long upper whisker | Tail of high values | Check for heavy tails |
| Very short box | Values tightly clustered | Check for rounding or capping |
| Many outliers on one side | Skew or mixed populations | Split by another variable |
| Boxes not overlapping | Clear difference between groups | Confirm with a statistical test |
- State the whisker rule in a caption or note, because readers cannot infer it from the chart.
- Show group sizes, since a box built from eight values looks as authoritative as one built from eight thousand.
- Sort groups by median when the categories have no natural order.
- Use a log scale for strongly skewed quantities such as income, latency or file size.
Limitations and misinterpretations
The box plot compresses data aggressively, which makes it efficient but also easy to over-interpret. Many viewers outside statistics are unfamiliar with quartiles and may read the box as a range of all values or as a confidence interval.
Outlier points in a box plot are flagged by a rule, not by meaning. In large datasets with long tails, the 1.5 IQR rule can mark hundreds of perfectly valid observations as outliers, so they should be investigated, not removed automatically. Conversely, with very small samples, quartiles are unstable and the box can change substantially with a single added value.
In everyday language
A box plot is a quick sketch of how numbers are spread out. The box shows where the middle half of the values lie, and the line inside the box marks the middle value.
The lines sticking out show the usual lowest and highest values, and any dots beyond them are unusually small or large cases. Putting several boxes side by side is like lining up classes by height: one glance shows which group is taller and which is more varied.
Seen in the real world
An operations team monitors the response times of an online service across eight data center regions. Averages look similar, around 120 milliseconds, but customers in some regions still complain about slow pages.
The team plots one box plot per region on a logarithmic axis. Six regions show compact boxes with few outliers, while two have long upper whiskers and many outlier points above one second, even though their medians match the others.
The chart directs attention to the tail rather than the average. Investigation finds an overloaded cache cluster serving the two regions, and after capacity is added, their boxes and whiskers shrink to match the rest, which the team confirms by repeating the same chart a week later.