Box plot maker
A box plot squeezes a whole data set into five numbers. Add a second group to compare them at a glance.
| Group | Min | Q1 | Median | Q3 | Max | IQR | Outliers |
|---|---|---|---|---|---|---|---|
| Group A | 58 | 68 | 73.5 | 82 | 95 | 14 | — |
Reading a box and whisker plot
- The box runs from Q1 to Q3 and holds the middle 50% of the data. Its width is the interquartile range.
- The line inside is the median.
- The whiskers reach to the smallest and largest values that are not outliers.
- Circles are outliers: values more than 1.5 × IQR beyond the box.
Comparing two groups
Paste a second group to stack the plots on the same scale. Compare the medians first (which group is typically higher?), then the box widths (which is more variable?), then look for skew: a median near one end of the box, or one whisker much longer than the other, indicates a skewed distribution.
A box plot hides detail, such as two separate peaks. Check the shape with the histogram maker, and see every step of the five-number summary in the quartile calculator.
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Questions students ask
What are the five numbers in a box plot?
Minimum, first quartile (Q1), median, third quartile (Q3) and maximum. When outliers are shown separately, the whiskers stop at the most extreme values inside the 1.5 × IQR fences.
How do you read a box plot?
The box holds the middle 50% of the data, the line inside is the median, and the whiskers show the rest of the typical range. A longer whisker or a median off-centre in the box suggests skew.
What does a dot outside the whisker mean?
It is a value more than 1.5 IQRs beyond the box, a potential outlier worth checking. It is not automatically an error.
Box plot or histogram?
Box plots are best for comparing several groups compactly. Histograms show more detail about shape, such as two peaks, which a box plot hides.