CK-12 Basic Probability and Statistics - A Short Course

http://www.ck12.org Chapter 7. Organizing and Displaying Data - Basic

Length of Fish (in.)

13 14 6 9 10

21 17 15 15 7

10 13 13 8 11

Since the box-and-whisker plot is based on medians, the first step is to organize the data in order from smallest to
largest.

6 7 8 9 10

10 11 13 13 13

14 15 15 17 21

6 , 7 , 8 , 9 , 10 , 10 , 11 , 13 , 13 , 13 , 14 , 15 , 15 , 17 , 21

This is an odd number of data, so the median of all the data is the value in the middle position which is 13. There
are 7 numbers before and 7 numbers after 13. The next step is the find the median of the first half of the data –the 7
numbers before the median. This is called the lower quartile since it is the first quarter of the data. On the graphing
calculator this value is referred to asQ 1.

6 , 7 , 8 , 9 , 10 , 10 , 11

The median of the lower quartile is 9.

This step must be repeated for the second half of the data –the 7 numbers below the median of 13. This is called the
upper quartile since it is the third quarter of the data. On the graphing calculator this value is referred to asQ 3.

13 , 13 , 14 , 15 , 15 , 17 , 21

Now that the medians have all been determined, it is time to construct the actual graph. The graph is drawn above a
number line that includes all the values in the data set (graph paper works very well since the numbers can be placed
evenly using the lines of the graph paper). Represent the following values by using small vertical lines above their
corresponding values on the number line:

Smallest Number− 6 Median of the Lower Quartile− 9 Median− 13

Median of the Upper Quartile− 15 Largest Number− 21

The five data values listed above are often called the five-number summary for the data set and are used to graph
every box-and-whisker plot.

Join the tops and bottoms of the vertical lines that were drawn to represent the three median values. This will
complete the box.