Box Plot Worksheet Generator

Quartiles are where box-plot worksheets go wrong: there is more than one accepted way to find them, and an answer key built one way marks a pupil wrong for using another. This sheet uses one method throughout and prints it at the top — the lower quartile is the median of the values below the median, the upper quartile the median of those above, and the median itself is left out when the count is odd. Where a spreadsheet's QUARTILE.INC would give a different answer, the answer key says so. Questions alternate between drawing a box plot from a list and reading two drawn plots on a whole-number scale to compare them.

Level

Questions

How many questions

1 to 12.

Sheet code (optional)

Leave empty for a fresh sheet. The same code and settings make the same sheet again while the generator is unchanged. The code is a seed: deterministic, not cryptographic, and not a secret.

Paper size

Print size

Margin

Millimetres of blank edge, 5 to 40.

Turn the paper sideways

How to print this, or save it as a PDF

There is no PDF to download, and there does not need to be. Open the print command in your browser and choose “Save as PDF” as the destination. Your browser decides whether the page address and date print across the top and bottom; if they appear, turn off “Headers and footers” in the print dialog.
Set the scale to 100%, not “fit to page”. This sheet is already the exact size of the paper you chose, so anything that resizes it makes every measurement on it wrong.
Leave the paper size in the dialog set to the same one you chose here.

The questions will appear here.

What this generator does

Draws a fresh list of whole numbers for each question and works out the smallest value, the quartiles, the median and the largest value by the stated method. Comparison questions draw two plots on a scale marked in whole numbers; their quartiles are kept whole so they can be read off the scale, and their medians and interquartile ranges are kept different so each comparison has one answer.

How to use this tool

Choose a level, the kind of questions and how many.
Press Make the sheet; the quartile method is printed at the top.
Press Show the answers to see the five numbers, the range, the interquartile range and the finished plot.
Print the questions and the answer pages, or type a sheet code to make the same sheet again.

Understanding the controls

Level: Gentle uses 7 to 9 values between 0 and 30; standard 9 to 13 values up to 60; stretch 12 to 17 values up to 100.
Questions: Drawing a box plot from a list, reading and comparing two plots, or the two alternating.
How many questions: 1 to 12. Questions are spread over as many printed pages as they need, with the answers on their own pages.
Sheet code: Leave empty for a fresh sheet from the browser's secure generator; with a code, the same code and settings make the same sheet again while the generator is unchanged.

Worked examples

Code harbour, standard, question 1: Draw a box plot for 32, 19, 14, 20, 24, 17, 9, 17, 33: smallest 9, lower quartile 15.5, median 19, upper quartile 28, largest 33; QUARTILE.INC would give 17 and 24.
Code harbour, standard, question 2: Morning against Afternoon: medians 12 and 27, so Afternoon's is higher by 15; Morning has the larger interquartile range, 21 against 7.

Common use cases

A lesson on drawing box plots from raw data
Practice comparing two groups by median and interquartile range
Settling which quartile method a class will use before a test

How this generator works

Sort the list. The median is the middle value, or the mean of the middle two. With n values, the lower half is the first n ÷ 2 values rounded down and the upper half the last n ÷ 2 rounded down, so the median is left out when n is odd; the quartiles are the medians of those halves. A spreadsheet's QUARTILE.INC instead interpolates at position (n − 1) × ¼ and (n − 1) × ¾, so for 1 to 7 it gives 2.5 and 5.5 where this method gives 2 and 6. Every printed quartile and median is then re-checked by counting rather than by repeating the calculation: at least half its list must lie at or below it and at least half at or above it.

Randomness and fairness

The values come from the browser's secure generator, or a seeded one when you type a code. A code repeats a sheet while the generator is unchanged. Codes are deterministic, not cryptographic, and not a secret.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

Values are whole numbers and a box plot shows no separate outliers: the whiskers run to the smallest and largest values.

Limitations and good to know

One quartile method only; a class taught to interpolate, or to include the median in both halves, will get different quartiles for odd counts.
Outliers are not marked separately, so the 1.5 × IQR fences some courses use are not drawn.
Comparison plots are kept to whole-number quartiles so they can be read from the scale, which makes those data sets slightly less varied than the drawing questions.

Common mistakes

Finding quartiles from the unsorted list: Sort first; the quartiles, like the median, are positions in the ordered list.
Comparing the lengths of the whiskers to judge spread: The interquartile range — the width of the box — is the spread of the middle half and is not stretched by one extreme value.

Privacy and your data

Sheets are made in your browser. With analytics consent, a count records how many questions a sheet had; the values and any code are not sent.