Box and whisker plot

Box-and-whisker plots are fundamental tools in descriptive statistics. They provide a graphical and compact representation of a data set’s distribution, highlighting its structure without displaying every individual value.

A box plot is constructed from five key numbers:

1. Minimum value
2. First quartile (Q1)
3. Median (Q2)
4. Third quartile (Q3)
5. Maximum value

This set is known as the five-number summary.

Interactive chart 1

Drag the black points upward or downward to increase or decrease the number of data values in each group and modify the bar chart accordingly. The updated data will be automatically displayed in the summary table. Use the checkboxes on the right to adjust the applet settings, such as showing or hiding elements like the box plot, colors, mean, or summary. Click the “Exercises” button to begin practicing.

Interactive chart 2

Use the “+” and “–” buttons below each value to increase or decrease the number of dots in the dot plot. As you modify the data, the box-and-whisker plot will automatically update to reflect the new distribution. This allows you to explore how changes in the data affect the shape and key features of the box plot.

Self-grading exercise

Click the “Sort Numbers” button to organize the data set. Then, drag the vertical lines of the box-and-whisker plot to adjust its features according to the correct calculations based on the given data. Press the “Check” button to verify your answer; you have three attempts, and hints may appear before your final attempt. If all three attempts are used, the correct solution will be displayed.

See also

Probability and statistics formula sheet