How to read a box plot
A box plot (or box-and-whisker plot) summarizes a data set with five numbers: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum.
- The box spans Q1 to Q3, the middle 50% of the data. Its length is the interquartile range (IQR).
- The line in the box is the median. If it sits off-center, the data is skewed.
- The whiskers reach the most extreme values that aren’t outliers.
- Circles beyond the whiskers are outliers (more than 1.5 × IQR from the box).
- The diamond marks the mean. A mean far from the median also signals skew.
Worked example
Take the 14 values: 2, 5, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 21, 35.
- The median is the average of the 7th and 8th values: (12 + 13) ÷ 2 = 12.5.
- The lower half is 2, 5, 7, 8, 9, 11, 12, so Q1 = 8. The upper half is 13, 14, 15, 17, 18, 21, 35, so Q3 = 17.
- IQR = 17 − 8 = 9. The fences are 8 − 13.5 = −5.5 and 17 + 13.5 = 30.5.
- 35 is above 30.5, so it is an outlier. The upper whisker stops at 21, the largest value that isn’t an outlier.
Load “Small example” above to see this exact box plot.
Comparing groups with box plots
Box plots shine when you compare several groups: test scores by class, delivery times by courier or salaries by department. Compare the medians (which group is typically higher?), the box lengths (which is more consistent?) and the whiskers and outliers (which has extreme values?). If two boxes don’t overlap at all, the groups are clearly different.
Box plot or histogram?
A box plot compresses a distribution into five numbers, which makes it great for comparing many groups but hides details such as two peaks. A histogram shows the full shape. Switch on “Show all data points” to get the best of both, or use the five-number summary calculator for the working.
The anatomy of a box plot
Reading shape from a box plot
| What you see | What it means |
|---|---|
| Median in the middle of the box, whiskers about equal | Roughly symmetric data |
| Median closer to Q1, long right whisker | Skewed right (a tail of high values) |
| Median closer to Q3, long left whisker | Skewed left (a tail of low values) |
| Short box | The middle 50% of values are consistent |
| Points beyond the whiskers | Outliers worth checking |
Common mistakes to avoid
- Drawing whiskers to the min and max when there are outliers. With the 1.5 × IQR rule, whiskers stop at the last value inside the fences, and outliers are plotted separately.
- Mixing quartile methods. Your calculator, Excel and textbook may compute Q1 and Q3 differently. Pick one method and state it.
- Comparing box plots of very small samples. With fewer than about 10 values, quartiles jump around. Show the points too, or use a dot plot.
- Reading meaning into the box width. In a standard box plot the width is just a design choice; only the length along the axis matters.
- Hiding two peaks. A box plot cannot show bimodal data. Check with a histogram before drawing conclusions.
Box plots in Excel, Google Sheets, TI-84, Desmos and Python
| Software | How |
|---|---|
| Excel 2016+ | Insert › Insert Statistic Chart › Box and Whisker. In Format Data Series, choose Inclusive or Exclusive median for the quartile method. |
| Google Sheets | There is no built-in box plot; the candlestick chart is a common workaround, or use this tool. |
| TI-84 | STAT PLOT › Type: the first icon on the second row (modified box plot, shows outliers) › ZOOM 9. |
| Desmos | boxplot(L) |
| Python | plt.boxplot(data) or seaborn.boxplot(x=data). Both use 1.5 × IQR whiskers by default. |
Related tools: Five-Number Summary Calculator, IQR & Outlier Calculator, Dot Plot Maker, Histogram Maker and Relative Frequency Histogram.