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 18, and the class corresponding to this

frequency is 4000 - 5000,

So, the modal class is 4000 - 5000.

lower boundary l = 4000

Class size h = 5000 - 4000 = 1000

The frequency of modal class f_1 = 18

The frequency of the class preceding the modal class f_0 = 4

The frequency of the class succeeding the modal class. f_2 = 9

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

= 4000 + \frac{18 - 4}{2*18 - 4 - 9} * 1000

= 4000 + \frac{14}{23} * 1000

= 4000 + 0.608695 *1000

= 4000 + 608.695

= 4608.695

Hence, mode = 4608.695