How are outliers defined in a boxplot?

In a standard Tukey boxplot, outliers are values that lie more than 1.5 times the interquartile range (IQR) below the first quartile or above the third quartile. That is, any value less than Q1 − 1.5 × IQR or greater than Q3 + 1.5 × IQR is flagged as an outlier. Many tools, including this calculator, use this rule by default.

Can this tool create multiple boxplots on the same chart?

Yes. You can create grouped box and whisker plots by entering one dataset per line in the raw data input, or by using the summary statistics mode and adding multiple series. Each dataset will be drawn as a separate box on the same axis so you can compare distributions side by side.

How do I read a box and whisker plot?

Start with the box: its left edge is the first quartile (Q1), its right edge is the third quartile (Q3), and the line inside is the median. The box width represents the interquartile range (IQR), which contains the middle 50% of the data. The whiskers extend from the box to the smallest and largest non-outlier values. Points beyond the whiskers are outliers. A long box or whisker indicates high variability; a skewed box (median closer to one side) suggests a skewed distribution.

Can I export the boxplot as an image?

Yes. After generating the box and whisker plot, use the “Download PNG” button to export the current chart as a PNG image that you can paste into reports, slides, or homework solutions.

Box and Whisker Plot Generator

Create interactive boxplots from raw data or summary statistics. See quartiles, IQR, whiskers, and outliers, and export the chart as PNG.

Data (one value per line or comma/space separated)

For multiple boxplots, enter one dataset per line. You can optionally start a line with a label followed by a colon, e.g. Group 1: 3, 4, 5.

Delimiter

Outlier rule

Show mean marker

Enter five-number summary for each dataset. Whiskers will be drawn from min to max; outliers are not computed in this mode.

Label	Min	Q1	Median	Q3	Max	Remove

Box and whisker plot

Interactive

How this box and whisker plot calculator works

This tool computes a full five-number summary and draws a Tukey-style boxplot for each dataset you enter. It supports both raw data and pre-computed summary statistics, and can display multiple boxplots side by side for easy comparison.

From raw data

When you paste or type raw numeric data:

Non-numeric entries are ignored (with a warning).
Each non-empty line becomes one dataset (optionally labeled with Label: at the start).
For each dataset, the calculator computes:
- Minimum and maximum
- First quartile (Q1), median (Q2), and third quartile (Q3)
- Interquartile range (IQR = Q3 − Q1)
- Mean (optional marker)
- Outliers based on the selected rule

Quartiles and IQR

Let the sorted data be \(x_{(1)}, x_{(2)}, \dots, x_{(n)}\).

Median (Q2): middle value (or average of the two middle values if \(n\) is even).
Q1: median of the lower half of the data.
Q3: median of the upper half of the data.
Interquartile range: \(\text{IQR} = Q_3 - Q_1\).

Outlier detection (Tukey rule)

In a standard boxplot, the whiskers do not necessarily extend to the absolute minimum and maximum. Instead, they stop at the most extreme “non-outlier” values:

Lower fence: \( Q_1 - k \times \text{IQR} \)

Upper fence: \( Q_3 + k \times \text{IQR} \)

where \(k = 1.5\) for standard outliers, or \(k = 3\) for extreme outliers.

Any data point below the lower fence or above the upper fence is plotted as an individual outlier marker. You can also disable outlier detection and draw whiskers directly to the minimum and maximum.

Reading a box and whisker plot

Box: spans from Q1 to Q3 and contains the middle 50% of the data.
Median line: vertical line inside the box at Q2.
Whiskers: extend to the smallest and largest non-outlier values.
Outliers: individual points beyond the whiskers.
Mean marker (optional): shows the arithmetic average, which can differ from the median in skewed distributions.

Common use cases

Comparing test scores between classes or years.
Visualizing experimental measurements in science and engineering.
Exploring skewness and variability in business or finance data.
Teaching descriptive statistics and exploratory data analysis.

Tips for using this boxplot generator

Use one dataset per line to compare groups (e.g., “Control: …” and “Treatment: …”).
Switch to Summary statistics mode if you already know min, Q1, median, Q3, and max.
Toggle the outlier rule to see how robust your conclusions are to extreme values.
Use the PNG export for reports, slides, or homework submissions.

Box and whisker plot FAQ

What is a box and whisker plot?

A box and whisker plot (boxplot) is a compact way to visualize the distribution of a numeric variable. It shows the median, spread, and potential outliers at a glance, making it ideal for comparing multiple groups side by side.

How many data points do I need?

Technically you can draw a boxplot with as few as 5 data points, but it becomes more informative as the sample size grows. With very small samples, consider also looking at the raw values or a dot plot.

Why don’t the whiskers reach the minimum and maximum?

In Tukey boxplots, whiskers stop at the most extreme non-outlier values. Points beyond the fences are shown as outliers. If you want whiskers to reach the min and max, choose “No outliers” in the outlier rule dropdown.

What’s the difference between mean and median in the plot?

The median splits the data into two halves and is robust to outliers. The mean is the arithmetic average and can be pulled toward extreme values. When the mean and median are far apart, the distribution is likely skewed or has outliers.