Mode of Grouped Data

The mode of a list of data values is simply the most common value. Eg. find the mode of the ungrouped data 2, 3, 4, 4, 3, 9, 6, 3, 5, 3

Here the mode is 4 because the highest frequently occured number is 4.

But this was about ungrouped data. In this concept we will learn to find mode of a grouped data. The mode of a grouped data is found with the help of formula.

Mode= `l+ [(f1-fo)/ (2f1-fo-f2)] xx h`

where, l= lower limit of modal class

f1= frequency of the modal class

fo i.e f not= frequency of the class preceeding the modal class

f2= frequency of the class succeeding the modal class

h= Class size= Upper limit- Lower limit

Let's take a example for better understanding,

Find the mode of the given data:

Solution:

The maximum frequency is 8

Therefore, Modal class= 3-5,

then l= 3, h=2, f1=8, fo=7, f=2

`Mode= l+ [(f1-fo)/ (2f1-fo-f2)] xx h`

          = `3+ [(8-7)/ (16-7-2)] xx 2`

          = `3+ (1 xx 2)/7`

          = `3+ 0.285`

Mode= 3.285