Modal Class

In statistics, the modal class is the class or interval having the greatest frequency in a data set. Assume you have a set of numbers indicating, say, the heights of kids in a classroom. If you group these heights into intervals, such as “120-130 cm,” “130-140 cm,” and so on, then the modal class will be the one have the most pupils. So, if the majority of pupils are between 130-140 cm tall, that range would be considered the median class. It’s an easy technique to identify the most prevalent range or category in your data.

What is Modal Class

Modal class in math, is the class or interval in a frequency distribution that has the greatest frequency or mode. It is the class interval with the highest number of observations or data points. For example, if you have a frequency distribution of test scores with class intervals representing ranges of scores (e.g., 0-10, 11-20, 21-30, etc.), and the interval 11-20 has the highest frequency of scores, the modal class is 11-20. Identifying the modal class can help you comprehend a dataset’s central tendency and draw conclusions about its most prevalent values.

Modal classes are determined by examining the frequency distribution of data points. They give insight into the central tendency of the data set and help in the identification of significant trends or patterns.

Definition of Modal Class

A modal class is the class or category that appears the most frequently in a set of data. It indicates the most common value or range in the data.

Modal Class Formula

Modal class, which indicates the data interval with the highest frequency in grouped data, is calculated using a particular formula. This formula helps us to find the mode, which is the value or range that appears the most frequently in a dataset. In the context of grouped data, the modal class denotes the interval or range with the highest frequency of observations. Identifying this modal class allows us to determine the mode of the dataset. Thus, the mode may be computed using the following formula:

Mode = l + (f₁-f₀ / 2f₁-f₀-f₂) × h

Where,

• f₁ represents the frequency of the modal class.
• f₀ represents the frequency of the class before the modal class.
• f₂ is the frequency of the class that follows the modal class.
• h represents the size of the class intervals.
• l is the lower limit of the modal class.

How to Find Modal Class?

Here are the steps for finding the modal class in simple lines, with an example:

Step 1: If your data isn’t already organised, divide it into intervals or classes.

Step 2: Count the frequency of each class interval, that is, how many data points are in each interval.

Step 3: Determine the class interval with the highest frequency. This interval is known as the modal class.

Step 4: Once you’ve determined the modal class, use this formula:

Mode = l + (f₁-f₀ / 2f₁-f₀-f₂) × h

Step 5: Enter the values of L, f₀​, f₁, f₂​, and ℎ h into the formula.

Step 6: Run the computations to determine the mode, which reflects the value in the modal class where the data is most concentrated.

Related Reads
Mean, Median and Mode	Median in Statistics
Measure of Central Tendency in Statistics	Mean, Median and Mode of Grouped Data
Relation between Mean, Median and Mode	Cumulative Frequency

Example of Modal Class

Example 1: A group of students surveyed 51 families in a locality, as indicated in the frequency distribution table below. Find the mode of the provided data.

Class interval	5-10	10-15	15-20	20-25	25-30
Frequency	8	10	15	12	6

Solution:

The above table shows that the highest class frequency is 15, and the corresponding class interval is 15-20. As a result, the modal classification for the provided data is 15-20.

The bottom limit of modal class is l = 15.
Class size i.e. h = 5
The frequency of modal class is f₁ = 15.
Frequency of class progressing to modal class f₀ = 10
The frequency of a class progressing to the modal class is f₂ = 12.
We know that the formula for finding the mode of the grouped data is:

Mode = l + (f₁-f₀ / 2f₁-f₀-f₂) x h

Now, inserting the values in the mode formula yields,

Mode = 15 + (15 -10 / 2(15) – 10 – 12) x 5

Mode = 15 + 3.125

Mode = 18.125

As a result, the mode of the combined data is 18.125.

Example 2: Sham carries the weight of 60 people from her organisation. She must locate the modal class in the supplied table. What would the modal class be?

Class interval	10-20	20-30	30-40	40-50	50-60
Frequency	18	12	7	15	8

Solution:

Given these frequencies: 18, 12, 7, 15, 8

Let’s organise this in increasing order: 7, 8, 12, 15, 18

The class interval with the greatest frequency is known as the modal class. The highest frequency is 15.

Thus, the modal class ranges from 40 – 50.

Practice Problem of Modal Class

Q1: Find out the mode for the following table:

X	10-20	20-30	30-40	40-50	50-60
Frequency	12	26	34	53	45

Q2: Find out the modal class for the following distribution:

Class Interval	11-22	22-33	33-44	44-55	55-66	66-77	77-88
Frequency	15	20	34	43	52	38	45

Q3: Determine the modal class using the provided frequency table.

X	70-60	60-50	50-40	40-30	30-20	20-10
Frequency	62	56	34	48	26	38

Modal Class Frequently Asked Questions

What is the modal class in statistics?

The modal class is the interval in a frequency distribution that has the highest frequency, or mode. It reflects the dataset’s most commonly occurring range or category.

What is the importance of finding the modal class?

Identifying the modal class allows you to comprehend the data’s central tendency and discover the most common values or ranges. It gives information on the distribution and properties of the dataset.

What is the formula to calculate the mode using the modal class?

The formula for finding the mode from grouped data is: Mode = l + (f₁-f₀ / 2f₁-f₀-f₂) × h, where l is the lower limit of the modal class, f₀ ​is the frequency of the class before the modal class, f₁ ​is the frequency of the modal class, f₂ ​is the frequency of the class after the modal class, and h is the class size.

How do you locate the modal class step by step?

Step 1: Separate the data into intervals or classes.
Step 2: Determine the frequency of each class interval.
Step 3: Find the class interval with the highest frequency, which is known as the modal class.
Step 4: Using the mode formula, determine the mode based on the modal class.

What data does the modal class provide?

The modal class represents the most common range or category in the sample. It aids in analysing the concentration of data and spotting notable patterns or trends.

Can a dataset have many modal classes?

Yes, a dataset can contain several modal classes if two or more intervals have the same maximum frequency. In such instances, the dataset is said to as multimodal.