# Mode of Grouped Data

## Notes

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:

 Family size 1-3 3-5 5-7 7-9 9-11 No. of families 7 8 2 2 1

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

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