3.2 – Median

The second measure of center is the median. The median is the middle point of a distribution of scores. In other words, it is the score at which 50% of the scores in the distribution are above this score, and 50% of the scores in the distribution are below this score. To calculate the median, just list out the scores in order and find the middle score. Finding the middle score depends on whether you have an odd number of scores or even number of scores.

• If you have an odd number of scores, find the middle score.
• If you have an even number of scores, find the two middle scores and average them.

Let’s say we have the following set of scores:

First, we would put the scores in numerical order (from lowest to highest):

(Helpful hint: cross out the numbers from the original set as you put them in the new list in numerical order.) Next, we can count the number of scores and we see that we have 9 scores, which is an odd number so we will need to find the one score in the middle. The score of 4 is in the middle:

There are four scores above and four scores below this point. Thus, our median is 4.

When the median is calculated, it is only sensitive to the middle score (or the middle two scores). Let’s say that the score of 8 was instead a score of 100. You can see that the median wouldn’t change at all:

Thus, the median contains less information than the mean, but it is also much less sensitive to outliers.

Now, let’s add a score of 8 to the above distribution:

Because we now have 10 scores, which is an even number, we need to find the middle two scores:

Then we just take the average of these two scores:

[latex]\text{Median}=\frac{4+5}{2}=4.5[/latex]

Thus, our median is 4.5. Halfway between 4 and 5:

You can now see that half of the scores (5 scores) are above the median, and half the scores (5 scores) are below the median.