Median

Another measure of central tendency is the median. The median is the middle number of a set of numbers when arranged in increasing order or listed from least to greatest. The caveat is that there are two cases when finding the median of a set of numbers.

Case 1: There is an odd number of numbers in the set.

In this case, we write the numbers in ascending order then find the middle number.

Example: Find the median of 8, 5, 7, 10, 0, 11, 3.

If we arrange these numbers from least to greatest, we have 0, 3, 5, 7, 8, 10, 11 . This falls under Case 1 because there are seven (7) numbers or elements in the set which is an odd number. When there is an odd number of numbers in a set, there is only one middle number.

Therefore, the median for this set of numbers is 7.

Case 2: There is an even number of numbers in the set.

For this case, we write the numbers from least to greatest then find the mean or average of the two middle numbers to get the median.

Example: Find the median of 15, 9, 2, 21, 25, 18.

When listed in ascending order, we get 2, 9, 15, 18, 21, 25. As you can see, there are six (6) numbers in the set. Since there is an even number of numbers in this group, we have two middle numbers namely, 15 and  18.

To get the median, we calculate the mean or average of 15 and  18.

{{15 + 18} \over 2} = {{33} \over 2} = 16.5

Therefore, the median is 16.5.