A picture is attached and will help a lot throughout this explanation. This is also a long explanation.
key for picture: Q1 - lower quartile, Q3 - upper quartile, min - minimum, max - maximum
Box and Whisker plots are confusing until you get to understand them. I am going to explain how to make one using an example. So first you need to take the set of numbers you are dealing with and put them in numerical order from smallest to largest. The numbers I am using will be 2, 3, 3, 3, 4, 5, 6, 8, 8, 9, 9, 10, 11, 12, and 14. The you need to draw a number line that fits your data set. Since the highest number is 14 and the lowest number is 2 make a number line numbered 1-15. Next we have to find the median. To do that find the number that is exactly in the middle of the numbers. so if you have
2 3 3 3 4 5 6 8 8 9 9 10 11 12 14
find the number in the middle. In this case it is 8. Now find 8 on your number line and draw a vertical line above the 8. This is the median. Now we have to find the maximum and minimum. This is the highest and lowest number in you data set. So in this case our numbers would be 2 and 15. Draw a line over top of the 2 and 15 on your number line like you did with the 8, just make the lines a little bit smaller. The lines above the 2 and 15 are the end lines and the line above the 8 is the line that is in the middle of the box. Now we have to find the lower quartile and the upper quartile. To do this you find the median of the numbers below and above the original median. So since 8 is our median. we find the median of the numbers below 8 for the lower quartile, but leave the original median out. (in bold)
2 3 3 3 4 5 6 8 8 9 9 10 11 12 14
The median of the lower quartile is 3, so on your number line draw a line above the 3 the exact same size as the 8. No connect the line above the 3 with the line above the 8 and you have half of the "Box" part done. Also connect the line above the 2 to the lie above the 3 for the first 'Whisker." Now just repeat the same thing on the other side. So median of upper quartile,
2 3 3 3 4 5 6 8 8 9 9 10 11 12 14
which is 10. Draw a line above the 10 like you did the 8. Connect to finish the box. Then connect the line above the 10 to the 15. You have made a box-and-whisker plot. It should look somewhat like the picture below but if it doesn't just try again with your own set of data.
