There are several techniques to find an average of a set of numbers. The most common way is to
find the mean. Calculating the mean has some disadvantages, as outliers, or data points that don't follow the tendencies of the majority of the data, can often skew results.
There is another way to find an average (or central tendancy) called the median. The median will often give you a better average then finding the mean because the outliers don't have as much of an effect on the final answer.
The median is the central value in a set of numbers.
Let's look at two examples. The first will have an odd set of numbers and the second will have an even set of numbers:
Example 1:
We are going to find the median of the following numbers:
3, 5, 8, 4, 1, 6, 0, 4, 1, 9, 19
The first step is to put the numbers in order from smallest to largest:
0, 1, 1, 3, 4, 4, 5, 6, 8, 9, 19
The median is the number that is in the middle. In this case the second 4 is the median. The numbers 0, 1, 1, 3 and 4 are on one side and 5, 6, 8, 9, 19 are on the other:
0, 1, 1, 3, 4,
4, 5, 6, 8, 9, 19
Our median is 4.
Example 2:
Now we are going to find the median of an even set of numbers:
10, 5, 8, 6, 1, 5, 4, 9
The first step is to put the numbers in order from smallest to largest:
1, 4, 5, 5, 6, 8, 9, 10
We must now find the middle number. In this case since there are an even number of values we must find the two numbers that would be in the middle of the rest. In this case, the second 5 and 6:
1, 4, 5,
5,
6, 8, 9, 10
We now calculate the mean of those two numbers:
(5 + 6)/2 = 11/2 = 5.5
Our Median is 5.5
Median vs Mean
How does the calculating of the median help us versus calculating the mean? Lets take a look at the problem we faced when
calculating the mean that included an outlier.
Let's pretend a test was given and there were 5 scores on the test. Here are the test scores:
85, 92, 91, 0, 90
As you can see just by looking at the numbers 4 students did well, and 1 not so well because they slept in and missed the test. Let's see what the mean score is:
85 + 92 + 91 + 0 + 90 = 358
358 / 5 = 71.6
Using the following grading scale: A=> 90, B=80-89, C=70-79, D=60-69 and F=<60 we would say, based on the mean, the average grade in the class was a low C, yet there were 3 A's, 1 B and an F. Looking at just the scores it seems like those students that showed up knew the material very well, however because of that one low grade it threw the average off making it look like the class was performing at a low C average.
Now lets calculate the median:
First we put the scores in order:
0, 85, 90, 91, 92
Now we find the middle score to be 90
0, 85,
90, 91, 92
Based on our above grading scale, we can say the average score was around 90 or a low A. This is much more representative of the scores since 3 people got A's and 1 got a B. As you can see, with the median, the outliers do not have as great of an impact on the average.