Class 8 - Grouping Of Data: Methods & Examples

Grouping of data plays a significant role when we have to deal with large data. This information can also be displayed using a graph. Grouping of data is the process of organizing raw data into categories or classes. Data formed by arranging individual observations of a variable into groups, so that a frequency distribution table of these groups provides a convenient way of summarising or analyzing the data is termed as grouped data.

Table of Contents

• What is Grouping of Data
• Types of Grouping of Data
• Frequency Distribution Table
• Class Interval and Class Limits
• Mean, Median and Mode of Grouped Data
  
  

What is Grouping of Data?

Grouping of data refers to the method of arranging individual data points into groups or classes based on a common characteristic or range. Instead of looking at 100 different test scores individually, we might group them into categories like 0 - 20, 21- 40, 41- 60, 61- 80, and 81-100. This organization makes it easier to see how many students fall into each score range.

Read more: Important Questions on Data Handling - Class 8

Benefits of Grouping Data

• Makes large datasets easier to understand

• Helps identify patterns and trends

• Simplifies calculation of statistical measures

• Makes data visualization clearer

• Reduces space needed to store information

Types of Grouping of Data

Data can be grouped in two main ways: discrete and continuous. Understanding the difference is important because each type requires a different approach to organization and analysis.

1. Discrete Data

Discrete data consists of values that are distinct and separate from each other. These are countable values that cannot have decimal points. Examples include the number of students in a classroom, number of books in a library, number of cars in a parking lot, or number of goals scored in a match.

• Values are whole numbers only

• Cannot be subdivided into smaller parts

• Results from counting

• Has gaps between values

Suppose we survey 50 families and count the number of children in each family. The results could be:

Number of Children	Frequency (Number of Families)
1	8
2	15
3	18
4	7
5	2

2. Continuous Data

Continuous data can take any value within a given range and can be measured to any degree of accuracy. This data is measured rather than counted. Examples include height, weight, temperature, time, distance, and speed. These values can have decimal points.

• Can take decimal values

• Can be subdivided infinitely

• Results from measurement

• Can take any value in a range

Consider the heights of 40 students in a class. Heights are continuous data because they can be 160 cm, 160.5 cm, 160.75 cm, etc. We organize this into ranges:

Height Range (cm)	Frequency (Number of Students)
150 - 155	5
155 - 160	12
160 - 165	15
165 - 170	8

 

Feature	Discrete Data	Continuous Data
Type	Counted	Measured
Values	Whole numbers only	Decimal values allowed
Examples	Goals, marks, students	Height, weight, time

Frequency Distribution Table

A frequency distribution table is a simple tool used to show how often each value or group of values occurs in a dataset. It has two main columns: one for the values or class intervals, and another for the frequency, which is the number of times each value appears.

Structure of a Frequency Distribution Table

A typical frequency distribution table includes:

• Data values or class intervals

• Frequency count for each value or interval

• Sometimes: relative frequency (percentage)

• Sometimes: cumulative frequency

Example: Imagine a teacher records the test scores of 30 students (marks out of 100):

Raw Data: 45, 52, 65, 78, 52, 89, 65, 72, 45, 88, 65, 75, 82, 90, 52, 68, 75, 85, 72, 65, 78, 82, 45, 92, 55, 70, 75, 88, 65, 72

When organized into a frequency distribution table:

Score Range	Frequency	Percentage (%)
40 - 50	3	10%
50 - 60	2	6.67%
60 - 70	6	20%
70 - 80	10	33.33%
80 - 90	6	20%
90 - 100	3	10%

Class Interval and Class Limits

When organizing continuous data, we divide the entire range into smaller groups called class intervals. Understanding class intervals and class limits is essential for creating proper frequency distribution tables.

What is a Class Interval?

A class interval is a range of values that groups data into smaller, manageable categories. For example, in the score range 40-50, the class interval is 10 (from 40 to 50). This divides a large dataset into equal or unequal groups, making analysis easier.

What are Class Limits?

Class limits are the boundary values of each class interval. Every class interval has two limits:

• Lower Class Limit: The smallest value in the interval

• Upper Class Limit: The largest value in the interval

Example:

Consider the class interval 60-70:

Class Interval: 60-70

Lower Class Limit: 60 (the starting point)

Upper Class Limit: 70 (the ending point)

Class Width: 10 (difference between upper and lower limits)

Different Ways to Write Class Limits

There are three common methods to express class limits:

Method	Notation	Meaning	Example
Inclusive	60-69	Includes both 60 and 69	60, 61...69
Exclusive	60-70	Includes 60 but excludes 70	60, 61...69.9
Class Boundary	59.5-69.5	Exact boundaries for continuous data	Between classes

 

Visual Representation of Class Intervals

Here is a simple diagram showing how class intervals are divided:

 

Data Range: 0 to 100

 

|----0-20----|----20-40----|----40-60----|----60-80----|----80-100---|

 

Each segment is a class interval with a width of 20

 

Mean, Median and Mode of Grouped Data

Mean, median, and mode are three important measures of central tendency. They help us find a single value that best represents an entire dataset. When working with grouped data, calculating these measures requires a slightly different method than with raw data.

1. Mean of Grouped Data

The mean is the average value of all data points. For grouped data, we use the midpoint of each class interval and multiply it by the frequency.

 

Formula for Mean

Mean = (Sum of (Class Midpoint × Frequency)) / Total Frequency

 

Step-by-Step Calculation

• Find the midpoint of each class interval: (Lower Limit + Upper Limit) / 2

• Multiply each midpoint by its frequency

• Add all these products together

• Divide by the total frequency

 

Example: Calculating Mean

Using the test score data from our earlier example:

 

Score Range	Frequency (f)	Midpoint (x)	f × x
40-50	3	45	135
50-60	2	55	110
60-70	6	65	390
70-80	10	75	750
80-90	6	85	510
90-100	3	95	285
Total	30		2180

 

Mean = 2180 / 30 = 72.67

This means the average score of all students is 72.67 marks.

 

2. Median of Grouped Data

The median is the middle value when all data is arranged in order. For grouped data, the median falls within the class interval that contains the middle position. We use a formula to find the exact value.

 

Formula for Median

Median = L + [(n/2 - F) / f] × h

 

Where:

• L = Lower limit of median class

• n = Total frequency

• F = Cumulative frequency before median class

• f = Frequency of median class

• h = Width of class interval

How to Find the Median

• Calculate n/2 to find the middle position

• Find the class where cumulative frequency first exceeds n/2

• Use the median formula with values from that class

3. Mode of Grouped Data

The mode is the value that appears most frequently in a dataset. For Mode of grouped data, it is the class with the highest frequency, called the modal class. The mode represents what is most common.

Formula for Mode:Mode=L+(f1−f02f1−f0−f2)×h

Where:

• L = Lower limit of modal class
• f1 = Frequency of modal class
•  f0 = Frequency of class before modal class
• f2 = Frequency of class after modal class
• h = Width of class interval

Method for Mode

The simplest way to find the mode is to identify the modal class the class interval with the highest frequency. Then use the midpoint of that class as an approximate mode value.

Visual Comparison: Mean, Median, and Mode

Here is a simple visual representation of how these three measures relate:

Number Line showing distribution:

0----10----20----30----40----50----60----70----80----90----100

| | M |

Mode Median Mean

(Most common) (Middle value) (Average of all)

Mean vs Median vs Mode

Measure	Definition	How to Use It	Best For
Mean	Average value	Sum of (midpoint × frequency)	General overview
Median	Middle value	Find n/2 position	Skewed data
Mode	Most frequent value	Find modal class	Categorical data

Conclusion

Grouping of data is an essential skill in statistics that transforms raw, disorganized information into meaningful categories and patterns. By understanding discrete and continuous data types, creating frequency distribution tables, and calculating mean, median, and mode, we gain powerful tools to analyze and interpret real world information.