Introduction to Statistics - Median

The next introductory statistical concept I will discuss is the median. It is similar to the mean in that it is a form of an average, or a measure of central tendency, though most likely not in the terms that you have thought of an average before.

While the mean is the sum of a group of values divided by the number of values, the median is the point at which half of the data points of the set are below it, and half of the data points are above it. In other words, the median is the midpoint of the data set, with 50% of the data points on either side of it. As you will see, while this number CAN be equal to the mean, it does not have to be.

Let's continue with the example given in the post about means.

Example:
The grades received for a test in a math class, composed of 12 students, were:
65, 98, 92, 43, 76, 64, 69, 72, 75, 85, 96, 90
What is the median of this set of data?

The first thing to do is to rearrange the data points from lowest to highest.
43, 64, 65, 69, 72, 75, 76, 85, 90, 92, 96, 98

To determine the median, you simply have to pick out the MIDDLE value of this data set. For data sets with an odd number of values, this is easy. This data set, however, has 12 values, so the median is actually represented by the AVERAGE of the center TWO values. In this case, the middle 2 values are the 6th and 7th values, 75 and 76. Therefore, the median of this data set is the average of 75 and 76, which is 75.5

Let us pretend that one student was sick on test day, and when he took it later on, he scored a 90 on the exam. If we now factor this in, we have a data set of 13 values (an odd number), and so as you can see, the middle point is the 7th point, which is 76.

Also, convince yourself that that addition of this student's score increases the mean to 78%.

The final concept to discuss is the mode, which I will explain next. See my post here for tips on how to choose which of these measures of central tendency to use.

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