Median
Another measure of center you may recall is the median. This value is computed by ordering the data values and identifying the value in “the middle.”
If we consider the sample data from above, ordering these values from least to greatest, we get:
[latex]1.2\qquad 3.3\qquad 3.6\qquad 4.5\qquad 5.8\qquad 8.7\qquad 10.0[/latex]
The value [latex]4.5[/latex] is the “middle number” in the ordered set; we see there are three values less than [latex]4.5[/latex] ([latex]1.2, 3.3, 3.6[/latex]) and three values greater than [latex]4.5[/latex] ([latex]5.8, 8.7, 10.0[/latex]). The value [latex]4.5[/latex] is the median.
[latex]\cancel{1.2}\qquad \cancel{3.3}\qquad \cancel{3.6}\qquad 4.5\qquad \cancel{5.8}\qquad \cancel{8.7}\qquad \cancel{10.0}[/latex]
If there are an odd number of observations, the “middle number” is the number that is left alone after all of the others have been crossed out. If there are an even number of observations, the “middle number” is the mean of the middle two observations. Check out the following videos to practice finding the median. The first video is using an odd number of observations, and the second is using an even number of observations.
finding the median using an odd numbered data set
Need a video demo showing the “counting in from the ends” to find the middle-most number in an odd numbered set.–>video starts at 2:00, it should stop around 2:48.
finding the median using an even numbered data set
Need a video demo showing the “counting in from the ends” to find the middle-most number in an even numbered set.–>same video but starting at 10:32 and it should stop around 11:22.
Examples
Calculate the median of each small data set below. These are the same sets used earlier to calculate the mean.
a) [latex]7, 4, 8, 2, 3, 6[/latex]
b) [latex]1.2, 3.9, 5.3, 4.2[/latex]
c) [latex]79, 86, 92, 93, 88[/latex]
Now you try it by taking the mean and median of the small set of data below.
