Mode of Grouped Data

In the ungrouped data the most frequently occurring no. is the mode of the sequence, but in the grouped data we can find the class interval only which has the maximum frequency number i.e. the modal class.

The value of mode in that modal class is calculated by

Mode =1+\dfrac{f_1+f_0}{2f_1-f_0-f_2}\times h

l = lower class limit of the modal class

h = class interval size

f1 = frequency of the modal class

f0 = frequency of the preceding class

f2 = frequency of the succeeding class

Example

The table of the marks of the students of a class is given. Find the modal class and the mode.

Marks0 – 2020 – 4040 – 6060 – 8080 – 100
No. of students48675

Solution

Here we can see that the class interval with the highest frequency 8 is 20 – 40.

So this is our modal class.

Modal class = 20 – 40

Lower limit of modal class (l) = 20

Class interval size (h) = 20

Frequency of the modal class(f1) = 8

Frequency of the preceding class(f0) = 4

Frequency of the succeeding class (f2) = 6

Mode =1+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h

=20+\dfrac{8-4}{16-4-6}\times20

=20+\dfrac{4}{6}\times20

=20+13.33=33.33

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