Mode Of Grouped Data Explained with Formula and Examples

The concept of Mode of Grouped Data is essential in mathematics and statistics, especially for board exam preparation and understanding data trends. It helps students analyze and interpret real-world datasets effectively.

Understanding Mode of Grouped Data

Mode of Grouped Data refers to finding the most frequently occurring value—in other words, the value that appears with the highest frequency—in a grouped frequency distribution. Unlike ungrouped data, where the mode can be spotted directly, grouped data requires a formula-based approach. This concept is widely used in statistics, data analysis, and central tendency calculations.

Why is Mode of Grouped Data Important?

Learning about the Mode of Grouped Data is important for several reasons:

• It is a key measure of central tendency (along with mean and median).
• Featured in CBSE class 10 syllabus and competitive exams.
• Helps make sense of large datasets in surveys, reports, and business.
• Enables you to summarize information with one representative value.
• Builds foundational skills for advanced statistics and data science.

Grouped vs Ungrouped Data: What’s the Difference?

Ungrouped data lists individual values, making it easy to spot the mode directly. Grouped data organizes values into class intervals with corresponding frequencies. In grouped data, you must use a specific formula to accurately estimate the mode.

Type	How to Find Mode	Example
Ungrouped Data	Identify the value with highest frequency.	For 2, 6, 4, 2, 5, 2: Mode = 2
Grouped Data	Find modal class, then apply formula.	Class intervals with frequencies

Key Definitions in Mode of Grouped Data

• Class Interval: Range of values grouped together (e.g., 0–10, 10–20).
• Frequency: Number of data points in a class interval.
• Modal Class: The class interval with the highest frequency.
• Mode: The value that appears most frequently, estimated for grouped data using a formula.

Mode of Grouped Data Formula

The standard formula to calculate the mode for grouped data is:

Mode = l + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h

Where:

• l = Lower limit of the modal class
• h = Class size (interval width)
• f₁ = Frequency of modal class
• f₀ = Frequency of class before modal class
• f₂ = Frequency of class after modal class

Step-by-Step Calculation of Mode of Grouped Data

Let’s see the entire process in a full example, as you would solve it in class 10 board exams:

1. Prepare the frequency distribution table of the data.

2. Identify the modal class—the class interval with the highest frequency (f₁).

3. Note down:
4. Plug all these values into the mode formula.

5. Calculate stepwise as follows:

(a) Subtract f₀ from f₁ and from 2f₁.
(b) Subtract f₂ from result.
(c) Divide (f₁ - f₀) by (2f₁ - f₀ - f₂).
(d) Multiply the outcome by h.
(e) Add this to l to get the mode.

6. Final answer: Write it clearly and highlight as your mode.

Mode of Grouped Data Table Example

Here’s a table to illustrate how to find the mode of grouped data:

Class Interval	Frequency
0 – 2	6
2 – 4	7
4 – 6 (Modal Class)	8
6 – 8	2
8 – 10	1

In this table, 4 – 6 is the modal class as it has the highest frequency.

Worked Example – Solving a Problem

Let’s solve the above example step by step:

1. Modal class = 4 – 6, so:

2. Use the mode formula:

3. Calculate numerator and denominator:

4. Final value:

So, the mode of this grouped data is 4.29.

Special Cases: Two Modal Classes and Unequal Intervals

If two or more class intervals share the highest frequency, both are called modal classes and the distribution is bimodal or multimodal. In such cases, mode is usually not calculated unless specified by your exam or teacher. For unequal class intervals, mode calculation is generally not expected at school level; consult your textbook or Data Management page for advanced steps.

Common Mistakes to Avoid

• Choosing the highest frequency but not checking for adjacent intervals.
• Plugging in the wrong frequencies (f₀, f₁, f₂).
• Forgetting to use the lower boundary (l) of the modal class.
• Using incorrect class size (h).

Practice Problems

• Given frequencies for class intervals 0–10, 10–20, ..., which is the modal class and what is the mode?
• If a dataset's highest frequency occurs in two intervals, what type of distribution is it?
• Find the mode for the class intervals: 0–5 (3), 5–10 (5), 10–15 (8), 15–20 (6), 20–25 (2).
• Explain what happens if all class intervals have the same frequency.

Real-World Applications

The concept of Mode of Grouped Data is used in real-world scenarios like finding the most common marks range in school results, analyzing sales data, and understanding survey outcomes. Vedantu often uses practical worksheets and visual explanations to connect students to these applications.

We explored the idea of Mode of Grouped Data, how to calculate it step by step, and its importance in statistics and everyday applications. To master more statistics concepts, keep practicing on Vedantu and try out similar central tendency measures like mean and median.

Quick Revision Table

Key Point	Details
Formula	Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
Modal Class	Class interval with highest frequency
Common Error	Wrong value for l, h, f₀, f₁, or f₂
Used In	Board exams, business, surveys

Explore Related Concepts

• Mean, Median, Mode – See all central tendency measures together.
• Central Tendency – Theory and in-depth explanation for exams.
• CBSE Class 10 Maths Important Topics – Syllabus mapping for easier study.
• Variance – Learn more about spread of data.
• Statistics – Applications of data analysis and handling.