The Cat is Back; What is He Plotting?

After learning about the measures of central tendency in my math class, we were introduced to the Box and Whisker Plot. This type of plot uses numerical data and focuses around the median. It is also known as the Five Number Summary due to the five numbers used to create the plot:

1. minimum
2. maximum
3. median (or Q2)
4. Q1 (or first or lower quartile) 
5. Q3 (or third or upper quartile) 

I found this data display to be quite interesting; particularly, because it provides the data spread in terms of the median. As a future teacher, I think this plot would provide a better pulse of how my students are actually doing. Using just the median for example, would only provide me with the middle grade received on the quiz. The median isn't affected by outliers, so I could have a median of a "C", but I could also have a few "F's" and not be aware of them. You can see how this may be deceiving; enter the Box and Whisker Plot.

My previous post Mean, Median, and Mode...Oh My! provides the details involved in finding the median of a data set, therefore, I am not going to reiterate it here. Feel free to check that out first if you need clarification.

Work by me

The steps to creating a Box and Whisker Plot are as follows; please reference my plot above as well, it makes it easier:

1. Determine the minimum and maximum data points in your set, and create a number line accordingly.
2. Draw a dot above the number line where both the minimum and maximum fall.
3. Determine the median (or Q2) of your data set and draw a line above the number line.
4. Strike a line through your data set to signify where your median is; this has divided your data set into two halves.
5. Determine the median of the first half (Q1), and draw a line above the number line.
6. Determine the median of the second half (Q3), and draw a line above the number line.
7. Using the Q1 and Q3 lines as end points, draw a rectangle to represent the "box" portion of the Box and Whisker Plot.
8. Draw a line from each end of the box to connect it to the minimum/maximum dots; this represents the "whisker" portion of the Box and Whisker Plot.

That's all it takes to create it! I do suggest making your own. I looked for simulators for the purpose of this post, and found some at shodor.org or meta-chart.com. However, I did not like the feel of them, and they weren't very user friendly.

Now, for reading it; which brings me back to my statement earlier about how this plot would provide a better pulse of how my students are actually doing. Basically, each section of the plot depicts 25% of your data points (as you can see in my image above). This may be confusing, because they are not equal sections. Remember though, my data points are not equally spaced either. So, if my data set above represented quiz scores, I would be able to determine a few things just by reading the plot. To name a few, I would see: the minimum/maximum scores, that 50% of the class scored between 10-15 points, that 25% scored between 4-10 points, and that 25% scored between 15-19 points.

So, you can see how the Box and Whisker Plot can be much more useful than just the median.

Happy Teaching!

-Amanda