Q₁ · Md · Q₃

Box and Whisker Plot

Learn what a box and whisker plot is, see it constructed step by step, then find the five-number summary and draw the plot yourself.

1. What is a Box and Whisker Plot?

A Box and Whisker Plot (also called a Box Plot) is a graphical method used to represent the distribution of numerical data.

It helps us understand:

  • The minimum and maximum values.
  • The middle value (median).
  • The lower and upper quartiles.
  • How the data is spread out.
  • Whether the data contains unusually high or low values (outliers).

A box and whisker plot is based on the five-number summary.

2. Five-Number Summary

The five-number summary consists of the following values:

Symbol
Name
Meaning
Minimum
Minimum value
The smallest value in the data
Q₁
First quartile
The value below which approximately 25% of the data lies
Q₂
Second quartile (Median)
The middle value of the data
Q₃
Third quartile
The value below which approximately 75% of the data lies
Maximum
Maximum value
The largest value in the data
Remember: Q₁, Q₂ and Q₃ divide an ordered data set into four parts.

3. Structure of a Box and Whisker Plot

Consider the following illustration:

Smallest value First quartile Median Third quartile The largest value.

The plot consists of three main parts:

  1. Box: The box extends from Q₁ to Q₃. It represents the middle 50% of the data.
  2. Median line: The line inside the box represents Q₂, the median.
  3. Whiskers: The lines extending from the box show the spread of the data toward the minimum and maximum values, when there are no outliers.
Example 1 of 3
Question 1 of 10
Draw a box and whisker plot from the following data and present it on a graph.
Draw the box and whisker plot on the number line

You solved all questions! 🎉