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CBSE Class 8 Mathematics Chapter 4 Data Handling Worksheet with Answers

Data Handling is a crucial chapter in CBSE Class 8 Mathematics that builds statistical literacy and probability foundations needed for higher secondary studies. This printable worksheet offers a complete practice set covering frequency distribution tables, bar graphs, pie charts, histograms, and the concept of equally likely outcomes in probability. With varied question types from MCQs to HOTS problems, students gain exam confidence and clarity on NCERT concepts.

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Key takeaways

  • ✓Covers all NCERT Chapter 4 topics: frequency distribution, graphical representation (bar graphs, pie charts, histograms), and probability.
  • ✓Includes 6 multiple-choice questions testing conceptual understanding of data representation techniques.
  • ✓Features 5 short-answer and 3 long-answer questions aligned with CBSE marking schemes and Class 8 board exam patterns.
  • ✓Case-study question mirrors the latest CBSE exam format, demanding real-world application of data handling skills.
  • ✓Complete answer key with step-by-step explanations ensures independent learning and immediate feedback.
  • ✓Medium difficulty level; suggested time 90 minutes for thorough practice of all question types.
  • ✓Printable format ideal for weekend practice, holiday revision, or pre-exam preparation at home or in tuition centres.

Quick Chapter Recap: Data Handling Fundamentals

Before attempting the worksheet, revisit these key concepts from NCERT Class 8 Mathematics Chapter 4. A frequency distribution table organises raw data by showing how often each value or class interval appears. Pictorial representation through bar graphs displays categorical data with rectangular bars, while pie charts use sectors of a circle to show parts of a whole, with each sector angle calculated as (frequency/total frequency) × 360°. Histograms differ from bar graphs because they represent continuous class intervals with no gaps between bars, and the area of each bar is proportional to frequency. Probability measures the chance of an event occurring, expressed as number of favourable outcomes divided by total number of equally likely outcomes, always lying between 0 and 1. Understanding these distinctions is vital for accurate data interpretation and representation in assessments.
  • Frequency distribution: tabular organisation of data showing counts or occurrences
  • Bar graph: categorical data with distinct bars; pie chart: parts-of-whole using circle sectors
  • Histogram: continuous data with adjacent bars; bar width represents class interval
  • Probability formula: P(E) = (Number of favourable outcomes) / (Total equally likely outcomes)
  • Class intervals: groups like 0-10, 10-20 used in frequency tables and histograms

Worksheet Details: Difficulty and Time Allocation

This worksheet is designed at medium difficulty, suitable for students who have completed the NCERT Class 8 Mathematics Chapter 4 exercises and want focused exam-pattern practice. The recommended time is 90 minutes for attempting all sections without rushing, mirroring a typical school unit test duration. Section A (MCQs) should take about 12-15 minutes, Section B (fill-in-the-blanks) around 10 minutes, Section C (matching or true/false) approximately 8 minutes, Section D (short answers) roughly 25-30 minutes, Section E (long answers and HOTS) about 20-25 minutes, and the case study around 10 minutes. Keep a calculator, ruler, and protractor handy for pie chart calculations and graph construction. Parents can use this as a weekend diagnostic tool to identify weak areas before term exams. Teachers will find it ideal for classroom assignments or homework that covers the entire chapter systematically.
  • Difficulty level: Medium (post-NCERT exercise practice)
  • Suggested time: 90 minutes (mimics school unit test format)
  • Materials needed: calculator, ruler, protractor, coloured pencils for graphs
  • Sections progress from objective to subjective, building complexity gradually
  • Answer key provided for self-assessment and independent learning

Section A: Multiple Choice Questions (1 mark each)

Multiple-choice questions test quick recall and conceptual clarity on Data Handling. Each question has four options with only one correct answer. Read the question stem carefully, eliminate obviously incorrect options, and choose the best answer. These MCQs cover identification of graph types, calculation of pie chart angles, interpretation of histograms, and basic probability. In the 2024-25 CBSE pattern, objective questions carry significant weight, so practicing MCQs builds speed and accuracy. Avoid second-guessing; your first instinct after careful reading is often correct. Mark answers clearly in the answer key section provided at the end of this worksheet. Time management is critical — do not spend more than two minutes per MCQ during timed practice.
  • Question 1: In a pie chart, if a category has frequency 15 out of total 60, what is the sector angle? (a) 45° (b) 60° (c) 90° (d) 120°
  • Question 2: Which graph is most suitable for showing temperature variation over 12 months? (a) Pie chart (b) Bar graph (c) Histogram (d) Frequency polygon
  • Question 3: A coin is tossed twice. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1
  • Question 4: In a histogram, the width of bars represents: (a) Frequency (b) Class interval (c) Range (d) Mean
  • Question 5: The probability of an impossible event is: (a) 0 (b) 1 (c) 0.5 (d) Cannot be determined
  • Question 6: A frequency distribution table shows class intervals 10-20, 20-30, 30-40. This data is: (a) Discrete (b) Continuous (c) Qualitative (d) None

Section B: Fill in the Blanks (1 mark each)

Fill-in-the-blank questions require precise terminology and numerical accuracy. Write your answers in the space provided, ensuring correct spelling of mathematical terms like 'histogram', 'frequency', and 'outcomes'. These questions test your memory of formulas, definitions, and key properties from NCERT Class 8 Mathematics Chapter 4. Pay attention to units and context; sometimes the blank requires a number, other times a word or phrase. If a formula is involved, do rough work in the margin before writing the final answer. This section bridges objective and subjective questions, demanding both recall and minimal calculation. Review your CBSE Class 8 Mathematics notes on data representation and probability before attempting these questions to ensure terminology matches NCERT standards exactly.
  • Question 1: The sum of all probabilities in an experiment equals __________.
  • Question 2: In a pie chart, the total angle at the centre is __________.
  • Question 3: A __________ is used to represent continuous class intervals with adjacent bars.
  • Question 4: If a die is rolled, the probability of getting a number less than 7 is __________.
  • Question 5: The number of times an observation occurs in data is called its __________.

Section C: Match the Following (5 marks)

This matching exercise connects concepts, formulas, and applications from Data Handling. Column A lists terms or scenarios; Column B provides definitions, graph types, or outcomes. Draw lines or write letters to match correctly. Each correct match earns one mark, with no negative marking for wrong matches. Read all items in both columns before starting, as some options may seem similar. This format appears frequently in CBSE internal assessments and helps reinforce connections between theoretical concepts and practical representations. For instance, match 'data on students' favorite subjects' with 'bar graph', or 'probability of sure event' with '1'. Understanding why each pairing is correct deepens your grasp of when to use which data handling tool. If uncertain, use elimination: match the items you are confident about first, then deduce the remaining pairs logically.
  • Column A: (i) Data showing parts of a whole (ii) Continuous class intervals (iii) Tossing a fair coin (iv) Categorical data comparison (v) Probability of impossible event
  • Column B: (a) Histogram (b) 0 (c) Pie chart (d) 1/2 (e) Bar graph

Section D: Short Answer Questions (2 marks each)

Short-answer questions demand concise explanations or calculations within three to four sentences or a few calculation steps. Each question is worth 2 marks, typically split as 1 mark for method and 1 mark for the correct answer. Show all working clearly; even if the final answer is incorrect, you can earn partial credit for correct steps. Topics include constructing frequency tables from raw data, calculating sector angles for pie charts, finding probabilities, and interpreting given graphs. Use NCERT terminology precisely: write 'equally likely outcomes' rather than just 'outcomes', and 'frequency distribution' instead of vague terms. Time allocation for this section should be about 25-30 minutes. If stuck on one question, move to the next and return later; these are independent problems. Class 8 Mathematics solutions for similar questions are available in your NCERT textbook exercises 4.1, 4.2, and 4.3, so revise those before attempting this section.
  • Question 1: The marks obtained by 20 students are: 15, 18, 15, 20, 16, 18, 15, 17, 16, 15, 20, 18, 16, 15, 17, 18, 20, 16, 15, 17. Prepare a frequency distribution table.
  • Question 2: In a survey of 40 students, 10 like cricket, 15 like football, 8 like tennis, and 7 like hockey. Draw a bar graph to represent this data.
  • Question 3: A bag contains 5 red, 4 blue, and 3 green balls. What is the probability of drawing a blue ball?
  • Question 4: The following data shows the number of books read by students in a month: 0-2 (5 students), 2-4 (8 students), 4-6 (6 students), 6-8 (3 students). Draw a histogram.
  • Question 5: A die is thrown. Find the probability of getting (i) a prime number, (ii) a number greater than 4.

Section E: Long Answer and HOTS Questions (3-4 marks each)

Long-answer questions require detailed solutions with complete reasoning, graph construction, or multi-step calculations. Question 1 and 2 are worth 3 marks each, while Question 3 (HOTS) carries 4 marks. Begin by reading the question twice to identify what is asked — a graph, a probability, an interpretation, or a combination. For graphical questions, use graph paper if available, label axes with titles and units, choose an appropriate scale, and ensure neatness. For probability HOTS, list all possible outcomes systematically (use tree diagrams or tables for two-step experiments), then count favourable cases. In CBSE Class 8 board exams and school assessments, these questions differentiate average students from toppers. Show every step: writing the formula, substitution, intermediate calculations, and the final answer with units. HOTS questions test application and analysis — you might need to combine data handling with logical reasoning or real-world contexts. Allocate 20-25 minutes for this section and do not skip steps to save time; marks are awarded for the process, not just the answer.
  • Question 1 (3 marks): The daily wages (in ₹) of 30 workers are: 150, 200, 150, 180, 200, 220, 150, 180, 200, 220, 150, 200, 180, 220, 200, 150, 180, 200, 220, 150, 200, 180, 150, 200, 220, 180, 200, 150, 180, 200. (i) Prepare a frequency distribution table using class intervals 150-170, 170-190, etc. (ii) Draw a histogram.
  • Question 2 (3 marks): In a school, 120 students participated in extracurricular activities: Dance 30, Music 25, Sports 40, Art 25. (i) Calculate the sector angle for each activity in a pie chart. (ii) Draw the pie chart.
  • Question 3 (4 marks - HOTS): Two dice are thrown simultaneously. (i) Find the probability that the sum of numbers is 8. (ii) Find the probability that both dice show the same number. (iii) Which event is more likely and why?

Section F: Case Study Question (4 marks)

The case-study format is a hallmark of the current CBSE examination pattern, integrating real-world scenarios with mathematical concepts from Data Handling. Read the passage or data presentation carefully, noting all numerical values, categories, and the context. Sub-questions (usually three to four, totaling 4 marks) test comprehension, calculation, and interpretation. Underline or highlight key information in the case study to avoid missing details. Answers must relate back to the scenario; generic formula statements without context earn fewer marks. This question type assesses your ability to apply NCERT Class 8 Mathematics Chapter 4 concepts to everyday situations like sports statistics, survey results, or market data. Time allocation should be about 10 minutes. Even if one sub-question seems difficult, attempt the others; they are often independent. Case studies are excellent for developing analytical thinking and are increasingly common in CBSE internal assessments, so regular practice pays off significantly.
  • Case Study: A school conducted a survey of 200 students to find their preferred mode of transport. The results were: Bus 80 students, Bicycle 50 students, Walk 40 students, Car 30 students.
  • Sub-question (i) (1 mark): What fraction of students prefer the bus?
  • Sub-question (ii) (1 mark): Calculate the central angle for 'Bicycle' in a pie chart representing this data.
  • Sub-question (iii) (1 mark): If one student is selected at random, what is the probability that the student walks to school?
  • Sub-question (iv) (1 mark): Which mode of transport is least preferred, and what percentage of students use it?

Complete Answer Key with Explanations

This answer key provides correct answers and brief explanations for every question in the worksheet, enabling self-assessment and concept reinforcement. For MCQs and fill-in-the-blanks, the correct option or term is stated with reasoning. For short and long answers, step-by-step solutions mirror CBSE marking schemes, showing formula application, calculation steps, and final answers with units. Use this key only after attempting all questions honestly; premature checking hinders learning. If your answer differs, compare your method with the given solution to identify mistakes in concept or calculation. Discussing errors with a teacher or peer deepens understanding more than simply copying the correct answer. Parents can use this section to guide their child through problem-solving strategies. For students preparing independently, this answer key acts as a personal tutor, clarifying doubts immediately. CBSETUTOR.ai offers 24×7 AI-powered help where students can upload photos of their worksheet attempts and receive instant, personalized feedback — a valuable resource for tackling difficult questions or verifying complex calculations at just ₹999 per month for all classes (6-12), with a 3-day free trial to explore the platform.

Section A Answer Key

Question 1: (c) 90°. Explanation: Sector angle = (frequency/total) × 360° = (15/60) × 360° = 90°. Question 2: (b) Bar graph. A bar graph shows categorical data over time periods like months; pie chart shows parts of whole, histogram for continuous intervals. Question 3: (c) 3/4. Outcomes: HH, HT, TH, TT (4 total). At least one head: HH, HT, TH (3 favourable). Probability = 3/4. Question 4: (b) Class interval. In histograms, bar width represents the range of each class interval, while height represents frequency. Question 5: (a) 0. Impossible events have zero probability; certain events have probability 1. Question 6: (b) Continuous. Class intervals like 10-20, 20-30 indicate continuous data where values can fall anywhere within the range, unlike discrete data with distinct separate values.

Section B, C, D, E, F Answer Keys

Section B: (1) 1 or unity. (2) 360°. (3) Histogram. (4) 1 (certain event). (5) Frequency. Section C: (i)–(c), (ii)–(a), (iii)–(d), (iv)–(e), (v)–(b). Section D Q1: Frequency table — Marks: 15 (freq 6), 16 (freq 4), 17 (freq 3), 18 (freq 4), 20 (freq 3). Q3: Probability = 4/12 = 1/3. Q5: (i) Prime numbers: 2,3,5 → P=3/6=1/2. (ii) >4: 5,6 → P=2/6=1/3. Section E Q2(i): Dance 90°, Music 75°, Sports 120°, Art 75° (total 360°). Q3(i): 5/36. (ii) Same number outcomes: (1,1),(2,2)...(6,6)=6, P=6/36=1/6. (iii) Sum 8 (5/36) more likely than same number (1/6=6/36) — actually same number is slightly more likely. Section F: (i) 80/200 = 2/5. (ii) 90°. (iii) 40/200 = 1/5. (iv) Car, 15%.

Frequently asked questions

What topics from NCERT Class 8 Mathematics Chapter 4 are covered in this worksheet?+
This worksheet covers all key topics: frequency distribution tables, bar graphs, pie charts with sector angle calculations, histograms for continuous data, and probability of equally likely outcomes. Each section aligns with NCERT exercises 4.1 to 4.3.
How much time should my child spend on this Data Handling worksheet?+
The recommended time is 90 minutes for a complete attempt, matching typical school unit test durations. Students can split it into two 45-minute sessions if needed, tackling Sections A-C first, then D-F later.
Are the questions in this worksheet similar to CBSE board exam patterns?+
Yes, the worksheet mirrors the latest CBSE exam pattern with MCQs, short answers (2-3 marks), long answers (3-4 marks), HOTS questions, and a case study. This prepares students for both internal assessments and term exams effectively.
Can I use this worksheet for quick revision before school exams?+
Absolutely. The quick chapter recap and varied question types make it ideal for pre-exam revision. Attempting it 3-4 days before exams helps identify weak areas, and the answer key enables immediate self-correction and concept reinforcement.
What materials does my child need to complete this worksheet?+
Students need a calculator for probability and angle calculations, a ruler and protractor for drawing graphs and pie charts, graph paper for histograms, and coloured pencils to differentiate bars or sectors in visual representations.
How are marks distributed across different sections of this worksheet?+
Section A (MCQs): 6 marks, Section B (fill-in-blanks): 5 marks, Section C (matching): 5 marks, Section D (short answers): 10 marks, Section E (long answers): 10 marks, Section F (case study): 4 marks — totaling 40 marks, a standard unit test weightage.
My child struggles with probability questions. Which sections focus on this?+
Probability appears in Section A (MCQs 3 and 5), Section B (question 4), Section D (question 5), and Section E (HOTS question 3). The answer key provides step-by-step solutions, and CBSETUTOR.ai offers personalized help for such topics.
Does the answer key explain why certain answers are correct?+
Yes, every answer includes a brief explanation or solution steps. For calculations, formulas and intermediate steps are shown. For conceptual questions, reasoning is provided to help students understand the logic, not just memorize answers.
Is this worksheet suitable for students who have just started Chapter 4?+
This is a medium-difficulty worksheet best suited for students who have completed NCERT exercises 4.1 to 4.3. Beginners should first work through textbook examples and initial exercises before attempting this comprehensive practice set.
How can CBSETUTOR.ai help if my child gets stuck on difficult questions?+
CBSETUTOR.ai provides a 24×7 AI tutor where students upload photos of problems and receive instant, step-by-step solutions tailored to NCERT and CBSE standards. At ₹999/month for all classes (6-12) with a 3-day free trial, it is an affordable personal guide for Data Handling and every chapter.

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