Krishna
1

Step 1: Recall the mode formula for the grouped data

Mode =   l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h

Where,

l - The lower boundary of the modal class,

h -  The class size,

f_1 - The frequency of modal class,

f_0 - The frequency of the class preceding the modal class,

f_2 - The frequency of the class succeeding the modal class.

Step 2:  Identify the modal class and locate the values of the frequencies.

NOTE:  Locate a class with the maximum frequency, called the modal class.

(The mode is a value inside the modal class)

Here the maximum class frequency is 8, and the class corresponding to this

frequency is 3-5.

So, the modal class is 3-5.

lower boundary l = 3

Class size h = 5 - 3 = 2

The frequency of modal class   f_1  = 8

The frequency of the class preceding the modal class f_0  = 7

The frequency of the class succeeding the modal class. f_2 = 2

Step 3: Substitute the values in the formula and calculate the mode.

Mode =   l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h

=   3 + \frac{8 - 7}{2*8 - 7 - 2} * 2

=   3 + \frac{1}{7} * 2

=  3 + 0.2857

=  3.286

Hence, mode = 3.286