Box plot maker

Make a box-and-whisker plot for one or more groups, with the five-number summary, outliers and every step of the working.

  • Free, no sign-up
  • Step-by-step working
  • Runs in your browser

For one group, paste the numbers. For several, put each group on its own line as Name: 1, 2, 3, or paste spreadsheet columns with the names in the first row.

How to use the box plot maker

  1. Paste your numbers. For more than one group, start each line with the group's name and a colon, or paste spreadsheet columns with a header row.
  2. Add a title and an axis label, and choose a horizontal or vertical layout.
  3. Pick the quartile method your course or software uses. If you're not sure, keep the default.
  4. Click Make box plot. Outliers appear as separate dots and the mean as a small ×.
  5. Check the five-number summary table and the working, then download the chart as a PNG.

Box plot formulas

A box plot is built from the five-number summary, plus two fences that decide which values count as outliers:

Interquartile range: IQR = Q3 − Q1

Lower fence: Q1 − 1.5 × IQR    Upper fence: Q3 + 1.5 × IQR

Min, max
The smallest and largest values
Q1
The first quartile: a quarter of the data are below it. With the exclusive method, it is the median of the lower half
Median
The middle value once the data are sorted (the second quartile)
Q3
The third quartile: three quarters of the data are below it. With the exclusive method, it is the median of the upper half
IQR
The interquartile range: the width of the box, covering the middle 50% of the data
Fences
Values beyond the fences are outliers. The whiskers end at the most extreme values inside the fences

Worked example

Nine customers wait 3, 5, 7, 8, 9, 11, 13, 15 and 30 minutes. Find the five-number summary and any outliers.

  1. The data are already sorted; n = 9 is odd, so the median is the 5th value
    Median = 9
  2. Q1 is the median of the lower half (3, 5, 7, 8); Q3 of the upper half (11, 13, 15, 30)
    Q1 = 5 + 72 = 6, Q3 = 13 + 152 = 14
  3. Interquartile range and fences
    IQR = 14 − 6 = 8,   fences = 6 − 12 = −6 and 14 + 12 = 26
  4. 30 is above 26, so it is an outlier; the upper whisker stops at 15
    Five-number summary: 3, 6, 9, 14, 30

What it means: the typical wait is 9 minutes, and the middle half of customers wait between 6 and 14 minutes. The 30-minute wait is unusually long compared with the rest and is plotted as a separate dot, so it doesn't stretch the whisker and hide the shape of the other values.

How to read a box plot

  • The line in the box is the median: half the values are below it and half above.
  • The box spans Q1 to Q3, the middle 50% of the data. A longer box means more spread.
  • The whiskers show the range of the rest of the data, excluding outliers.
  • Dots beyond the whiskers are outliers. Check them: they can be errors or genuinely unusual cases.
  • Shape: a median off-center in the box, or one whisker much longer than the other, means the data are skewed in that direction.

Box plots are especially useful side by side, because they make it easy to compare the center and spread of several groups at a glance. For the full shape of a single group, pair the box plot with a histogram.

Frequently asked questions

What does a box plot show?

A box plot (box-and-whisker plot) shows the five-number summary of a data set: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. The box covers the middle 50% of the data, the line inside it is the median, and the whiskers reach out to the most extreme values that aren’t outliers. Outliers are drawn as separate dots.

How are outliers defined in a box plot?

This tool uses the standard 1.5 × IQR rule. The interquartile range is IQR = Q3 − Q1. Any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is marked as an outlier. These limits are called fences; they aren’t drawn, but the whiskers stop at the last data value inside them.

Why are my quartiles different from Excel or my calculator?

There are several accepted ways to calculate quartiles. The default here, “exclusive”, takes the median of the lower and upper halves of the data, leaving out the overall median when the count is odd; it matches TI-83/84 calculators and most US textbooks. “Inclusive” interpolates between values and matches Excel’s QUARTILE.INC. Pick the method your class or software uses.

How do I compare groups with box plots?

Compare the medians first: is one group’s typical value higher? Then compare the box lengths (IQR) to see which group is more spread out. If the boxes don’t overlap at all, the groups are clearly different. If they overlap a lot, the difference may not be meaningful; a t-test can check formally.

How can I tell if the data are skewed from a box plot?

In a symmetric distribution, the median sits near the middle of the box and the whiskers are about the same length. If the right part of the box and the right whisker are longer, the data are skewed to the right; if the left parts are longer, they are skewed to the left. A histogram shows the shape in more detail.

How do I enter several groups?

Put each group on its own line, starting with its name and a colon, for example Morning: 62, 68, 71. You can also paste columns straight from a spreadsheet with the group names in the first row. If you paste plain numbers with no names, they are treated as a single group.

Last reviewed November 11, 2026