Modal Class
2026-02-28 09:13 Diff
https://brightchamps.com/en-us/math/data/modal-class

To find the modal class from a chart or graph, follow the steps mentioned below: 


Step 1: Identify the highest bar or peak:


In a histogram, look for the tallest bar (highest frequency). In a frequency polygon, find the highest peak on the graph. For the bar chart, locate the category with the highest bar.


Step 2: Read the class interval:


The modal class is the interval corresponding to the tallest bar or peak. If two bars have the same highest frequency, then the given dataset is bimodal or multimodal.


Step 3: Estimate the mode using the formula:


If needed, apply the mode formula for grouped data:


           \(\text{Mode} = L + \left( \frac{(f_{1} - f_{0})}{(2f_{1} - f_{0} - f_{2})} \right) \times h\)


Where,


L is the lower limit of the modal class


fm is the frequency of the modal class


f1 is the frequency of the class preceding the modal class


f2 is the frequency of the class succeeding the modal class


h is the class width.

For example, find the modal class from the graph.
 

Marks Number of Students 0-10 5 10-20 8 20-30 12 30-40 20 40-50 10 50-60 5

Here, the tallest bar corresponds to 30-40, so this is the modal class. 

Using the Mode formula: \(\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \)

Where, 

\(L = 30 \\ \ \\ f_1 = 20 \\ \ \\ f_0 = 12 \\ \ \\ f_2 = 10 \\ \ \\ h = 10 \)


​​\(\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h \)

\(= 30 + \frac{20 - 10}{2 \times 20 -12- 12} \times 10 \)
 

\(= 30 + {8 \over 18} \times 10\)
 

\(= 34.44\)


So, modal class is 30-40 and mode is 34.44 marks.