Calculating Student Performance - Why Median is Better than Mean

From http://www.noovah.com/grade-conscious-moms/

 

It is common knowledge that the majority of teachers use the mean (or 'average') statistical method to determine students final marks.  But does the mean accurately represent a good summary of student performance? 

According to the Merriam-Webster dictionary, the mean is "a middle point or something (as a place, time, number, or rate) that falls at or near a middle point".  Median however, is defined as "the middle value in a series of values arranged from smallest to largest" (Merriam-Webster dictionary).  Although these two definitions appear to be the same, they are in fact quite different.  Let's take a closer look at the application of each...



Figure 1:  Mean, Median and Mode in Symmetric vs Skewed Distributions; http://www.cdc.gov

Looking at Figure 1, it is apparent that when the distribution of data is symmetrical, the mean value is equal to the median.  As such, it would be safe to assume that the validity of the central tendency values are at their highest.  However, in real life, the distribution is more likely to be skewed to one side.  This can be demonstrated by differences in student achievement which can be affected by various factors (including multiple intelligence, student abilities/interests, teaching strategies) and/or circumstances (late assignments, illness, etc).  So which method should be used for skewed distributions?

Well, the mean shouldn't be used in skewed distributions because it can be distorted by extreme values (such as when a student receives a '0' on an incomplete assignment).  Because all values have an equal weight, the '0' mark could gravely affect the overall mark.  The median on the other hand, does not get affected by such outlier values.  This is because it focuses on the middle value of the entire collection.

Also, the purpose of using the mean is "to compare values with another sample or population" (Learn and Teach Statistics, 2013).  Although this may be appropriate for third-party testing such as EQAO, it shouldn't be used in normal classroom assessments.  What we want to do is determine a student's knowledge and understanding of a concept, by finding a value that best represents the overall abilities of that student.  And this is exactly what the median's purpose is:  "to find one value of data that best represents a summary of the overall collection of data" (Learn and Teach Statistics, 2013).

So... since researchers indicate that the mean value is best used when a distribution is symmetrical, and that a median value best represents the data when the distribution is skewed, then why to we keep using the mean? 

After doing some research and compiling median vs mean student data myself, I have realized that the mean is much easier to calculate while the median is much more time-consuming to compute.  This could possibly be one of the main reasons why it is not used often.  You have to find a common denominator for all of your data, then arrange it from smallest to biggest before finding the median value.  Having to do this for 30+ students each time an assessment is done, can be exhausting!  Additionally, we've been socialized to use the mean as the standard method for averages.  When you want to find an average, for whatever reason, the first thing we all do is calculate the mean.

But really, these aren't good enough reasons to throw in the towel and continue using the mean.  There are a vast number of software that can be used today (ie. Excel) where teachers can easily formulate a way to get the median calculated in an instant.  Also, it is just a matter of forming a habit out of changing old ways into better ways. 

To conclude, I believe that median is much more suitable for student assessment purposes then the mean 'average'.  But I'd like to hear from educators who use the median regularly.  If you have any tips or hints which you'd like to share, please post in the comments below.  Thanks!