Let's consider an example data set. We will choose 10 numbers between 1 and 9.
{ 1,2,3,3,5,5,5,6,8,9 }
Now, let's add three outliers to this data set.
{ -10,1,2,3,3,5,5,5,6,8,9, 30, 100 }
We can calculate the mean and the median of this data set. Since most of our data is between 1 and 9, the good measure of central tendency should also be within this interval. We will start with the mean.
The mean is approximately 13 which is greater than eleven of the thirteen values in the data set. Therefore, the mean is not an accurate representation of a typical data value in our data set. Let's move to the median now. For data sets that have an odd number of elements, the median is the middle value.
{ -10,1,2,3,3,5, 5,5,6,8,9,30,100 }
The median of the data set is 5, so most of the data values are quite close to it. Therefore, in cases of data sets with several outliers, the median seems to be a better representation of typical data values. This conclusion is in agreement with a widely accepted truth that median is the best measure for data sets with outliers.
