Concept of Mode

Mode is the value which occurs the greatest number of times in the data. When each value occurs the same number of times in the data, there is no mode. If two or more values occur the same number of times, then there are two or more modes and the distribution is said to be multi-mode. If the data has only one mode the distribution is said to be uni-model, and for data having two modes the distribution is said to be bi-model.

Mode from Ungrouped Data
Mode is calculated from ungrouped data by inspecting the given data. We pick out the value which occurs the greatest number of times in the data.

Mode from Grouped Data
With frequency distribution with equal class interval sizes, the class which has the maximum frequency is called the model class.

Mode = l + \frac{{{f_m} - {f_1}}}{{\left( {{f_m} - {f_1}} \right) + \left( {{f_m} - {f_2}} \right)}} \times h

Here
l= Lower class boundary of the model class
{f_m}= Frequency of the model class (maximum frequency)
{f_1}= Frequency preceding the model class frequency
{f_2}= Frequency following the model class frequency
h= Class interval size of the model class

Mode from Discrete Data
When the data follows a discrete set of values, the mode may be found by inspection. The mode is the value of X corresponding to the maximum frequency.

 

Example:
Find the mode of the values 5, 7, 2, 9, 7, 10, 8, 5, 7

Solution:
The mode is 7 because it occurs the greatest number of times in the data.

Example:
The weights of 50 college students are given in the following table. Find the mode of the distribution.

Weight (Kg)
60 – 64
65 – 69
70 – 74
75 – 79
80 – 84
No of Students
5
9
16
12
8

 

Solution:

Weight (Kg)
No of Students
f
Class Boundary
60 – 64
5
59.5 – 64.5
65 – 69
9
64.5 – 69.5
70 – 74
16
69.5 – 74.5
75 – 79
12
74.5 – 79.5
80 – 84
8
79.5 – 84.5

Mode = l + \frac{{{f_m} - {f_1}}}{{\left( {{f_m} - {f_1}} \right) + \left( {{f_m} - {f_2}} \right)}} \times h


Mode = 69.5 + \frac{{19 - 9}}{{\left( {16 - 9} \right) + \left( {16 - 12} \right)}} \times 5


Mode = 69.5 + \frac{7}{{7 + 4}} \times 5 = 72.68