Grouped Data

For calculating mode from a frequency distribution, the following formula

Mode

=

Lmo +

x W

where,

   L_mo      =    Lower limit of the modal class which is the class having the maximum frequency

   f₁, f₂     =    Frequencies of the classes preceding and succeeding the modal class respectively

    f         =    Frequency of the modal class

    W        =    Class interval

Let us find the mode for the data given below:

Here the largest frequency is 43, and it lies in the class 24-32. So the modal class is 24-32. Therefore,

 L_mo = 24, f₂ = 28, f₁ = 36, W = 8, f = 43

Mode	=	Lmo +		x W
	=	24 +		x 8

              =  24 + 2.55 = 26.55