Assignments: 07-Box and Whisker Plot
We’re going to use the following data set to help us create and understand Box-and-Whisker plots:
14, 21, 19, 12, 13, 24, 26, 19, 15, 25, 19
Step 1: Find the median of the data.
To find the median, remember, we have to put the numbers in order and find the middle number.
12, 13, 14, 15, 19, 19, 19, 21, 24, 25, 26
The median of this set of data is 19.
Step 2: Find the upper and lower quartiles. If you look at the root of the word, quart. A quart is a fourth of a gallon. A quarter is a fourth of a dollar. The root tells us to divide the data into fourths. The median split the data in half. to find the quartiles, you find the median of each of the halves.
12, 13, 14, 15, 19 —————— 19, 21, 24, 25, 26
The median of the lower half is 14. This number represents our lower quartile. The median of the upper half is 24. This number represents the upper quartile.
Step 3: Find the extremes. These are exactly as they sound. The extremes are the greatest and least values in the set: 12 and 26.
Step 4: Draw a line that includes all of the numbers in the data set. This should include all numbers from 12 to 26. It is drawn in green in the plot below.
Step 5: Above the line, draw a point for each of the numbers we’ve previously calculated: The median, 19, the quartiles, 14 and 24, and the extremes 12 and 26. This step is pictured in red below.
Step 6: Draw a box that begins at the lower quartile and ends at the upper quartile. Draw a line in the box at the median. This is pictured in blue below.
Step 7: Draw the whiskers. This is lines that come from both ends of the box and end at the extremes. This is purple in the picture below.
This type of graph is an easy way for us to represent those hot spots (upper and lower extremes, upper and lower quartiles, and the median) all in one quick and easy to read graph.