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CBSE Class 7 Mathematics Chapter 14 Data Handling and Probability Worksheet with Answers

Data Handling and Probability forms a critical foundation for statistical thinking in CBSE Class 7 Mathematics. This printable worksheet has been designed strictly following the NCERT Class 7 Mathematics Chapter 14 syllabus, covering mean, median, mode, bar graphs, pie charts, and basic probability concepts. With 30+ questions across multiple formats and complete solutions, this resource helps students build confidence before their term examinations.

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Key takeaways

  • ✓Mean is the average of data values; median is the middle value when arranged in order; mode is the most frequently occurring value
  • ✓Bar graphs show data using rectangular bars while pie charts display data as sectors of a circle representing parts of a whole
  • ✓Probability of an event = Number of favourable outcomes ÷ Total number of possible outcomes, always between 0 and 1
  • ✓Sample space is the set of all possible outcomes of an experiment; understanding this is crucial for calculating probability
  • ✓Data handling involves collecting, organising, and interpreting information using statistical measures and graphical representations
  • ✓This 90-minute worksheet follows NCERT Class 7 Mathematics Chapter 14 structure with answers for self-assessment
  • ✓CBSETUTOR.ai provides 24×7 AI tutoring for instant doubt-clearing on probability and data handling problems at ₹999/month for all classes 6-12

Quick Chapter 14 Recap: Data Handling and Probability

Before attempting the worksheet, revisit these core concepts from NCERT Class 7 Mathematics Chapter 14. Mean (arithmetic average) is calculated by summing all observations and dividing by the total count. Median requires arranging data in ascending or descending order and finding the middle value; for even number of observations, it is the average of the two middle values. Mode is the observation with the highest frequency. Bar graphs use rectangular bars to represent data, with height or length proportional to the value. Pie charts divide a circle into sectors, each representing a category as a proportion of 360 degrees. Probability measures the likelihood of an event occurring, expressed as a fraction between 0 (impossible) and 1 (certain). The sample space includes all possible outcomes of a random experiment. Understanding these definitions ensures accuracy in solving data handling and probability problems.
  • Mean = Sum of all observations ÷ Number of observations
  • Median = Middle value when data is arranged in order
  • Mode = Most frequently occurring observation
  • Probability = Number of favourable outcomes ÷ Total number of outcomes
  • Sample space = Set of all possible outcomes of an experiment

Worksheet Instructions and Structure

This CBSE Class 7 Mathematics worksheet is structured in six progressive sections to build your understanding systematically. Section A contains 6 multiple-choice questions testing your conceptual clarity on mean, median, mode, and probability. Section B has 5 fill-in-the-blank questions requiring precise terminology. Section C presents 5 true/false statements to test your understanding of data representation and probability rules. Section D comprises 5 short-answer questions requiring calculations and brief explanations, typically 2-3 marks each in CBSE exams. Section E features 3 long-answer and higher-order thinking skill (HOTS) questions worth 4-5 marks that demand multi-step reasoning. Finally, one case-study question integrates real-world data handling scenarios. Attempt all questions on separate sheets, then verify using the detailed answer key provided. Difficulty level: Moderate. Suggested time: 90 minutes. Keep a calculator, ruler, and compass handy for graph-related questions.
  • Section A: 6 MCQs (1 mark each)
  • Section B: 5 Fill-in-the-blanks (1 mark each)
  • Section C: 5 True/False (1 mark each)
  • Section D: 5 Short answers (2-3 marks each)
  • Section E: 3 Long answers/HOTS (4-5 marks each)
  • Case Study: 1 integrated problem (4 marks)

Section A: Multiple Choice Questions (1 mark each)

Choose the correct option for each question. These MCQs test fundamental concepts from NCERT Class 7 Mathematics Chapter 14, focusing on definitions, calculations, and interpretation of data handling and probability. Read each question carefully, eliminate obviously incorrect options, and select the most appropriate answer. Show working for calculation-based MCQs in the margin for partial credit consideration during actual exams. These questions mirror the pattern seen in recent CBSE Class 7 term assessments and help reinforce your understanding of mean, median, mode, graphical representation, and basic probability. Remember that probability values always lie between 0 and 1, and the sum of probabilities of all outcomes in a sample space equals 1. Take approximately 12 minutes for this section, spending about 2 minutes per question. Mark difficult questions and return to them after completing easier ones to manage time effectively during the worksheet practice session.
  • Q1. The mean of 8, 12, 15, 20, 25 is: (a) 15 (b) 16 (c) 18 (d) 20
  • Q2. If a die is rolled once, the probability of getting a prime number is: (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
  • Q3. The median of 3, 7, 9, 11, 15, 18, 21 is: (a) 9 (b) 11 (c) 12 (d) 15
  • Q4. In a pie chart, if a category represents 90°, it forms what fraction of the whole? (a) 1/2 (b) 1/3 (c) 1/4 (d) 1/6
  • Q5. The mode of 2, 3, 5, 3, 7, 3, 8 is: (a) 2 (b) 3 (c) 5 (d) 7
  • Q6. When a coin is tossed, the sample space is: (a) {H} (b) {T} (c) {H, T} (d) {H, T, E}

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

Complete each statement with the appropriate term, number, or concept from Class 7 Mathematics Chapter 14. These questions require precise recall of definitions, formulas, and key terminology related to data handling and probability. Write your answers clearly in the spaces provided. Pay attention to mathematical accuracy—for numerical answers, show units where applicable and round to two decimal places unless otherwise specified. Fill-in-the-blank questions often appear in CBSE Class 7 term exams and test your grasp of fundamental vocabulary and concepts. Review the NCERT textbook definitions before attempting these. This section should take approximately 8-10 minutes. Ensure you spell statistical terms correctly, as spelling errors may result in mark deductions in actual examinations. If unsure about an answer, leave it blank initially and return after completing other sections rather than writing incorrect information that might confuse your revision process later when reviewing your worksheet performance.
  • Q7. The __________ is the sum of all observations divided by the number of observations.
  • Q8. The probability of an impossible event is __________.
  • Q9. In a bar graph, the __________ of each bar represents the frequency of data.
  • Q10. The middle value of data arranged in order is called the __________.
  • Q11. A pie chart uses __________ degrees to represent the complete data.

Section C: True or False (1 mark each)

Determine whether each statement is true or false. Write 'True' or 'False' next to each question number. If a statement is false, you may write the correct version in brackets for better learning, though this is optional for the worksheet. These questions test your conceptual understanding of data handling principles and probability rules covered in NCERT Class 7 Mathematics. Think carefully about absolute statements containing words like 'always', 'never', or 'only'—these are often false because they do not account for exceptions. Consider edge cases and special scenarios when evaluating each statement. True/false questions frequently appear in CBSE assessments as they efficiently test breadth of knowledge. This section should take 6-8 minutes. Avoid random guessing; if uncertain, use logical reasoning to eliminate obviously incorrect options. Remember that in probability, the sum of all probabilities in a sample space must equal 1, and individual probabilities cannot be negative or greater than 1. Understanding these boundaries helps evaluate probability-related true/false statements accurately and builds examination confidence for Class 7 Mathematics assessments.
  • Q12. The mode of a data set can have more than one value.
  • Q13. The probability of getting a 7 when rolling a standard six-faced die is 1/6.
  • Q14. Mean is always one of the values in the data set.
  • Q15. A pie chart is useful for showing parts of a whole.
  • Q16. The median is affected by extreme values in the data.

Section D: Short Answer Questions (2-3 marks each)

Answer the following questions in 2-4 sentences or show the required calculations with steps. Each question carries 2-3 marks as per typical CBSE Class 7 Mathematics marking schemes. Write clearly, showing all working steps to earn full credit even if your final answer contains a minor error. These short-answer questions test your ability to apply mean, median, mode formulas, interpret graphs, and calculate basic probabilities as outlined in NCERT Class 7 Mathematics Chapter 14. Remember to write units where applicable and present data neatly in tables if required. For probability questions, clearly identify the sample space and favourable outcomes before calculating the probability fraction. Simplify all fractions to lowest terms. This section typically takes 25-30 minutes—allocate about 5-6 minutes per question. If a question asks you to 'find and explain', ensure you provide both the numerical answer and a brief justification. Refer to worked examples in your NCERT textbook if you need guidance on presentation format and level of detail expected in short-answer responses for term examinations.
  • Q17. Find the mean and median of the following data: 12, 18, 14, 16, 20, 22, 15. (3 marks)
  • Q18. A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is drawn at random, what is the probability it is blue? (2 marks)
  • Q19. The marks obtained by 6 students are: 45, 50, 55, 50, 60, 50. Find the mode and explain why it is useful. (3 marks)
  • Q20. In a class of 40 students, 25 like cricket, 10 like football, and 5 like both. Represent this data using a bar graph. (3 marks)
  • Q21. A coin is tossed twice. Write the sample space and find the probability of getting at least one head. (3 marks)

Section E: Long Answer and HOTS Questions (4-5 marks each)

Solve the following questions with complete working and explanations. These long-answer questions require multi-step reasoning, application of multiple concepts, and clear mathematical communication. Each question is worth 4-5 marks in CBSE examinations and tests higher-order thinking skills. Show all calculations, draw neat diagrams where required, and explain your reasoning at each step. These HOTS questions often combine mean, median, mode with practical applications or integrate probability with sample space analysis. Read each question twice to understand what is being asked—identify keywords like 'compare', 'analyse', 'justify', or 'verify' that indicate the depth of response expected. Allocate 30-35 minutes for this section, spending 10-12 minutes per question. For graph-based questions, use a ruler and label axes clearly with appropriate scales. In probability problems involving multiple events, consider using tree diagrams or systematic listing to ensure you account for all possible outcomes. These questions mirror the complexity of problems in CBSE Class 7 annual examinations and help develop analytical skills essential for higher mathematics.
  • Q22. The runs scored by a cricket team in 8 matches are: 250, 300, 275, 225, 280, 310, 265, 290. Calculate the mean, median, and mode. If the team wants to maintain an average above 270 in the next match, what is the minimum score required? (5 marks)
  • Q23. Draw a pie chart for the following data showing how a student spends 24 hours: Sleep - 8 hours, Study - 6 hours, Play - 4 hours, Other activities - 6 hours. Calculate the central angle for each activity. (5 marks)
  • Q24. A box contains cards numbered 1 to 20. One card is drawn at random. Find the probability that the number on the card is: (i) a multiple of 3, (ii) a prime number, (iii) an even number greater than 10. Explain the sample space and list favourable outcomes for each case. (5 marks)

Case Study Question (4 marks)

The case study integrates data collection, mode identification, probability calculation, and pie chart angle computation—all key learning outcomes from NCERT Class 7 Mathematics Chapter 14. Students must recognize that mode is the category with highest frequency (Mango, 15 students), calculate probability as favourable outcomes divided by total outcomes (10/50 = 1/5 for banana preference), and convert proportions to degrees for pie chart representation (Apple central angle = 12/50 × 360° = 86.4°). Such multi-part questions develop the ability to extract information, perform calculations, and present answers systematically—skills valued in CBSE examinations and beyond. Practice similar integrated problems to strengthen your data handling and probability application skills for better performance in Class 7 Mathematics assessments throughout the academic year.

Complete Answer Key with Explanations

This comprehensive answer key provides correct answers with step-by-step explanations for every question in the worksheet. Use this section for self-assessment after attempting all questions independently. Award yourself marks honestly and identify weak areas requiring revision. Understanding why an answer is correct is more important than just knowing the answer—read the explanations carefully. For calculation-based questions, verify each step of your working against the solution provided. If your answer differs, trace back through your steps to identify where the error occurred. Common mistakes in Data Handling and Probability include calculation errors when finding mean, incorrect ordering when finding median, misidentifying mode in datasets with multiple high-frequency values, angle calculation errors in pie charts, and confusion between favourable outcomes and sample space in probability. If you score below 70 percent, revisit the NCERT Class 7 Mathematics Chapter 14 text and work through additional examples before attempting another practice worksheet. CBSETUTOR.ai offers instant photo-upload doubt solving for tricky probability and data handling problems at just ₹999/month flat for classes 6-12 with a 3-day free trial, providing 24×7 AI tutor support whenever you encounter difficulties during self-study or homework practice sessions.
  • Section A Answers: 1(b), 2(a), 3(b), 4(c), 5(b), 6(c)
  • Section B Answers: 7-Mean/Arithmetic mean, 8-Zero/0, 9-Height/Length, 10-Median, 11-360
  • Section C Answers: 12-True, 13-False, 14-False, 15-True, 16-False

Detailed Solutions: Section D Short Answers

Q17: Arrange data in order: 12, 14, 15, 16, 18, 20, 22. Mean = (12+14+15+16+18+20+22)÷7 = 117÷7 = 16.71 (rounded to 2 decimal places). Median = 16 (middle value, 4th position in ordered data). Q18: Total balls = 5+3+2 = 10. Blue balls = 3. Probability of drawing blue ball = 3/10. Q19: Mode = 50 (appears 3 times, more than any other value). Mode is useful as it identifies the most common or typical value in a dataset, helpful in understanding what score most students achieved. Q20: Draw a bar graph with x-axis showing sports (Cricket, Football, Both) and y-axis showing number of students. Heights: Cricket=25, Football=10, Both=5. Use appropriate scale and label axes. Q21: Sample space when coin is tossed twice = {HH, HT, TH, TT} (4 outcomes). Favourable outcomes for at least one head = {HH, HT, TH} (3 outcomes). Probability = 3/4. These solutions demonstrate the level of detail expected in CBSE Class 7 Mathematics examinations—clear working, correct calculations, and appropriate explanations that communicate mathematical reasoning effectively to evaluators.

Detailed Solutions: Section E Long Answers and Case Study

Q22: Mean = (250+300+275+225+280+310+265+290)÷8 = 2195÷8 = 274.375 runs. Arranged data: 225, 250, 265, 275, 280, 290, 300, 310. Median = (275+280)÷2 = 277.5 runs (average of 4th and 5th values). No mode as all values appear once. For average > 270 in 9 matches: Total > 270×9 = 2430. Minimum 9th score = 2430 - 2195 = 235 runs. Q23: Total = 24 hours. Central angles: Sleep = 8/24×360° = 120°; Study = 6/24×360° = 90°; Play = 4/24×360° = 60°; Others = 6/24×360° = 90°. Draw circle, mark centre, use protractor to draw sectors with calculated angles, label each sector. Q24: Sample space = {1,2,3,...,20}, 20 outcomes. (i) Multiples of 3: {3,6,9,12,15,18}, Probability = 6/20 = 3/10. (ii) Primes: {2,3,5,7,11,13,17,19}, Probability = 8/20 = 2/5. (iii) Even > 10: {12,14,16,18,20}, Probability = 5/20 = 1/4. Case Study: (i) Mode = Mango. (ii) Probability = 10/50 = 1/5. (iii) Central angle for Apple = 12/50×360° = 86.4°.

Frequently asked questions

What is the difference between mean, median, and mode in CBSE Class 7 Mathematics Chapter 14?+
Mean is the arithmetic average (sum divided by count), median is the middle value when data is arranged in order, and mode is the most frequently occurring value. Each measures central tendency differently and is useful in different situations.
How do I calculate the central angle for a pie chart in Class 7 Data Handling?+
Central angle for a category = (Value of that category ÷ Total value) × 360°. For example, if a category represents 15 out of 60 total items, its angle = (15÷60)×360° = 90°.
What is sample space in probability, and how do I identify it?+
Sample space is the set of all possible outcomes of an experiment. For a coin toss, it is {H, T}. For rolling a die, it is {1, 2, 3, 4, 5, 6}. List all distinct outcomes systematically to find the sample space.
How much time should a Class 7 student spend on this Data Handling worksheet?+
Allocate 90 minutes for the complete worksheet. Spend 12 minutes on MCQs, 10 minutes on fill-blanks and true/false, 30 minutes on short answers, 35 minutes on long answers, and 12 minutes on the case study, leaving 6 minutes for review.
Can probability be greater than 1 or less than 0 in CBSE Class 7 Mathematics?+
No, probability always lies between 0 and 1 (inclusive). Probability 0 means the event is impossible, probability 1 means it is certain, and any value between 0 and 1 indicates the event may or may not occur.
How do bar graphs differ from pie charts in Data Handling Chapter 14?+
Bar graphs use rectangular bars to show individual values or frequencies, ideal for comparing quantities across categories. Pie charts show parts of a whole as sectors of a circle, best for displaying proportions or percentages of a total.
What are common mistakes students make when calculating median in Class 7?+
Common errors include forgetting to arrange data in order first, incorrectly identifying the middle position, and for even number of observations, not averaging the two middle values. Always arrange data before finding median.
How can CBSETUTOR.ai help with Class 7 Mathematics Data Handling and Probability doubts?+
CBSETUTOR.ai provides 24×7 AI tutoring with instant photo-upload doubt solving for probability, mean, median, mode, and graph problems. At ₹999/month for all classes 6-12 with a 3-day free trial, students get personalised help anytime during homework or revision.
Is mode always present in every data set in CBSE Class 7 Mathematics?+
No, if all values in a dataset occur with equal frequency (no value repeats more than others), there is no mode. A dataset can also have more than one mode if multiple values share the highest frequency.
How many marks does Chapter 14 Data Handling and Probability carry in Class 7 term exams?+
Typically, Data Handling and Probability carries 8-12 marks in CBSE Class 7 term examinations, with questions ranging from 1-mark MCQs and fill-blanks to 4-5 mark long-answer and case-study questions testing application and analysis skills.

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