How to Find Median Value of Odd and Even Set of Data

In this lesson we will learn how to calculate the median of a data set, when data set has odd and even numbers or observations.

To learn the median of a data set, first we should understand what is median.

(You can learn about median here)

To define the median in simplest way, we can say that the

Median is the midpoint of the given data.

Median = Middle number 

There are two possibilities, when we find the median of a data set.

1. The total number of observation is odd.

2. The total number of observation is even.

Formula for odd and even numbers

                         When n is odd

             Median = (n + 1)/2th term,

                       When n is even

Median = {(n/2)th + (n/2+1)th}term/2

1. If the total number of an observation is odd, then the number in the middle of the series is the median. 

2. If the total number of an observation is even then there two numbers in the middle, in this case we have to find the pair of middle numbers, adding them together and dividing by 2 (or average of middle two terms.)

Example: If we have numbers like 10, 12, 13, 15, 16, 21, 32, 38, 54. 

Here number of observation is odd that is 9. 

So the number in the middle of the series is the median.

Series is 10,  12 , 13,  15,  16,  21,  32,  38,  54.

Here we can say midpoint is 16, so median of the series is 16.

Example: If we have numbers like 20, 22, 24, 35, 43, 56, 62, 63, 68, 74, 85. Here number of observation is odd that is 11.

 20, 22, 24, 35, 43, 56, 62, 63, 68, 74, 85.

There are 11 numbers in the list so, the middle number will be

 (11 + 1)÷2 = 6th number.  

Here 6th number in the series is 56, 

So, median value of this set is 56.

Example: If we have numbers like 12, 14, 23, 35, 36, 42, 53, 68, 74, 85. Here number of observation is even that is 10.

Here n = 10

      12, 14, 23, 35, 36, 42, 53, 68, 74, 85.

Here are two numbers in the middle in this case we find the pair of middle numbers, adding them together and dividing by 2.

Two middle terms are (n/2)th term = 10/2 = 5th term = 36

and (n/2 + 1)th term = (10/2 +1)th term = 6th term = 42.

Now our two middle terms are 36 and 42.

Hence median = (36 + 42)/2

median = 78/2

median = 39

Example: What is the median age of these 5 students.

To find the median, numbers have to be arranged in ascending order.
The numbers are 20, 25, 28, 35, 39 are in ascending order.
Here number of observation is odd, that is 5. 

So the number in the middle of the series is the median.

Series is 20,  25 , 28,  35, 39.

Here we can say midpoint is 28, so median of the series is 28.