A box plot (box-and-whisker plot) shows how data is spread out using five numbers: the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. The box holds the middle half of the data.
Try it with your own problem ↓
The steps
- Put the data in order from smallest to largest.
- Find the median. It splits the list into a lower half and an upper half. If the count is odd, leave the median out of both halves.
- Q1 is the median of the lower half. Q3 is the median of the upper half.
- The minimum and maximum are the first and last values.
- Draw a number line. Make a box from Q1 to Q3 with a line at the median, and whiskers out to the minimum and maximum.
A worked example
Make a box plot for 3, 7, 8, 5, 12, 14, 21, 13, 18.
- Order the data: 3, 5, 7, 8, 12, 13, 14, 18, 21. There are 9 values.
- The median is the 5th value: 12.
- Lower half (without 12): 3, 5, 7, 8. Its median is (5 + 7) ÷ 2 = 6. So Q1 = 6.
- Upper half: 13, 14, 18, 21. Its median is (14 + 18) ÷ 2 = 16. So Q3 = 16.
- Minimum = 3, maximum = 21. The interquartile range (IQR) is Q3 − Q1 = 16 − 6 = 10.
The five-number summary is 3, 6, 12, 16, 21. The box runs from 6 to 16, with a line at 12.
Try it with your own problem
Open the free The Dot Plot with this example already filled in. It shows every step, and you can type over it with your own numbers.
Work it out: box plot 3,7,8,5,12,14,21,13,18Opens The Dot Plot with this example
Or try these
- A set with an even count
- Box plot of 5, 7, 9, 10, 12, 15, 30
- Box plot of 1,2,2,3,4,5,5,6
Common mistakes
- Not ordering the data first. Quartiles only make sense on a sorted list.
- Including the median in both halves. With an odd count, leave it out (your teacher may specify a different method).
- Drawing the whiskers to Q1 and Q3. Whiskers go out to the min and max (or the nearest non-outlier).
- Reading the box as the whole data set. The box holds the middle half of the data. Each whisker holds about a quarter more.
Questions people ask
What is an outlier in a box plot?
A value more than 1.5 × IQR below Q1 or above Q3. Here the fences are 6 − 15 = −9 and 16 + 15 = 31, so there are no outliers.
What does the IQR tell me?
How spread out the middle half of the data is. A big IQR means more variation.
Why do different tools give different quartiles?
There are several accepted methods, especially when the count is even. Check which one your class uses.
Keep learning
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