You would use box-and-whisker plots for the following reasons:

• They are good for large data sets (values of at least 15).

• They give the five key data points: maximum, minimum, median, upper quartile and lower quartile.

• They can compare two or more data sets.

• They show the similarities and differences among plots.

• They show outliers.

• They can be used to compare sets with different number of data points.

This is how to make a box-and-whisker plot:

1. Organize the data in sequential order. You can use a stem-and-leaf plot or arrange data from largest to smallest.

2. Determine the summary values — maximum, minimum, median, upper quartile, and lower quartile.

3. Make a number line with consistent intervals.

4. Construct the box-and-whisker plot:

Put in the mean and the upper and lower quartile. Make this into your box.

Determine if there are outliers by subtracting the lower quartile from the upper quartile. Multiply this amount by 1.5, subtract that amount from the lower quartile and add it to the upper quartile. If there are points that are beyond these values, make stars at those points to indicate outliers.

Make whiskers from the LQ and UQ to the extremes.

Label your plot.

5. If you are comparing plots, be sure that you use one number line.
   

The data: Math test scores 80, 75, 90, 95, 65, 65, 80, 85, 70, 100

Write the data in numerical order and find the first quartile, median, third quartile, smallest value and largest value. Median = 80 Lower quartile = 70 Upper quartile = 90 Minimum value = 65 Maximum value = 100
Place a circle beneath each of these values on a number line.
Draw a box with ends through the points for the lower and upper quartiles. Then draw a vertical line through the box at the median point. Now, draw the whiskers (or lines) from each end of the box to the smallest and largest values.

Example from http://regentsprep.org/regents/math/data/boxwhisk.htm