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Practice Class 7 Maths Chapter 3 Data Handling MCQ Questions with Answers based on the latest NCERT syllabus. Solve advanced MCQs on frequency tables, pictographs, bar graphs, averages, and data interpretation with detailed step-by-step solutions. Ideal for CBSE, State Board, Olympiad, and scholarship exam preparation.
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Data Handling
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Difficult (NCERT + HOTS)
Based On: NCERT Latest Syllabus (2026)
Introduction
Data Handling teaches students how to organize, represent, and interpret information systematically. By using frequency tables, pictographs, and bar graphs, students can analyze data efficiently and solve real-life mathematical problems. This practice set includes multi-step reasoning questions to strengthen conceptual understanding.
What You Will Learn?
✔ Frequency tables
✔ Pictographs
✔ Bar graph interpretation
✔ Average (Mean)
✔ Comparing grouped data
✔ Updating frequencies
✔ Higher Order Thinking Skills (HOTS)
Why This Topic Is Important?
Data Handling is widely used in surveys, education, healthcare, sports statistics, business analysis, weather forecasting, and scientific research. Mastering this chapter develops analytical thinking and decision-making skills.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Olympiad Preparation
✔ Scholarship Examinations
Q1. The following table shows the number of students participating in different events.
| Event | Students |
| Singing | $$36$$ |
| Dancing | $$28$$ |
| Quiz | $$44$$ |
| Art | $$32$$ |
If 4 students leave the Quiz event and join the Dancing event, what will be the new difference between Quiz and Dancing?
A) $$8$$
B) $$10$$
C) $$12$$
D) $$14$$
Answer: $$8$$
Useful Formula for this Question
When observations shift:
- Subtract from one category.
- Add to another category.
Concept Behind This Question
Students should update both frequencies before comparing them.
Step-by-Step Solution
Quiz
$$44-4=40$$
Dancing
$$28+4=32$$
Difference
$$40-32=8$$
Therefore, the correct answer is:
$$8$$
Exam Tip
Always update the frequencies first before calculating the difference.
Q2. In a pictograph,
1 📦 = 32 boxes
How many boxes are represented by 6¾ symbols?
A) $$208$$
B) $$212$$
C) $$216$$
D) $$224$$
Answer: $$216$$
Useful Formula for this Question
$$\text{Total Boxes}=\text{Number of Symbols}\times\text{Value of One Symbol}$$
Concept Behind This Question
Students should correctly interpret fractional symbols.
Step-by-Step Solution
$$6\frac{3}{4}=6.75$$
$$6.75\times32=216$$
Therefore,
the correct answer is
$$216$$
Exam Tip
Three-fourths of $$32$$ is $$24$$.
So,
$$6\times32+24=216$$
Q3. Four students scored the following marks in Mathematics.
| Student | Marks |
| A | $$74$$ |
| B | $$82$$ |
| C | $$78$$ |
| D | $$66$$ |
How many marks must Student D score additionally so that his total equals the class average?
A) $$8$$
B) $$9$$
C) $$10$$
D) $$11$$
Answer: C) $$10$$
Useful Formula for this Question
$$\text{Average}=\frac{\text{Total Marks}}{\text{Number of Students}}$$
Concept Behind This Question
Students should calculate the average before comparing individual scores.
Step-by-Step Solution
Total marks
$$74+82+78+66=300$$
Average
$$=\frac{300}{4}=75$$
Student D has
$$66$$ marks.
Additional marks required
$$75-66=9$$
The correct mathematical result is 9.
Correct Answer: B) $$9$$
Correction: Option C) 10 is incorrect. The correct option should be:
A) $$8$$
B) $$9$$ ✅
C) $$10$$
D) $$11$$
Exam Tip
Always verify calculations after finding the average.
Q4. Which of the following statements is always true?
A) The total frequency changes when observations move from one category to another.
B) The category with the lowest frequency is called the mode.
C) The sum of all frequencies gives the total number of observations.
D) Frequencies can be decimal numbers.
Answer: The sum of all frequencies gives the total number of observations.
Useful Concept for this Question
The total frequency represents the total number of observations.
Concept Behind This Question
Students should identify the correct statement about frequency.
Step-by-Step Solution
- Total observations remain unchanged when data shifts. ✘
- Mode is the category with the highest frequency. ✘
- Total frequency equals total observations. ✔
- Frequencies are whole numbers. ✘
Therefore, the correct answer is:
The sum of all frequencies gives the total number of observations.
Exam Tip
This is one of the most important concepts in Data Handling.
Q5. A survey records the favourite fruits of students.
| Fruit | Frequency |
| Apple | $$24$$ |
| Mango | $$30$$ |
| Orange | $$18$$ |
| Grapes | $$28$$ |
If 6 students who chose Mango now choose Grapes, which statement is correct?
A) Mango = $$24$$, Grapes = $$34$$
B) Mango = $$36$$, Grapes = $$22$$
C) Mango = $$30$$, Grapes = $$28$$
D) Apple becomes the highest frequency.
Answer: Mango = $$24$$, Grapes = $$34$$
Useful Formula for this Question
Subtract from one category and add to the other.
Concept Behind This Question
Students should update two frequencies correctly.
Step-by-Step Solution
Mango
$$30-6=24$$
Grapes
$$28+6=34$$
Therefore,
the correct answer is
Mango = $$24$$, Grapes = $$34$$
Exam Tip
The total number of observations remains unchanged.
Important Formulas & Concepts
1. Total Observations
$$\text{Total Observations}=\text{Sum of all Frequencies}$$
2. Average
$$\text{Average}=\frac{\text{Total Frequency}}{\text{Number of Categories}}$$
3. Pictograph Formula
$$\text{Total Items}=\text{Number of Symbols}\times\text{Value of One Symbol}$$
4. Updating Frequencies
- Subtract from the old category.
- Add to the new category.
- Total observations remain unchanged.
5. Mode
The observation with the highest frequency is called the mode.
FAQs
1. Does shifting observations change the total frequency?
No.
2. Can frequencies be decimal numbers?
No. Frequencies are whole numbers.
3. What is the mode?
The observation with the highest frequency.
4. Why is a pictograph key important?
It tells the value of each symbol.
5. How do you calculate the average?
Divide the total by the number of observations or categories, as applicable.
Common Mistakes
❌ Forgetting to update frequencies before solving.
❌ Ignoring fractional symbols.
❌ Confusing mode with the lowest frequency.
❌ Making calculation mistakes while finding averages.
❌ Assuming the total frequency changes after shifting observations.
Quick Revision Notes
✔ Total observations = Sum of frequencies.
✔ Average = Total ÷ Number of categories.
✔ Mode = Highest frequency.
✔ Frequencies are whole numbers.
✔ The total remains unchanged when observations shift.
✔ Every pictograph requires a key.
✔ Compare updated values carefully.
Conclusion
Data Handling strengthens students’ ability to organize and interpret data using mathematical reasoning. Advanced questions involving averages, frequency updates, and pictographs improve logical thinking and problem-solving abilities. Consistent practice with HOTS-based MCQs builds confidence for CBSE, State Board, Olympiad, and scholarship examinations.
Related links
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- Class 7 Maths Chapter 3 Data Handling part-4
- Class 7 Social Science Chapter 1 Tracing Changes Through a Thousand Years part-3
- Class 7 Science Chapter 1 Nutrition in Plants part-3
- Class 7 Maths Chapter 3 Data Handling part-3
- Class 7 English Chapter 1 The Rainbow part-1
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