What is the Median in Math

While the term 'Median' refers to middle value of an ordered set of values in math terms, 'Mode' refers to the most frequently occurring random variable in the set of data. Understanding median and mode is crucial in applied mathematics. Median can also be defined as the numeric value which separates the higher half of the data from the lower half. While that may be a bit confusing to understand, the information on calculation of median along with some examples given below will simplify it for you.

What is Median in Math?

Basically, median is calculated by arranging the numerical data in an ascending order i.e. starting from the lowest, and choosing the middle value in the set. While that may work fine when you have odd number of observations (values); you will have to calculate the arithmetic mean for the two middle values to find the median if you have even number of observations. Going through a couple of examples given below will help you get a better understanding of what is the median in math and how it is calculated.

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, 115 lbs respectively. The first thing to do while calculating the median is to arrange your data in an ascending order. When you execute this step, the numbers given above will be arranged in the following order - 88, 94, 98, 108, 115, 120, 145. As median is the middle value when it comes to odd number of observations, you will have to find the middle value of your data. As you took seven samples into consideration, the middle value will be fourth value in your data - which in this case is 108. This means that 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 the eight people in the group was 94, 108, 120, 145, 88, 98, 115, 130. (We will simply add another observation to the above example.) After arranging it in the ascending order, you get a list in the following order - 88, 94, 98, 108, 115, 120, 130, 145. There being no middle value, you cannot pinpoint on a particular number and call it the median. Instead, you will have to choose two middle values and find the arithmetic mean for the same. In this case the two middle values are 108 and 115. In order to find their arithmetic mean, you will have to add the two middle values and divide them 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?

Is median the same as average? If this question is to be answered in one word, the answer would be, No! If you try to find out what is average or arithmetic mean in math, you would realize that it is the average value which is calculated by summing 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 above (88, 94, 98, 108, 115, 120, 145) will be 108 (which is the middle value of the ordered data), the average for the same will be 109.71 ( i.e. the sum (768) of all the values divided by 7 i.e. the total number of values.)

Yet another important concept related to median is 'median economy' - 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 the median. If you have the basic understanding of what is median income, you'd realize that it is a better indicator of the average American income than mean or average - as it is not affected by extreme values like average is.