 Krishna
0

Step 1: Recall the mode formula for the grouped data

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

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 61, and the class corresponding to this

frequency is 60 - 80,

So, the modal class is 60 - 80.

lower boundary l = 60

Class size h = 80 - 60 = 20

The frequency of modal class f_1 = 61

The frequency of the class preceding the modal class f_0 = 52

The frequency of the class succeeding the modal class. f_2 = 38

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

= 60 + \frac{61 - 52}{2*61 - 52 - 38} * 20

= 60 + \frac{9}{32} * 20

= 60 + \frac{9}{8} * 5

= 60 + 5.625

= 65.625

Hence, mode = 65.625