The median is used to describe the center of the distribution of the
data. Or in other words the score where half the data is above and
half the data are below. For example let’s use the tree diameter
example from before but for simplicity lets assume we added another
sampling point with a diameter of 16.1 inches:
Example
Recall that the following ten scores are the diameters of trees
we sampled.
10.2, 6.5, 8.2, 9.6, 24.0, 16.6, 13.4 5.3, 6.7, 31.8 and now 16.1
The first step in calculating the median is to rearrange the data
so that they are in numerical order. Your data should now look like
this:
5.3, 6.5, 6.7, 8.2, 9.6, 10.2, 13.4, 16.1, 16.6, 24.0, 31.8
Since the data has an odd number of samples we simply find the
number with half the sample points above and below. In this case the
median is equal to 10.2.
Now why don’t you try to calculate the median?
We are lucky we had another data point to add, so what would we have
done if we still only had ten samples?
Well in such a case you simply average the two middle scores. So
for our original data set of 10.2, 6.5, 8.2, 9.6, 24.0, 16.6, 13.4
5.3, 6.7, 31.8
The two middle scores would be 9.6 and 10.2. So if we average
those we get 9.9 as our median.
Do the
interactive demonstration from Rice University
which shows the properties of the mean and median.
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