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Practice Class 7 Maths Chapter 3 Data Handling MCQ Questions with Answers based on the latest NCERT syllabus. Solve higher-level MCQs on frequency tables, pictographs, bar graphs, averages, and data interpretation with detailed step-by-step solutions. Best 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 + Higher Order Thinking)
Based On: NCERT Latest Syllabus (2026)
Introduction
Data Handling enables students to organize, analyze, and interpret data collected from different sources. This chapter develops logical thinking by helping students compare information, identify patterns, calculate averages, and solve practical problems using tables and graphs.
What You Will Learn?
✔ Frequency tables
✔ Tally marks
✔ Pictographs
✔ Bar graph interpretation
✔ Average (Mean)
✔ Comparing grouped data
✔ Higher-order reasoning questions
Why This Topic Is Important?
Data Handling is widely used in business, education, sports analytics, weather forecasting, scientific research, banking, and public surveys. Learning this chapter improves analytical thinking and prepares students for higher mathematics.
Exam Relevance
These MCQs are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Olympiad Preparation
✔ Scholarship Examinations
Q1. The table below shows the number of students participating in different competitions.
| Competition | Participants |
| Quiz | $$32$$ |
| Debate | $$28$$ |
| Drawing | $$36$$ |
| Music | $$24$$ |
If 10 new students join the Debate competition, what will be the new average number of participants?
A) $$30$$
B) $$31$$
C) $$32.5$$
D) $$33$$
Answer: $$32.5$$
Useful Formula for this Question
$$\text{Average}=\frac{\text{Total Participants}}{\text{Number of Categories}}$$
Concept Behind This Question
Students should update the frequency first and then calculate the average.
Step-by-Step Solution
Original total
$$32+28+36+24=120$$
After adding $$10$$ students to Debate
New total
$$120+10=130$$
Average
$$=\frac{130}{4}=32.5$$
Therefore, the correct answer is:
$$32.5$$
Exam Tip
Whenever data changes, calculate the new total before finding the average.
Q2. In a pictograph,
1 🏆 = 24 medals
How many medals are represented by 8½ symbols?
A) $$192$$
B) $$198$$
C) $$204$$
D) $$208$$
Answer: $$204$$
Useful Formula for this Question
$$\text{Total Medals}=\text{Number of Symbols}\times\text{Value of One Symbol}$$
Concept Behind This Question
Students should correctly use fractional symbols in pictographs.
Step-by-Step Solution
One symbol
$$=24$$ medals
Number of symbols
$$=8.5$$
$$8.5\times24=204$$
Therefore, the correct answer is:
$$204$$
Exam Tip
Half of $$24$$ is $$12$$.
So,
$$8\times24+12=204$$
Q3. A survey records the number of books read by four students.
| Student | Books Read |
| Aman | $$42$$ |
| Bharat | $$38$$ |
| Chirag | $$47$$ |
| Deepak | $$33$$ |
How many more books must Deepak read so that he reads as many books as the average of the four students?
A) $$5$$
B) $$6$$
C) $$7$$
D) $$8$$
Answer: $$7$$
Useful Formula for this Question
$$\text{Average}=\frac{\text{Total}}{\text{Number of Students}}$$
Concept Behind This Question
Students should first calculate the average and then compare it with Deepak’s score.
Step-by-Step Solution
Total books
$$42+38+47+33=160$$
Average
$$=\frac{160}{4}=40$$
Deepak has read
$$33$$ books.
Required
$$40-33=7$$
Therefore, the correct answer is:
$$7$$
Exam Tip
Find the average first before comparing individual values.
Q4. Which one of the following statements is always true?
A) Every category must have the same frequency.
B) The category with the highest frequency is called the most common observation.
C) Frequencies may be fractions.
D) A pictograph can be drawn without a key.
Answer: The category with the highest frequency is called the most common observation.
Useful Concept for this Question
The observation with the greatest frequency occurs most often.
Concept Behind This Question
Students should identify the correct concept related to frequency.
Step-by-Step Solution
- Frequencies need not be equal. ✘
- Highest frequency represents the most common observation. ✔
- Frequencies are whole numbers. ✘
- Every pictograph requires a key. ✘
Therefore, the correct answer is:
The category with the highest frequency is called the most common observation.
Exam Tip
The highest frequency always represents the most preferred or most common item.
Q5. The frequencies of favourite sports are given below.
| Sport | Frequency |
| Cricket | $$30$$ |
| Football | $$22$$ |
| Volleyball | $$18$$ |
| Badminton | $$26$$ |
If 4 students change their choice from Cricket to Football, which statement is correct?
A) Cricket = $$26$$, Football = $$26$$
B) Cricket = $$34$$, Football = $$18$$
C) Cricket = $$30$$, Football = $$26$$
D) Cricket = $$28$$, Football = $$24$$
Answer: Cricket = $$26$$, Football = $$26$$
Useful Formula for this Question
When students change categories:
- Subtract from one category.
- Add to the other category.
Concept Behind This Question
Students should update two frequencies simultaneously.
Step-by-Step Solution
Cricket
$$30-4=26$$
Football
$$22+4=26$$
Other categories remain unchanged.
Therefore, the correct answer is:
Cricket = $$26$$, Football = $$26$$
Exam Tip
Changing categories does not change the total number of observations.
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 Two Frequencies
- Subtract from the old category.
- Add to the new category.
- Total observations remain unchanged.
5. Most Common Observation
The category with the highest frequency is called the most common observation.
FAQs
1. Does changing categories change the total frequency?
No. Only the frequencies of individual categories change.
2. Can the average be a decimal number?
Yes.
3. What does the highest frequency represent?
The most common observation.
4. Why is a key compulsory in a pictograph?
Without a key, the symbols cannot be interpreted correctly.
5. Can frequencies be fractions?
No. Frequencies are always whole numbers.
Common Mistakes
❌ Forgetting to update the total before calculating the average.
❌ Adding instead of subtracting while changing categories.
❌ Ignoring half-symbol values in pictographs.
❌ Assuming the total frequency changes when observations shift between categories.
❌ Confusing average with total frequency.
Quick Revision Notes
✔ Average = Total ÷ Number of Categories.
✔ Frequencies are whole numbers.
✔ The total number of observations remains unchanged when data shifts between categories.
✔ The highest frequency represents the most common observation.
✔ Every pictograph must include a key.
✔ Half-symbols represent half the key value.
✔ Bar graphs are useful for comparing categories.
Conclusion
Data Handling is an important chapter that strengthens students’ ability to organize, analyze, and interpret information accurately. Higher-order questions involving averages, frequency updates, and comparative analysis develop critical thinking and prepare students for CBSE examinations, Olympiads, and scholarship tests.
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