What is Median?

When elements in the data set are organised sequentially, that is, in either an ascending or descending order of magnitude, the median can be referred to as the middle value of the data set. Its value locates in a distribution in such a way that 50% of the items are below it and 50% are above it. It focuses on the center or middle of a distribution.

What is Discrete Series?

In discrete series (ungrouped frequency distribution), the values of variables represent the repetitions. It means that the frequencies are given corresponding to the different values of variables. The total number of observations in a discrete series, N, equals the sum of the frequencies, which is Σf.

Example of Discrete Series

If 3 students score 60 marks, 9 students score 70 marks, 5 students score 80 marks, and 2 students score 90 marks, then this information will be shown as:

Marks	Number of Students
60	3
70	9
80	5
90	2

Calculation of Median in Discrete Series

The steps required to determine median of a discrete series are as follows:

Step 1: Arrange the given distribution in either ascending or descending order.

Step 2: Denote the variables as X and frequency as f.

Step 3: Determine the cumulative frequency; i.e., cf.

Step 4: Calculate the median item using the following formula:

Where, N = Total of Frequency

Step 5: Find out the value of   We can find it by firstly locating the cumulative frequency, which is equal to higher than  and then find the value corresponding to this cf. This value will be the Median value of the series.

Example 1:

Calculate the median of the following data:

 

Solution:

 

= Size of 25^th item

Since the 25^th item falls under the cumulative frequency 27 and the size of the distribution against this cf value is 2500.

Median = 2,500 

Example 2:

Find out the missing value in the following series, with a median of 12.

 

Solution:

Let’s suppose the missing frequency is x.

 

Since we know the Median of the given series is 12. Putting the value of the median in its formula, the value of the missing frequency will be:

24-21 = x

Thus, Missing Frequency = 3

Example 3:

The table below shows the distribution of students’ heights. Calculate the median of the distribution.

 

Solution:

First of all, the data must be arranged in ascending order of magnitude.

 

= Size of 23^rd item

Since the 23^rd item falls under the cumulative frequency 26, and the size of the distribution against this cf value is 155. 

Median = 155