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Box Plot


A box plot (also called a box and whisker plot) shows data using the middle value of the data and the quartiles, or 25% divisions of the data.

Drawing a box and whisker plot

Example :

Construct a box plot for the following data:

12, 5, 22, 30, 7, 36, 14, 42, 15, 53, 25


Step 1: Arrange the data in ascending order.

Step 2: Find the median, lower quartile and upper quartile

Median (middle value) = 22
Lower quartile (middle value of the lower half) = 12
Upper quartile (middle value of the upper half) = 36

(If there is an even number of data items, then we need to get the average of the middle numbers.)

Step 3: Draw a number line that will include the smallest and the largest data.

Step 4: Draw three vertical lines at the lower quartile (12), median (22) and the upper quartile (36), just above the number line.

Step 5: Join the lines for the lower quartile and the upper quartile to form a box.

Step 6: Draw a line from the smallest value (5) to the left side of the box and draw a line from the right side of the box to the biggest value (53).

This following video shows how to draw a box and whiskers plot for a set of data.

Interpret a box and whisker plot

Learn that Box and Whisker Plots are graphs that show the distribution of data along a number line. See how to construct box plots by ordering a data set to find the median of the set of data, median of the upper and lower quartiles, and upper and lower extremes. Draw a Box and Whisker plot and learn how to use box plots to solve a real world problem. See how to construct box plots if there are no middle values.


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget which allows your to practice solving Algebra, Trigonometry, Calculus and other math topics.

You can use the Mathway widget below to practice Statistics or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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