What is a box and whisker plot?

A graph that shows how data is spread using five numbers: the minimum, Q1, the median, Q3 and the maximum. The box covers the middle half of the data and the whiskers reach the smallest and largest values.

How do you find Q1 and Q3?

Put the data in order and find the median. Q1 is the median of the lower half and Q3 is the median of the upper half. With an odd number of values, leave the median out of both halves.

What is the five-number summary?

The minimum, lower quartile (Q1), median, upper quartile (Q3) and maximum. For 12, 15, 18, 20, 22, 25, 26, 28, 30, 35, 40, it is 12, 18, 25, 30, 40.

How do you find the interquartile range?

Subtract Q1 from Q3. If Q1 is 18 and Q3 is 30, the IQR is 30 − 18 = 12.

What percent of the data is inside the box?

About 50%. Each whisker covers about 25% of the data, and each half of the box covers about 25%.

What grade learns box and whisker plots?

In the US, grade 6 (6.SP.B.4 and 6.SP.B.5.c), with comparing two groups in grade 7. In England, box plots and quartiles are part of the GCSE Higher tier, usually in Years 10 and 11.

Is there a free box and whisker plot worksheet with answers?

Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Grades 6 and 7 (GCSE Higher tier in England)

Box and whisker plots: quartiles, IQR and the five-number summary

Here is how to make and read a box and whisker plot: put the data in order, find the five-number summary, and use the quartiles and interquartile range to describe the spread. Try the free practice below, then print a fresh box and whisker plot worksheet with an answer key.

The method, step by step

Put the data in order from smallest to largest.
Write down the minimum and the maximum, the first and last values.
Find the median, the middle value, or halfway between the middle two if there is an even number of values.
Find Q1, the median of the lower half, and Q3, the median of the upper half, leaving the median out of both halves when there is an odd number of values.
Draw a number line, make a box from Q1 to Q3 with a line at the median, and draw whiskers out to the minimum and maximum.

CCSS 6.SP.B.4CCSS 6.SP.B.5.CCCSS 7.SP.B.3CCSS 7.SP.B.4England: GCSE Higher StatisticsEngland: KS3 StatisticsEngland: GCSE Foundation Statistics

Worked example

Eleven students recorded how many minutes they spent on homework: 12, 25, 18, 30, 22, 15, 40, 28, 20, 35, 26. Find the five-number summary and the interquartile range, and describe the box plot.

In order: 12, 15, 18, 20, 22, 25, 26, 28, 30, 35, 40.
The minimum is 12 and the maximum is 40.
There are 11 values, so the median is the 6th one: 25.
The lower half, left of the median, is 12, 15, 18, 20, 22, so Q1 = 18.
The upper half, right of the median, is 26, 28, 30, 35, 40, so Q3 = 30.
The interquartile range is Q3 − Q1 = 30 − 18 = 12.
The five-number summary is 12, 18, 25, 30, 40: the box runs from 18 to 30 with a line at 25, the whiskers reach 12 and 40, and the IQR is 12.

Practice now

Question 1 of 100 correct

Find the median: 16, 29, 33, 23, 26, 14

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What a box and whisker plot shows

A box and whisker plot, or box plot, shows how a set of numbers is spread out using just five numbers: the minimum, the lower quartile (Q1), the median, the upper quartile (Q3) and the maximum. Together they are called the five-number summary.

The box stretches from Q1 to Q3, with a line inside it at the median. The whiskers are lines from the box out to the smallest and largest values. The four sections, whisker, half box, half box, whisker, each hold about a quarter of the data. A longer section does not hold more data. It means that quarter of the data is more spread out.

How to find the quartiles

Quartiles split ordered data into four groups of the same size. This page uses the method taught in most US middle schools: find the median, split the data into a lower half and an upper half, and find the median of each half. When there is an odd number of values, the median itself is left out of both halves.

An odd number of values, 7, 9, 10, 13, 15, 18, 22: the median is 13. The lower half is 7, 9, 10, so Q1 = 9. The upper half is 15, 18, 22, so Q3 = 18.
An even number of values, 3, 5, 6, 8, 9, 11, 12, 14, 15, 20: the median is halfway between 9 and 11, which is 10. The lower half is 3, 5, 6, 8, 9, so Q1 = 6. The upper half is 11, 12, 14, 15, 20, so Q3 = 14.
Halves with an even count, 4, 7, 9, 10, 12, 15, 18, 21: the lower half is 4, 7, 9, 10, so Q1 = (7 + 9) ÷ 2 = 8. The upper half is 12, 15, 18, 21, so Q3 = (15 + 18) ÷ 2 = 16.5.

Calculators, spreadsheets and some textbooks use slightly different rules and can give slightly different quartiles. If an answer is a little off, check which method the class uses.

Range, interquartile range and outliers

The range is the maximum minus the minimum. It is quick to find, but one unusual value can make it much bigger. The interquartile range (IQR) is Q3 − Q1, the width of the box. It measures the spread of the middle half of the data, so one very large or very small value hardly changes it.

In the homework example, the range is 40 − 12 = 28 minutes and the IQR is 30 − 18 = 12 minutes. So the middle half of the students spent between 18 and 30 minutes on homework.

Many classes call a value an outlier if it is more than 1.5 × IQR below Q1 or above Q3. Here 1.5 × 12 = 18, so an outlier would be below 18 − 18 = 0 or above 30 + 18 = 48. Nobody is that far out, so there are no outliers. When there is one, it is often drawn as a dot beyond the end of the whisker.

Reading and comparing box plots

About 25% of the data is below Q1, 50% is below the median and 75% is below Q3.
The median line shows a typical value. Compare medians to see which group is generally higher.
The width of the box, the IQR, shows consistency. A narrower box means the middle half of the data is closer together.
A median close to one end of the box, or one whisker much longer than the other, shows the data is bunched up at one end (skewed).
A box plot does not show the mean or how many values there are.

For example, two basketball players both have a median of 18 points a game. One has an IQR of 4 and the other an IQR of 10. They score about the same on a typical night, but the first player is much more consistent.

How it is taught in school

In the US, Common Core introduces box plots in grade 6. Students display data in dot plots, histograms and box plots (6.SP.B.4) and summarize data with the median and the interquartile range (6.SP.B.5.c). In grade 7, students compare two groups by looking at their centers and spreads (7.SP.B.3, 7.SP.B.4). High school statistics comes back to box plots in more depth (HSS-ID.A.1).

In England, quartiles, the interquartile range and box plots are part of the GCSE Higher tier, usually taught in Years 10 and 11. Pupils meet the range and the mean, median and mode first, in Key Stage 3.

How parents can help

Make sure finding the median feels easy first, including the even case where you find halfway between the middle two.
Use real data: the family's heights, a week of bedtimes or a favorite team's scores. Find the five-number summary together.
Show how to cross off one value from each end of the ordered list to reach the median. It makes the two halves easy to see.
Ask what the box plot says in words, such as: half the class spent between 18 and 30 minutes on homework.
Keep sessions short. Print a fresh worksheet, let your child mark it with the answer key, and go through the worked steps for any they missed.

Common mistakes

Forgetting to put the data in order. The median and quartiles only make sense once the values run from smallest to largest.
Putting the median into both halves when there is an odd number of values. For 7, 9, 10, 13, 15, 18, 22, the lower half is 7, 9, 10, not 7, 9, 10, 13.
Giving a position instead of a value. In a list of 11 values the median is the 6th value, not the number 6.
Mixing up the range and the IQR. The range is maximum − minimum; the IQR is Q3 − Q1, the width of the box only.
Thinking a longer section holds more data. Each of the four sections holds about a quarter of the values; a longer one is just more spread out.
Misreading the scale. Check what each tick mark on the number line is worth before reading off Q1, the median or Q3.

Questions people ask

What is a box and whisker plot?: A graph that shows how data is spread using five numbers: the minimum, Q1, the median, Q3 and the maximum. The box covers the middle half of the data and the whiskers reach the smallest and largest values.
How do you find Q1 and Q3?: Put the data in order and find the median. Q1 is the median of the lower half and Q3 is the median of the upper half. With an odd number of values, leave the median out of both halves.
What is the five-number summary?: The minimum, lower quartile (Q1), median, upper quartile (Q3) and maximum. For 12, 15, 18, 20, 22, 25, 26, 28, 30, 35, 40, it is 12, 18, 25, 30, 40.
How do you find the interquartile range?: Subtract Q1 from Q3. If Q1 is 18 and Q3 is 30, the IQR is 30 − 18 = 12.
What percent of the data is inside the box?: About 50%. Each whisker covers about 25% of the data, and each half of the box covers about 25%.
What grade learns box and whisker plots?: In the US, grade 6 (6.SP.B.4 and 6.SP.B.5.c), with comparing two groups in grade 7. In England, box plots and quartiles are part of the GCSE Higher tier, usually in Years 10 and 11.
Is there a free box and whisker plot worksheet with answers?: Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated November 4, 2026.

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