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 25th item
Since the 25th 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 23rd item
Since the 23rd item falls under the cumulative frequency 26, and the size of the distribution against this cf value is 155.
Median = 155