Box plot maker

Type your data as a list and get a box and whisker plot showing the minimum, lower quartile, median, upper quartile and maximum. Stack several to compare data sets, and add a dot plot or histogram underneath.

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Two data sets compared with box plots, and a dot plot of the first.

How to use the box plot maker

1
Type your data as a list: D = [2.1, 2.5, 2.8, 3.0, 3.1, 3.3]. You can also paste a column into a table.
2
Add boxplot(D, 1, 0.5): the box is drawn at height 1 and 0.5 units tall.
3
Add more box plots at different heights to compare data sets on the same scale.
4
Add dotplot(D, 0) or histogram(D, 0.5) to see the individual values or their distribution.
5
Type quartile(D, 1), median(D) or stdev(D) to get the numbers themselves.

Reading a box plot

A box plot is a five-number summary drawn to scale:

The whiskers run from the minimum to the maximum.
The box runs from the lower quartile Q1 to the upper quartile Q3, so it holds the middle half of the data. Its width is the interquartile range, IQR = Q3 − Q1.
The line inside the box is the median.

A median that sits off-centre in the box, or one whisker much longer than the other, shows a skewed distribution. For a full guide, see how to read a box plot.

How the quartiles are computed

There are several conventions for quartiles. This calculator uses the one taught in most schools and used by TI calculators: sort the data, take the median, then take Q1 as the median of the lower half and Q3 as the median of the upper half, leaving out the median itself when the number of values is odd. Spreadsheet functions such as Excel’s QUARTILE.INC interpolate instead and can give slightly different values for small data sets.

Outliers

The whiskers here extend to the minimum and maximum. Many textbooks also flag outliers as values more than 1.5 × IQR below Q1 or above Q3. To check, compute quartile(D, 1) - 1.5(quartile(D, 3) - quartile(D, 1)) and the matching upper fence, then look for values beyond them.

Examples to try

With a histogram

D = [2.1, 2.5, 2.8, 3.0, 3.1, 3.3, 3.4, 3.6, 3.9, 4.4, 4.6, 5.2]histogram(D, 0.5)boxplot(D, -0.5, 0.6)

The same data as a distribution and as a summary.

Open this example

A skewed data set

S = [1, 2, 2, 3, 3, 3, 4, 4, 5, 6, 8, 11, 15, 20]boxplot(S, 1.5, 0.8)dotplot(S, 0)

A long right whisker: skewed right.

Open this example

Frequently asked questions

How do I make a box plot?

Type your data as a list, D = [ … ], then add boxplot(D, y, height) to draw it at height y.

How do I compare two data sets?

Draw a box plot for each at different heights on the same axis, for example boxplot(A, 2, 0.6) and boxplot(B, 1, 0.6).

Which quartile method does it use?

The median-of-halves method used by most schools and TI calculators, which excludes the median from both halves when there is an odd number of values.

Does it show outliers?

The whiskers run to the minimum and maximum. You can compute the 1.5 × IQR fences with quartile() to identify outliers.