Question

How to calculate mode in case of continous series

Answer 1

Answer:

When data is given based on ranges alongwith their frequencies. Following is an example of continous series:

Items 0-5 5-10 10-20 20-30 30-40

Frequency 2 5 1 3 12

Formula

Mo=L+f1−f02f1−f0−f2×i

Where −

Mo = Mode

f1 = Frquencey of modal class

f0 = Frquencey of pre-modal class

f2 = Frquencey of class succeeding modal class

i = Class interval.

Explanation:

Example

Problem Statement:

Calculate the Arithmetic Mode from the following data:

Wages

(in Rs.) No. of workers

0-5 3

5-10 7

10-15 15

15-20 30

20-25 20

25-30 10

30-35 5

Solution:

Using following formula

Mo=L+f1−f02f1−f0−f2×i

L = 15

f1 = 30

f0 = 15

f2 = 20

i = 5

Substituting the values, we get

Mo=15+30−152×30−15−20×5=15+3=18

Thus Arithmetic Mode is 18.