A box plot — also called a box-and-whisker plot — is a standardized chart that displays the distribution of a numeric dataset using a five-number summary: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Invented by statistician John Tukey in the 1970s, it remains one of the most widely used tools in exploratory data analysis because it compresses thousands of data points into a shape you can read in seconds.
The Five Numbers, One by One
- Minimum — the smallest value within the lower fence (not always the raw minimum).
- Q1 (first quartile) — the 25th percentile: a quarter of the data falls below it.
- Median (Q2) — the middle value: half the data is above, half below.
- Q3 (third quartile) — the 75th percentile.
- Maximum — the largest value within the upper fence.
The box spans Q1 to Q3. Its width is the interquartile range (IQR = Q3 − Q1) — the spread of the middle 50% of your data. A line inside the box marks the median.
Whiskers and Outliers
The whiskers extend from the box to the most extreme points still inside the Tukey fences: Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Points beyond the fences are drawn as individual dots — potential outliers. This convention is important: on a Tukey box plot, the whisker tips are usually not the raw min and max.
A Quick Numerical Example
For the ten scores 52, 58, 63, 67, 71, 74, 78, 82, 85, 88, the median is (71 + 74) / 2 = 72.5, Q1 = 63, Q3 = 82, and IQR = 19. The fences are 34.5 and 110.5, so every value stays inside — no outliers, and the whiskers reach the true extremes 52 and 88. The median sitting left of center inside the box hints at mild right skew.
When to Use a Box Plot
- Comparing groups — side-by-side boxes make median shifts and spread differences obvious.
- Screening for outliers before modeling or reporting averages.
- Summarizing large datasets where plotting every point would be noise.
Its main limitation is shape blindness: a box plot cannot show how data is distributed inside the quartiles, so bimodal data can hide in a perfectly normal-looking box. When distribution shape matters, pair it with a violin plot or histogram.