MODE OF A GROUPED DATA

In case of a grouped frequency distribution, the exact values of the variables are not known and as such it is very difficult to locate mode accurately. In such cases, if the class intervals are of equal width, an appropriate value of the mode may be determined by

The class interval with maximum frequency is called the modal class.

Where

l - lower limit of the modal class

f - frequency of the modal class

f₁ - frequency of the class just preceding the modal class

f₂ - frequency of the class succeeding the modal class

c - width of the class interval

Example : 

Find the mode for the following data.

Solution :

To convert discontinuous class interval into continuous class interval, 0.5 has to be substracted from the lower limit and 0.5 has to be added at the upper limit for each class interval.

Modal class is 16 -20 since it has the maximum frequency.

l  =  15.5, f  =  32, f₁  =  16, f₂  =  24,

c  =  20.5 – 15.5  =  5

f - f₁  =  32 - 16  =  16

2f - f₁ - f₂  =  2(32) - 16 - 24  =  24

Then, 

Mode  =  15.5 + (16/24) x 5

=  15.5 + 3.33

=  18.83

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