Box Plot Comparison Tool
Example format: a header row like Class A,Class B,Class C, followed by one row of numbers per line, one value per column. Blank or non-numeric cells are skipped automatically. Loading a file switches you to the Enter Data tab with the columns filled in and the comparison generated.
Load one of these ready-made comparisons to see the tool in action, then edit the numbers to match your own data.
Box Plot Comparison Examples
Browse ready-made comparisons or generate your own above
What Is a Box Plot Comparison Tool?
A box plot comparison tool takes several datasets and draws their box plots — also called box-and-whisker plots — on one shared scale, so you can line up medians, spreads, and outliers across groups without recalculating anything by hand. Each box plot on its own summarizes a dataset using five numbers: the minimum, the first quartile, the median, the third quartile, and the maximum. Put several of them side by side on the same axis, and a comparison that would otherwise take a table of statistics — or a wall of raw numbers — becomes something you can read in a few seconds.
This tool computes the five-number summary, the interquartile range, and any outliers for each dataset you enter, then renders the plots as a downloadable SVG. It's part of the free calculators and guides at Statistics Fundamentals, alongside the single-dataset Box Plot Generator and the site's other visual tools.
The Five-Number Summary
Every box plot is built from the same five values. Using a worked example of 12 quiz scores — 62, 68, 71, 74, 75, 77, 79, 80, 82, 85, 88, 95 — here's what each one means and how it's found:
| Statistic | What it tells you | How it's found | Example value |
|---|---|---|---|
| Minimum | The smallest value in the dataset | First value once the data is sorted | 62 |
| Q1 (first quartile) | 25% of the data falls below this value | Median of the lower half of the sorted data | 72.5 |
| Median (Q2) | The middle value; 50% of the data falls below it | Middle of the sorted data | 78 |
| Q3 (third quartile) | 75% of the data falls below this value | Median of the upper half of the sorted data | 83.5 |
| Maximum | The largest value in the dataset | Last value once the data is sorted | 95 |
From there, the interquartile range is IQR = Q3 − Q1 = 83.5 − 72.5 = 11, and the outlier fences sit at Q1 − 1.5×IQR = 56 and Q3 + 1.5×IQR = 100. Since none of the 12 scores fall outside that range, this particular dataset has no outliers under the standard rule.
How to Compare Box Plots
Applications of Box Plot Comparisons
Box Plot Comparisons vs Other Charts
A box plot isn't always the right chart. Here's how it stacks up against the other charts people reach for when comparing groups or exploring a distribution.
| Feature | Box Plot | Histogram | Violin Plot | Dot Plot | Scatter Plot | Bar Chart |
|---|---|---|---|---|---|---|
| Shows distribution shape | Partial | Yes | Yes | Partial | No | No |
| Shows outliers directly | Yes | No | Partial | Yes | Yes | No |
| Shows quartiles / IQR | Yes | No | Partial | No | No | No |
| Shows the median directly | Yes | No | Partial | No | No | No |
| Compares many groups cleanly | Excellent | Fair | Good | Fair | Fair | Good (means only) |
| Works well with large samples | Yes | Yes | Yes | No | Yes | Yes |
Glossary
| Term | Definition |
|---|---|
| Box plot | A chart that displays a dataset's five-number summary as a box with whiskers extending to either side. |
| Five-number summary | The minimum, first quartile, median, third quartile, and maximum of a dataset. |
| Quartile | One of three values (Q1, Q2, Q3) that split ranked data into four equal-sized groups. |
| Interquartile range (IQR) | The distance between the third and first quartiles (Q3 − Q1); the height of the box. |
| Whisker | The line extending from the box to the smallest or largest value that isn't classified as an outlier. |
| Outlier | A value far enough from the rest of the data, conventionally beyond 1.5×IQR from the nearest quartile, that it's plotted as an individual point. |
| Fence | The cutoff value (Q1 − 1.5×IQR or Q3 + 1.5×IQR) used to decide whether a point counts as an outlier. |
| Skewness | A measure of how asymmetric a distribution is; on a box plot it shows up as an off-center median or whiskers of very different lengths. |
Related Topics
Sources & further reading:
- NIST/SEMATECH Engineering Statistics Handbook — Box Plot
- Tukey, J.W. (1977). Exploratory Data Analysis. Addison-Wesley. [Origin of the box-and-whisker plot and the 1.5×IQR outlier rule]
- Khan Academy — Box Plot Review
Frequently Asked Questions
It's a calculator that takes two or more lists of numbers, works out the five-number summary — minimum, Q1, median, Q3, maximum — for each one, and draws the results as box plots on a shared scale. That makes it possible to see at a glance whether groups differ in their typical value, their spread, or the number of unusual observations, without doing the arithmetic by hand.
Line the two plots up on the same axis and look at three things: where the median sits, how tall each box is, and whether the boxes overlap. If the boxes barely overlap, the two groups are probably genuinely different; heavy overlap suggests the difference could just be noise. Enter both datasets in the Enter Data tab above to see this side by side.
A single box plot shows five things about a dataset: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. The box spans Q1 to Q3 — the middle 50% of the data — with a line at the median. Whiskers extend out to the smallest and largest values that aren't flagged as outliers, and anything beyond that is plotted as an individual point.
The standard method, often called Tukey's rule, flags any value more than 1.5 times the interquartile range (IQR) below Q1 or above Q3. The lower fence is Q1 − 1.5×IQR and the upper fence is Q3 + 1.5×IQR — anything outside that range is drawn as a separate point rather than folded into the whisker. This tool applies that rule automatically and can also flag extreme outliers past 3×IQR if you turn that option on in the Enter Data tab.
Both are conventions for deciding when a value is unusual enough to plot separately rather than extend the whisker to it. The 1.5×IQR fence, the default in most statistics courses and software, catches moderate outliers. The 3×IQR fence is stricter and only flags values that are far more extreme, sometimes labeled "extreme outliers" to distinguish them from the milder ones caught by 1.5×IQR.
Use a box plot when you're comparing three or more groups and want medians, spread, and outliers side by side without the chart getting cluttered. Use a histogram when you care about the actual shape of a single distribution — whether it's bimodal, for instance — since a box plot compresses that shape down to five numbers. For a single-distribution histogram, see our Histogram Maker.