Class 7 Maths Chapter 3 Data Handling

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Practice Class 7 Maths Chapter 3 Data Handling MCQ Questions with Answers based on the latest NCERT syllabus. Solve high-quality moderate to difficult MCQs on frequency tables, tally marks, 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: Moderate to Difficult

Based On: NCERT Latest Syllabus (2026)

Introduction

Data Handling enables students to organize and interpret information effectively. Through frequency tables, pictographs, and bar graphs, students learn how to compare data, calculate averages, and draw meaningful conclusions. These skills are widely used in everyday life and higher mathematics.

What You Will Learn?

✔ Frequency tables

✔ Tally marks

✔ Pictographs

✔ Reading and interpreting bar graphs

✔ Comparing data

✔ Calculating averages

✔ Solving real-life data-based problems

Why This Topic Is Important?

Data Handling plays an important role in surveys, scientific research, education, business, sports, healthcare, and government planning. It helps students understand information presented in tables and graphs and improves logical reasoning 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 table below shows the number of students participating in various competitions.

What is the average number of participants per competition?

A) $$20$$

B) $$21$$

C) $$22$$

D) $$23$$

Answer: $$22$$

Useful Formula for this Question

$$\text{Average}=\frac{\text{Sum of Frequencies}}{\text{Number of Categories}}$$

Concept Behind This Question

Students should calculate the average using the total frequency.

Step-by-Step Solution

Total participants

$$24+16+20+28=88$$

Number of competitions

$$4$$

Average

$$=\frac{88}{4}=22$$

Therefore, the correct answer is:

$$22$$

Exam Tip

Always divide the total by the number of categories, not by the highest frequency.

Q2. In a pictograph,

1 🏀 = 16 basketballs

How many basketballs are represented by 9½ symbols?

A) $$144$$

B) $$148$$

C) $$152$$

D) $$156$$

Answer: $$152$$

Useful Formula for this Question

$$\text{Total Items}=\text{Number of Symbols}\times\text{Value of One Symbol}$$

Concept Behind This Question

Students should correctly calculate values using full and half symbols.

Step-by-Step Solution

One symbol represents

$$16$$ basketballs.

Number of symbols

$$=9.5$$

Therefore,

$$9.5\times16=152$$

Hence, the correct answer is:

$$152$$

Exam Tip

A half-symbol always represents half the value of one complete symbol.

Q3. The following data shows the number of trees planted by four houses.

How many more trees were planted by House B and House D together than House A and House C together?

A) $$14$$

B) $$15$$

C) $$16$$

D) $$17$$

Answer: $$16$$

Useful Formula for this Question

$$\text{Difference}=(B+D)-(A+C)$$

Concept Behind This Question

Students should compare the totals of two groups.

Step-by-Step Solution

House B + House D

$$56+52=108$$

House A + House C

$$48+44=92$$

Difference

$$108-92=16$$

Therefore, the correct answer is:

$$16$$

Exam Tip

Calculate both totals first, then compare them.

Q4. Which one of the following statements is correct?

A) Raw data is already arranged in order.

B) The frequency of an observation may be zero.

C) A bar graph cannot represent survey data.

D) Every category in a frequency table must have the same frequency.

Answer: The frequency of an observation may be zero.

Useful Concept for this Question

A category may have zero observations in a survey.

Concept Behind This Question

Students should understand the basic properties of frequency.

Step-by-Step Solution

• Raw data is generally unorganized. ✘
• Frequency can be 0 if an observation does not occur. ✔
• Bar graphs can represent survey data. ✘
• Frequencies need not be equal. ✘

Therefore, the correct answer is:

The frequency of an observation may be zero.

Exam Tip

Frequency cannot be negative, but it can be zero.

Q5. A survey records the favourite seasons of students.

If 5 more students choose Winter, what will be the new frequency of Winter?

A) $$21$$

B) $$22$$

C) $$23$$

D) $$24$$

Answer: $$23$$

Useful Formula for this Question

$$\text{New Frequency}=\text{Old Frequency}+\text{Additional Observations}$$

Concept Behind This Question

Students should update a frequency after adding new observations.

Step-by-Step Solution

Current frequency of Winter

$$18$$

Additional students

$$5$$

New frequency

$$18+5=23$$

Therefore, the correct answer is:

$$23$$

Exam Tip

When new observations are added, simply add them to the existing frequency.

Important Formulas & Concepts

1. Total Number of Observations

$$\text{Total Observations}=\text{Sum of all Frequencies}$$

2. Average

$$\text{Average}=\frac{\text{Sum of Frequencies}}{\text{Number of Categories}}$$

3. Pictograph Formula

$$\text{Total Items}=\text{Number of Symbols}\times\text{Value of One Symbol}$$

4. Difference Between Two Totals

$$\text{Difference}=\text{Larger Total}-\text{Smaller Total}$$

5. Updating Frequency

$$\text{New Frequency}=\text{Old Frequency}+\text{New Observations}$$

FAQs

1. Can the frequency of a category be zero?

Yes. If no observation belongs to that category, its frequency is zero.

2. How do you calculate the average frequency?

Divide the total frequency by the number of categories.

3. Why are pictograph keys important?

They tell the value represented by each symbol.

4. Can frequencies be updated?

Yes. Add or subtract observations as required.

5. What is the purpose of a bar graph?

It helps compare quantities across different categories.

Common Mistakes

❌ Dividing by the wrong number while finding the average.

❌ Forgetting to calculate both group totals before comparing.

❌ Ignoring the pictograph key.

❌ Assuming frequency can never be zero.

❌ Adding incorrect values while updating frequencies.

Quick Revision Notes

✔ Total observations = Sum of all frequencies.

✔ Average = Total Frequency ÷ Number of Categories.

✔ Frequency can be zero, but never negative.

✔ Compare group totals carefully.

✔ Update frequencies by adding or subtracting observations.

✔ Every pictograph must include a key.

✔ Bar graphs are useful for comparing categories.

Conclusion

Data Handling develops the ability to collect, organize, analyze, and interpret information logically. Concepts such as averages, frequency tables, pictographs, and bar graphs strengthen analytical thinking and problem-solving skills. Regular practice with moderate-to-difficult MCQs helps students build confidence and perform well in CBSE, State Board, Olympiad, and scholarship examinations.

Related links

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