How to Draw a Box-And-Whisker Plot

Box and whisker plots help organize long columns of data into a quick snapshot.

A box and whisker plot is a graphical way of illustrating the quartiles and extremes of a collection of data. It is drawn above a number line encompassing the range of all the data, with the numbers labelled at reasonable intervals. This ensures the reader will clearly understand where each of the five values of the box and whisker plot lies.

Instructions

1. Determine the median of the data. List the numbers in order from smallest to largest and cross off pairs of numbers one at a time, one number from each side. If left with two numbers in the middle, average them by adding them together and dividing by two.

   Example:

   6, 17, 11, 13, 7, 14

   Reorganize and eliminate:

   6, 7, 11, 13, 14, 17

   7, 11, 13, 14

   11, 13

   Average:

   11 + 13 = 24

   24 / 2 = 12

   Median (or 2nd quartile) is 12.

2. Find the quartiles. Split the data in two by the median, then find the median of each half of the data.

   Example:

   6, 7, 11

   7

   1st (lower) quartile is 7.

   13, 14, 17

   14

   3rd (higher) quartile is 14.

3. Above your number line, draw a rectangle whose ends line up with your first and third quartile values.

4. Divide the rectangle, or box, in two with a line representing the value of the median.

5. Draw two points above the number line, one for your minimum value (6, in this example), and one with your maximum value (17, in this example). Connect the points with horizontal lines leading to the edges of your rectangle. These lines are the "whiskers" of the plot.

References

• Northern Michigan University; Box and Whisker Plot; Jennifer Nord
• Purplemath: Box-and-Whisker Plots: Quartiles, Boxes and Whiskers