In mathematics, median is the middle value of an ordered set of values. It is also defined as the numeric value which separates the higher half of the data from the lower half.
How is Median Calculated?
Median is calculated by arranging the numerical data in ascending order, i.e., starting from the lowest, and choosing the middle value in the set. While that works fine when you have odd number of observations, you have to calculate the arithmetic mean for the two middle values to find the median if you have even number of observations.
Example 1: Odd Number of Observations
You are supposed to calculate the median weight for a group of people. In order to do this, you weigh seven people who weigh 94, 108, 120, 145, 88, 98, and 115 lbs respectively. The first thing to do is, arrange the data in ascending order; that will be: 88, 94, 98, 108, 115, 120, and 145.
Like we said, median is the middle value when it comes to odd number of observations. As you took seven samples into consideration, the middle value will be the fourth value in your data, which in this case is 108. So, the median weight of the group of seven people you studied is 108 lbs.
Example 2: Even Number of Observations
Now let's consider you are calculating the median weight of a group of eight individuals. Let's assume that the data you compiled after weighing eight people in the group was 94, 108, 120, 145, 88, 98, 115, and 130. (We will simply add another observation to the previous example.)
After arranging it in the ascending order, you get a list in the following order: 88, 94, 98, 108, 115, 120, 130, and 145. There being no middle value, you cannot pinpoint a particular number and call it the median. Instead, you have to choose two middle values and find the arithmetic mean.
In this case the two middle values are 108 and 115. In order to find their arithmetic mean, you will have to add these two values and divide their sum by 2. When you add 108 + 115, the sum will be 223, and when you divide this 223 by 2, the sum will be 111.5, which will be the median weight for the group.
Is Median the Same as Average?
Average, as the name suggests, is the average value which is calculated by adding all the values in the set of data and dividing it by the total number of values. Median, on the other hand, is the middle value in the set of data arranged in ascending order.
While the median for the example we discussed earlier (88, 94, 98, 108, 115, 120, 145) will be 108, the average for the same will be 109.71, i.e., the sum of all the values (768) divided by the total number of values (7).
Yet another important concept related to median is 'median income'―a statistical number compiled by the U.S. Department of Housing and Urban Development, which divides households into two equal segments; one with income more than the median and the other with income less than it.
Interestingly, median income is a better indicator of the average American income, because, unlike average, it is not affected by extreme values.