The median is one of the ways we can measure the “center” of a distribution of data. One of the big benefits of the median, is that it is not as affected by outliers and something like the mean is.
Loosely, the median represents the middle value – in other words, about 50% of the values in the data set are less than the median (you know that saying about 50% of “whatever” is below average – well thats not always true!). Let’s look at the different ways to calculate it.
Finding the median by hand is not usually done by statisticians, but it is a good exercise to use to understand exactly how the median works. You remember how I said that it is the middle value? Well this helps us plan how to find the median but in reality there will be two different cases.
- Case 1: There are an odd number of data values. Suppose that my data set is 7, 9, 1, 4, 3. To find the median of this data set, I would write the numbers in order: 1, 3, 4, 7, 9 and the median would be the literal middle value. Med=4.
- Case 2: There are an even number of data values. Suppose instead my data set is 8, 2, 1, 5. This time when I order the numbers, there is no clear middle value! Instead, I will order the numbers and find the average of the two middle numbers by adding then and dividing by two. 1, 2, 5, 8 -> Med=(2+5)/2 = 3.5.
As you can guess, this method has its limitations. It may seem easy, but putting a list of say 100 numbers in order takes much longer than you would think!
Using a Graphing Calculator
In this video, I use a graphing calculator to find the median – specifically a TI84, but you should note that the same steps would be used on a TI83.
Excel has a ton of functions available to do common statistical calculations. This is one of those that is pretty easy to work with!
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