Concept of Mode

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

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

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

Where
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 discrete set of values, the mode may be found by inspection. 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:
Mode is 7 because it occur 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.

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

Solution:

Weights (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