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

Solution:

Step 1: Arrange the data in ascending order.

Step 2: Find the median, lower qurtile 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

We can also obtain informaion about the data given the box and whisker plot.

The following video shows how to find the median using a box-and-whisker plot

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