Box Plot Calculator

What the box plot calculator does

A box plot, or box-and-whisker plot, is a compact picture of how a data set is spread out. This calculator turns your numbers into the five values a box plot is built from, the minimum, first quartile, median, third quartile, and maximum, and draws the plot from them.

In one small diagram, a box plot shows the centre of the data, how spread out its middle is, and how far it reaches at each end. Below is how it is built and how to read one.

How to use it

1. Enter your dataset in the box, separated by commas, spaces, or new lines.
2. Press Calculate for the five numbers and the box-and-whisker plot, or Reset to clear it.

How the box plot is built

Everything starts from the five number summary. The calculator sorts your data, then finds the smallest and largest values, the median in the middle, and the first and third quartiles that mark the middle half. Those five numbers become the five landmarks of the plot.

The box is drawn from the first quartile to the third, with a line inside it at the median. From each end of the box, a line called a whisker reaches out to the minimum and the maximum. So the box holds the central half of the data, and the whiskers show how far it stretches beyond that.

Reading a box plot

Once you know the parts, a box plot reads quickly. The width of the box is the interquartile range, the spread of the middle half, so a narrow box means the bulk of the data is tightly grouped and a wide one means it is more spread. Where the median line sits inside the box hints at the shape: a median pushed toward one end suggests the data is skewed in the other direction.

The whiskers show the reach of the data. A long whisker on one side points to a stretched-out tail on that side, while a short one means the values there are packed close. Comparing two box plots side by side is where they really shine, since differences in centre and spread jump straight out, which is why they are a favourite for putting groups next to each other.

A worked example

Take the eight numbers 3, 5, 7, 8, 12, 13, 14, 18, already sorted. The minimum is 3 and the maximum is 18. The median is the point between the two middle values, (8 + 12) ÷ 2 = 10.

The lower half is 3, 5, 7, 8, whose median is 6, the first quartile. The upper half is 12, 13, 14, 18, whose median is 13.5, the third quartile. So the five numbers are 3, 6, 10, 13.5, and 18. The box runs from 6 to 13.5 with a line at 10, and the whiskers reach down to 3 and up to 18.

Entering your data, and the method

You can separate your numbers with commas, spaces, or new lines, in any mix, and the calculator sorts them for you. It finds the quartiles by taking the median of each half of the data. As with any quartile calculation, the exact rule for an odd number of values varies between tools, so the first and third quartiles here may differ slightly from another calculator, which is normal for these measures.

Questions people ask

What is a box plot?

A diagram of a data set built from five numbers: the minimum, first quartile, median, third quartile, and maximum. The box covers the middle half and the whiskers reach to the extremes.

What do the parts mean?

The box runs from the first to the third quartile, the line inside is the median, and the whiskers extend to the smallest and largest values. The box width is the interquartile range.

How can I see skew in a box plot?

Look at the median line and the whiskers. A median pushed toward one end of the box, or one whisker much longer than the other, points to a skewed data set.

Why use a box plot?

It shows centre, spread, and reach in one compact picture, and it is especially good for comparing several groups side by side, where differences stand out at a glance.

References

A quick note on where the methods here come from. The box plot and the five number summary it is drawn from are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers box plots and how to read them.

1. NIST/SEMATECH e-Handbook of Statistical Methods (box plots and quartiles). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (box plots and the five number summary). https://openstax.org/details/books/introductory-statistics-2e