Find the Median of a Grouped Data with example

Median of Grouped Data

Median of grouped data is the data that is continuous and is in the form of frequency distribution. Median is the middlemost value of the given data that separates the higher half of the data from the lower half. While calculating the median of grouped data, the middle value is not known as the data is divided into class intervals.

Now in a grouped data, first we find the cumulative frequencies of all the classes and n/2 th observation. Now, locating the class whose cumulative frequency is greater than or nearest to n/2 th , is known as median class.

What is Median of Grouped Data?

Median of a grouped data is data that is arranged in ascending order and is written in a continuous manner. The data is in the form of a frequency distribution table that divides the higher level of data from the lower level of data. One of the simplest methods of finding the median of grouped data is by using the formula.

The Median is to be calculated using the formula.

Median = l + [ n/2 – pcf ] / f x h

where,

l = Lower limit of a median class

h = size of the class interval

n = Number of Observations

f = Frequency of a median class

pcf = Cumulative Frequency of a class preceding the median class.

Definition of Median

Median is the middlemost value in a given data set after it is arranged in ascending order.

If the total number of items in the list is odd, then after arranging the values in the ascending order the middlemost value is taken as the median i.e. the median is given by the [(n+1)/2]th term, where ‘n’ is the total number of observations.

If the number of items in the data set is even, then the average of the two middle values is taken, that is, [(n/2)th term + ((n/2) + 1)th term] / 2, where ‘n’ is the total number of observations.

For example: Let’s consider the data: 48, 20, 50, 69, 73. What is the median?

Solution:

Arranging in ascending order, we get: 20, 48, 50, 69, 73. Here, n (no.of observations) = 5

So, to find the median of odd data we use the formula: [(n+1)/2] = (5 + 1)/2 = 6/2 = 3

Therefore, Median = 3rd observation

Median = 50.