HOW TO FIND MODE OF UNGROUPED DATA

Mode for Raw data

For an individual data mode is the value of the variable which occurs most frequently.

Example 1 : 

In a factory, seven labors are receiving the daily wages of $500, $600, $600, $800, $800, $800 and $1000, find the modal wage.

Solution : 

In the given data $800 occurs thrice. So, the mode is $800.

Example 2 : 

Find the mode for the set of values 17, 18, 20, 20, 21, 21, 22, 22.

Solution : 

In this example, three values 20, 21, 22 occur two times each. There are three modes for the given data!

Note : 

∙ A distribution having only one mode is called unimodal.

∙ A distribution having two modes is called bimodal.

∙ A distribution having Three modes is called trimodal.

∙ A distribution having more than three modes is called multimodal.

Example 3 :

Following are the margin of victory in the foot ball matches of a league.

1, 3, 2, 5, 1, 4, 6, 2, 5, 2, 2, 2, 4, 1, 2, 3, 2, 3, 2, 3, 1, 1, 2, 3, 2, 6, 4, 3, 2, 1, 1, 4, 2, 1, 5, 3, 4, 2, 1, 2.

Find the mode.

Solution : 

Since 2 has occurred more number of times (14 times), the mode of the given data is 2.

Example 4 :

The number of children in 20 families are

1, 2, 2, 1, 2, 1, 3, 1, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1

Find the mode.

Solution : 

Since 2 has occurred more number of times (15 times), the mode of the given data is 2.

Mode for Ungrouped Frequency Distribution

In a ungrouped frequency distribution, the value of the item having maximum frequency is taken as the mode.

Example 5 : 

A set of numbers consists of five 4’s, four 5’s, nine 6’s,and six 9’s. What is the mode ?

Solution :

6 has the maximum frequency 9.

So, 6 is the mode.

Example 6 : 

The demand of track suit of different sizes as obtained by a survey is given below :

Which size is in greater demanded?

Solution :

Since size 40 has the maximum frequency 37, mode of the above data is 40.

So, size 40 is in greater demand. 

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