What is median?

Median definition can be divided into two categories:

1. It is the middlemost number in a list having odd number of data arranged in an ascending order
2. It is the mean of the middle two numbers in a list having even number of data arranged in an ascending order


Below is a list of marks of students in Biology quiz with 30 maximum possible mark

27 , 12 , 16 , 15 , 11

Now , let’s find the median in this set of data values


  • To find median , we will first re-arrange the data set in ascending order like this

11, 12 , 15, 16 , 27

  • There are 5 (odd ) number of values .

  • Using 1st definition of median , we find the middle number. Hence, 15 is the median here


If the list given in Problem1 is changed like this

27 , 12 , 16 , 15 , 11, 7

Find median for this list


  • First re-arrange the list in an ascending order like this

7, 11, 12 , 15, 16 , 27

  • Using 2nd median definition as we have 6 (even) number of values here , we calculate median as
    median formula

    So , 8.5 is the median here


    In general , the following median formula is used for finding the median
    general median formula

    where n is the number of values in a dataset


    In order to have cluster analysis of large dataset , the terms range ,median ,mode ,mean are frequently used where mean , mode , median are three different measures of central tendency .Mostly , mean and median are used interchangeably but the fact is mean in contrary to median is as similar as average.

    Among mean ,median ,mode and range , mode and range are quite peculiar as range is the difference between largest and smallest value while mode is the value that appears frequently.

More topics in Median
Median Definition How do you Find the Median
Median Example
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