1281 LearnersLast updated on June 12th, 2025
Modal Class
The modal class is the class interval with the highest frequency in a grouped distribution. It represents the range where most data is concentrated. Unlike a single mode in ungrouped data, the modal class gives a broader perspective on data distribution. Let us now see more about modal classes and how to calculate them.
What is the Modal Class?
The modal class is the class interval with the highest frequency in a grouped frequency distribution. It represents the range in which most data points fall. Unlike the mode of ungrouped data, the modal class gives a range where the most frequent values occur. To estimate a modal class, we use the formula given below:
Mode = L + (f1- f0 / 2f1 - f0 - f2) x h
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How to Find Modal Class
To find a modal class, follow the following steps:
Step 1: If your data is not organized, divide it into intervals or classes.
Step 2: Count the frequency of each class interval with the highest frequency. The class interval with the highest frequency is called the modal class.
Step 3: Determine the class interval with the highest frequency. This interval is known as the modal class.
Step 4: Apply the formula:
Mode = L + (f1- f0 / 2f1 - f0 - f2) x h
Where,
L is the lower limit of the modal class
f0 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.
Step 5: Substitute the values and compute to get the modal class where the data is most concentrated.
How to Find the Modal Class from a Graph/Chart
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:
Mode = L + (fm - f1 / 2fm - f1 - f2) x 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.
Real-life Applications on Modal Class
There are many uses of the modal class. Let us now see the uses and applications of modal classes in different fields:
Education and Exam Analysis:
We use modal class in education and exam analysis to identify the most common score range in student performance, to find the most frequent grade range in a class, and to understand which subjects students struggle with the most based on score distributions.
Business and Sales Analysis:
We use modal class in business and sales analysis to determine the price range that attracts most customers, to identify the most sold product category in a retail store, and to analyze customer purchasing behavior to optimize stock levels.
Healthcare and Medicine:
We use modal classes in healthcare and medicine to identify the most common age group affected by a disease, analyze the most frequent blood pressure range among patients, and find the common BMI category in a population.
Common Mistakes and How to Avoid Them in Modal Class
When understanding the concept of modal class, students tend to make mistakes. Here, are some common mistakes and solutions:
Mistake 1
Confusing Mode with Mean or Median:
Students should remember that the modal class is the class interval with the highest frequency. The mean is the average and the median is the middle value. The mode represents the most frequently occurring category.
Mistake 2
Selecting the Wrong Modal Class:
Students should carefully examine the frequency distribution and choose the class with the highest frequency as the modal class.
Mistake 3
Ignoring Class Boundaries (Midpoint Confusion)
Students should remember to always use the lower boundary of the modal class in the mode formula, not the midpoint or upper boundary.
Mistake 4
Misinterpreting “No Mode” Situations:
Students should remember that if all frequencies are the same, there is no mode. They must also remember that if there are two or more modal classes with the same highest frequency, the distribution is bimodal or multimodal
Mistake 5
Rounding Errors in Calculations:
Students should remember to always use proper rounding rules and to maintain at least two decimal places for accuracy.
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Solved examples on Modal Class
Problem 1
Given the frequency distribution below, identify the modal class
The modal class here is 30 – 40.
Explanation
Look at the frequency column.
Identify the highest frequency
Frequencies: 5, 12, 20, 15
The highest frequency is 20
Class interval with frequency 20 is 30 – 40.
Problem 2
Consider the following frequency table. Identify the modal class or classes
The modal classes are 20 – 30 and 30 – 40
Explanation
The given frequencies: 3, 7, 10, 10, 8
The highest frequency is 10, and it appears in 20 – 30 and 30 – 40.
Since the two classes share the highest frequency, the distribution is bimodal
Problem 3
Given the grouped data below, find the mode of the data:
The estimated mode is 36.15
Explanation
Identify the modal class:
The highest frequency is 20, which is for the interval 30 – 40
Assign the values:
L = 30
f1 = 20
fm = 12
f2 = 15
h = 10
Apply the formula
Mode = 30 +(20 - 122(20) - 12 - 15) x 10
= 30 + (8/13) x 10 = 30 + 6.15 = 36.15
Problem 4
Using the mode formula, calculate the mode for the following data:
The estimated mode is approximately 66.67
Explanation
Identify the modal class:
The highest frequency is 25 in 60 – 70.
Assign the values:
L = 60
f1 = 25
fm = 15
f2 = 20
h = 10
Apply the formula:
Mode = 60 +(25 - 152(25) - 15 - 20) x 10
= 60 + (10/15) x 10 = 60 + 6.67 = 66.67.
Problem 5
Given the grouped data below, identify the modal class(s) and estimate the mode. Choose one modal class for the calculation.
The distribution is bimodal with modal classes 35 – 45 and 45 – 55; using the first modal class, the estimated mode is 45
Explanation
Identify the modal classes:
The highest frequency is 12, which occurs in both 35 – 45 and 45 – 55.
Choose one for calculation:
35 – 45.
Assign the values:
L = 35
f1 = 12
fm = 9
f2 = 12
h = 10
Apply the formula:
Mode = 35 +(12 - 9 / 2(12) - 9 - 12) x 10
= 35 + (3/3) x 10 = 35 + 10 = 45.
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FAQs on Modal Class
1.What is the modal class?
2.How do you identify the modal class in a frequency distribution?
3.Why is the modal class important in statistics?
4.Can a frequency distribution have more than one modal class?
5.What is the formula for calculating mode in grouped data?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
