Median-Measure of Central Tendency

Median in Statistics a branch of Mathematics is one of the measures of central tendency. We can define Median as the middle value of the given list when arranged in the numerical order.  For instance, let us consider the data, 10, 10, 9, 9, 8, 10, 7. Let us first arrange the given data in the numerical order that gives us 7,8,9,9,10,10,10. There are 7 data values, so the middle value would be the fourth value. Here the fourth value is 9 and hence the median.

To find the Median of a given set of data, first we need to arrange the given data list in the numerical order, then count the number of values in the given list. This is important as to know whether the count is even or odd. If the count is odd then we do not need to worry as the middle value in the arranged list would be the median, but if the count is even then we will have two middle values.  So, how do we go about, the middle of the two middle values in simple words the average of the two middle values gives us the median.  For instance, consider the data, 8, 7, 4, 3, 9, 10, 9, 8. First we arrange the given data in the increasing order or numerical order, 3, 4, 7, 8, 8, 9, 9, 10.

Now we count the data values, there are 8 data values which is an even number and hence we have two middle values. The two middle values are the fourth and fifth values which are 8, 8. To find median when the count of the data values is even is to find the average of the two middle values which would be (8+8)/2 = 16/2 = 8. So, the median is 8.

We can calculate median of the given data list using the Median Formula which is one more than the total number of data values divided by 2. Median Formula is given by (n+1)/2 , the value got is the position of the data value that would be the median when the list is arranged in the numerical order. For instance if there are 7 data values in the list, then (7+1)/2 = 8/2 = 4, which means the fourth value will be the median. If there are 8 values that is even number of values in the list, then (8+1)/2 = 9/2 = 4.5, a bit confusing, as we do not have 4.5th value. Here we take the average of the fourth and fifth values to calculate median as 4.5 lies between 4 and 5.