Theory:

The mode of the grouped frequency distribution can be determined using the formula:
 
Mode \(= l + (\frac{f - f_1}{2f - f_1 - f_2}) \times c\)
 
The class interval with maximum frequency is called the modal class.
 
Where \(l\) is the lower limit of the modal class,
 
\(f\) is the frequency of the modal class,
 
\(f_1\) is the frequency of the class preceeding the modal class,
 
\(f_2\) is the frequency of the class succeeding the modal class, and
 
\(c\) is the width of the class interval.
Example:
Find the mode of the following data:
 
Class interval\(130 - 140\)\(140 - 150\)\(150 - 160\)\(160 - 170\)\(170 - 180\)
Frequency\(5\)\(36\)\(14\)\(28\)\(1\)
 
Solution:
 
The maximum frequency is \(36\), and the modal class is \(140 - 150\).
The mode of the grouped frequency distribution can be determined using the formula:
 
Mode \(= l + (\frac{f - f_1}{2f - f_1 - f_2}) \times c\)
Here, \(l = 140\), \(f = 36\), \(f_1 = 5\), \(f_2 = 14\), \(c = 10\)
 
Substituting the known values in the above formula, we have;
 
Mode \(= 140 + (\frac{36 - 5}{72 - 5 - 14}) \times 10\)
 
\(= 140 + (\frac{31}{53}) \times 10\)
 
\(= 140 + 0.585 \times 10\)
 
\(= 140 + 5.85\)
 
\(= 145.85\)
 
Therefore, the mode of the given data is \(145.85\)