A box plot (also called a box and whisker plot) compresses an entire dataset into five numbers and draws them as a compact diagram. It's the standard chart for comparing the spread and center of multiple groups.
Use the free box plot maker to calculate quartiles and outliers from pasted or grouped data.
The five numbers behind a box plot
Every box plot is built from five statistics — the five-number summary:
| Part | Statistic | Position in chart |
|---|---|---|
| Q1 | 25th percentile | Bottom of the box |
| Median (Q2) | 50th percentile | Line inside the box |
| Q3 | 75th percentile | Top of the box |
| Lower whisker | Non-outlier minimum | Bottom of the lower line |
| Upper whisker | Non-outlier maximum | Top of the upper line |
Plus outlier dots: individual points beyond the whiskers.
The IQR and what the box represents
- IQR (Interquartile Range) — the height of the box. Calculated as Q3 − Q1. Represents the range of the middle 50% of your data.
- Tall box — high variability. The middle half of values is spread across a wide range.
- Short box — low variability. The middle half of values clusters tightly.
- Whisker length — extends 1.5 × IQR from each edge of the box. This is the boundary for outlier detection.
- Outlier — any point beyond the whiskers. Plotted as an individual dot.
How whiskers and outliers are calculated
The whiskers don't extend to the absolute minimum and maximum — they stop at the last data point within 1.5 × IQR of the box.
Lower whisker = smallest value ≥ (Q1 − 1.5 × IQR)
Upper whisker = largest value ≤ (Q3 + 1.5 × IQR)
Any data point outside these limits is flagged as an outlier and plotted individually. Outliers don't get absorbed into a bin — they appear as individual points.
Reading skewness from a box plot
The position of the median line inside the box reveals the distribution's skewness:
- Median centered in the box → roughly symmetric distribution. Values spread evenly above and below the middle.
- Median near the bottom of the box → right-skewed. More values cluster near the lower end; the upper tail stretches further.
- Median near the top of the box → left-skewed. More values cluster near the upper end; the lower tail stretches further.
You can also compare whisker lengths: a much longer upper whisker suggests a longer right tail even if the box itself looks symmetric.
Comparing groups
A single box plot summarizes one dataset. Multiple box plots in one chart — each representing a different group — is what box plots are built for.
Side-by-side box plots let you quickly answer:
- Which group has a higher median?
- Which group has more variability?
- Does one group produce more outliers?
- Do the groups overlap significantly?
This is why box plots appear in research papers, clinical trials, and A/B test reports often when the main question is how groups compare.
Box plot vs histogram
| Box plot | Histogram | |
|---|---|---|
| Shows distribution shape | Summary only | Full shape |
| Shows quartiles explicitly | Yes | No |
| Shows outliers explicitly | Yes | Hidden in bins |
| Good for group comparison | Excellent | Difficult |
| Good for single dataset exploration | Less detail | Better |
| Works with small datasets | Yes (≥4) | Needs 20+ |
Use a box plot to compare groups. Use a histogram to see the full shape of a single distribution.
When to use a box plot
- Comparing test scores, salaries, or response times across groups
- Detecting outliers in a dataset
- Summarizing a dataset for a report or publication
- Visualizing results of an experiment with multiple conditions
FAQ
What's the difference between a box plot and a violin plot?
A violin plot is a box plot combined with a density plot — it shows the distribution shape (like a histogram) wrapped around the summary statistics. Violin plots reveal whether a distribution is bimodal; box plots do not.
Can I have more than one box per chart?
Yes — that's the primary use case. A box plot with one box is just a summary. A box plot with several boxes, one per group, is where comparisons happen.
Why doesn't the median split the box in half?
The median marks the 50th percentile, not the midpoint between Q1 and Q3. If your data is skewed, the distance from Q1 to median will differ from the distance from median to Q3 — which is exactly what a skewed median position is showing you.
What does it mean if there are many outlier dots?
Many outliers can indicate heavy-tailed data, a mixture of populations, or data collection issues. It's worth investigating whether the outliers are real measurements or errors.
References
How this guide is reviewed
This guide is maintained by the ChartsMakers Editorial Team and reviewed for statistical accuracy, product behavior, and clarity. Sources used for factual checks are listed in the References section. See our editorial policy.