Data Handling

Data Handling Class 6 CBSE Maths Notes - Complete Guide with Examples

What is Data Handling?

Data handling is the systematic process of collecting, organizing, analyzing, and presenting information in a meaningful way. Data refers to a collection of numbers or facts gathered to provide specific information about a subject. In Class 6 mathematics notes, students learn fundamental techniques to transform raw data into organized formats that are easy to understand and interpret.

The process helps students develop analytical thinking and problem-solving skills essential for higher mathematics and real-world applications. Data handling forms the foundation for statistics and is crucial for making informed decisions based on collected information.

Main Steps of the Data Handling Process

Data handling involves four systematic steps that transform raw information into meaningful insights:

1. Collection of Data

The first step involves gathering relevant information from various sources such as surveys, observations, experiments, or existing records. For example, a teacher collecting students' food preferences for a mid-day meal program represents data collection.

2. Organization of Data

Raw data needs to be arranged systematically using methods like:

• Tally marks: Grouping data in sets of five for easy counting

• Frequency tables: Recording how many times each value appears

• Sorting: Arranging data in ascending or descending order

The organization phase makes data manageable and prepares it for analysis.

3. Analysis of Data

After organization, data is examined to identify patterns, trends, maximum values, minimum values, and frequencies. This step answers specific questions about the collected information.

4. Presentation of Data

The final step involves representing organized data visually through pictographs, bar graphs, or tables to make interpretation easier. Visual representation allows quick understanding of complex information at a glance.

Understanding Tally Marks

Tally marks provide an efficient method for counting and recording data. The system uses vertical lines grouped in sets of five, where the fifth mark is drawn diagonally across the first four marks.

Key features:

• Four vertical lines (||||) represent counts 1-4

• The fifth mark crosses diagonally (||||/) to complete a group of 5

• Groups of five make counting faster and reduce errors

Example: Seven tally marks appear as: ||||/ || (one group of five plus two individual marks) .

Types of Graphs Used in Data Handling

Pictograph

A pictograph uses pictures or symbols to represent numerical data. Each symbol stands for a specific number of units, making data visualization engaging and easy to understand.

When to use pictographs:

• Presenting simple data to younger audiences

• Making information visually appealing

• Showing data with whole number frequencies

• Comparing quantities at a glance

Advantages:

• Easy to understand and interpret

• Visually attractive

• Suitable for small datasets

Limitations:

• Time-consuming to draw multiple symbols

• Difficult to represent fractional values

• Not ideal for large numerical data

Bar Graph

Bar graphs represent data using rectangular bars of uniform width, where the length of each bar is proportional to the value it represents. Bars can be drawn vertically or horizontally with equal spacing between them.

When to use bar graphs:

• Comparing different categories of data

• Representing large numerical values

• Showing trends over time

• Displaying frequency distributions

Key components:

• X-axis (Horizontal axis): Categories or variables being compared

• Y-axis (Vertical axis): Numerical scale representing frequency or values

• Scale: Unit measurement for reading values accurately

• Bars: Rectangular representations of data values

Advantages:

• Accurate representation of numerical data

• Easy comparison between categories

• Suitable for large datasets

• Professional and clear presentation

How to Collect and Clean Data for a Class Project

Step 1: Define Your Objective

Clearly identify what information you need to collect.

Example: "Find out the favorite sports of students in your class."

Step 2: Choose Collection Method

• Surveys: Create questionnaires with specific questions

• Observation: Record data by watching and noting information

• Experiments: Conduct activities and record results

• Interviews: Ask individuals directly and note their responses

Step 3: Collect Raw Data

Gather information systematically, ensuring you record every response accurately. Use a notebook or form to avoid missing data.

Step 4: Clean the Data

Data cleaning involves:

• Removing duplicate entries

• Correcting spelling mistakes or inconsistent formats

• Identifying and handling missing values

• Ensuring all data falls within expected ranges

Step 5: Organize with Tally Marks

Create a frequency table using tally marks to count occurrences of each category. Group tally marks in fives for efficient counting.

Step 6: Verify Accuracy

Cross-check your totals to ensure the sum of frequencies equals the total number of observations collected.

Examples of Data Handling Problems

Class 7 Level Problems

Example 1: Double Bar Graphs
The following table shows the number of boys and girls in different sections of Class 7:

Section	Boys	Girls
A	20	18
B	22	20
C	19	21
D	21	19

Task: Represent this data using a double bar graph to compare boys and girls across sections.

Example 2: Central Tendency
Find the average height of 10 students if their heights (in cm) are: 145, 150, 148, 152, 146, 149, 151, 147, 150, 148.

Solution: Sum of heights = 1486 cm; Average = 1486 ÷ 10 = 148.6 cm

Class 8 Level Problems

Example 3: Grouped Data Analysis
A survey recorded the daily pocket money (in rupees) of 30 students:

Pocket Money Range	Number of Students
0-20	5
20-40	12
40-60	8
60-80	4
80-100	1

Questions:

• How many students receive less than ₹40?

• What percentage of students receive ₹60 or more?

Example 4: Probability Introduction
A die was thrown 50 times with the following results:

Number	1	2	3	4	5	6
Frequency	8	9	7	10	8	8

Calculate the experimental probability of getting an even number.

How to Present Data Using Pictographs and Bar Graphs

Creating a Pictograph

Step 1: Choose an appropriate symbol that relates to your data. Example: use fruit symbols for fruit preferences data.

Step 2: Decide the scale (value each symbol represents). Example: 1 symbol = 5 students.

Step 3: Create a table with categories in one column and symbols in another.

Step 4: Draw the required number of symbols for each category based on the scale.

Step 5: Add a title and key explaining what each symbol represents.

Example from the PDF:
A pictograph showing student absentees during a week uses one face symbol to represent one absent student. The graph clearly shows which day had maximum absentees.

Creating a Bar Graph

Step 1: Draw horizontal and vertical axes.

Step 2: Choose an appropriate scale for the vertical axis based on your data range. Example: 1 unit = 10 students.

Step 3: Mark categories evenly on the horizontal axis with equal spacing.

Step 4: Draw bars of uniform width for each category, with heights proportional to their values.

Step 5: Label both axes, add a title, and mention the scale used.

Example from the PDF:
The bar graph representing students in five sections (A, B, C, D, E) uses a scale of 1 unit length = 4 students. The graph allows quick comparison of student numbers across sections.

Formulas

Concept	Formula/Representation	Explanation
Frequency	Count of occurrences	Number of times a particular value appears in data
Tally Marks	||||/ = 5	Groups of five with the fifth mark diagonal across first four
Scale in Graphs	1 unit = n values	Determines how much each unit on axis represents
Total Frequency	∑fi	Sum of all individual frequencies equals total observations
Bar Height	Proportional to value	Height/length of bar = Value ÷ Scale factor
Pictograph Value	Symbols × Scale	Total value = Number of symbols × Value per symbol
Range	Maximum - Minimum	Difference between highest and lowest values in dataset

Practice Problems

Problem 1: Blood Group Classification

The blood groups of 25 students are recorded as: A, B, O, A, AB, O, A, O, B, A, O, B, A, AB, AB, A, A, B, B, O, B, AB, O, A, B.

Task: Arrange the information in a frequency table using tally marks.

Problem 2: Measurement Data

The lengths (in cm) of 30 carrots are: 15, 22, 21, 20, 22, 15, 15, 20, 20, 15, 20, 18, 20, 22, 21, 20, 21, 18, 21, 18, 20, 18, 21, 18, 22, 20, 15, 21, 18, 20.

Questions:

• How many carrots have length more than 20 cm?

• Which length occurs the maximum number of times?

Problem 3: Bar Graph Interpretation

A bar graph shows the number of houses using different fuels for cooking (out of 100 houses):

• Which fuel is used in the maximum number of houses?

• How many houses use coal as fuel?

Tips for Mastering Data Handling

• Practice regularly: Work through various types of data representation problems to build confidence

• Focus on accuracy: Double-check tally mark groupings and bar graph scales to avoid calculation errors

• Understand when to use each method: Choose pictographs for simple, visual data and bar graphs for numerical precision

• Label clearly: Always include titles, axis labels, and scales in your graphs for complete presentation

• Analyze before answering: Read the entire question carefully and examine the data representation before responding

Conclusion

Data handling is a fundamental skill in Class 6 CBSE Mathematics that teaches students how to work with information systematically. Mastering tally marks, frequency tables, pictographs, and bar graphs prepares students for advanced statistical concepts in higher classes and develops critical thinking abilities applicable across subjects.

At Home Tuition, our comprehensive approach to teaching data handling ensures students grasp both theoretical concepts and practical applications through solved examples and interactive practice sessions. Regular practice with diverse problem types builds exam confidence and enhances analytical capabilities essential for competitive examinations.