CBSE Class 9 Mathematics Chapter 12 Statistics Worksheet with Answers

Before you dive into the worksheet, refresh your memory on the core ideas of Chapter 12. Statistics is the science of collecting, organizing, and presenting numerical information so patterns become visible. You begin with raw data—numbers collected from surveys, experiments, or observations. Data can be primary (collected by you directly) or secondary (obtained from published sources like government reports). Next, you classify and organize data into frequency distributions, using class intervals for grouped data and computing class marks (midpoints) to represent each interval. The class width is the range covered by one class. Finally, you present data visually: bar graphs for discrete categories, histograms for continuous grouped data (bars touch each other), pie charts to show proportions of a whole (each slice angle equals frequency divided by total frequency times 360°), and frequency polygons or ogives for cumulative trends. Mastering these tools—tables, graphs, and the formulae for class mark and pie-chart angles—equips you to interpret real-world datasets confidently and score full marks in CBSE exams.

This worksheet is designed at medium difficulty, suitable for regular practice and thorough revision of NCERT Class 9 Mathematics Chapter 12 Statistics. Allocate 90 minutes to complete all sections under exam-like conditions—no book, no calculator unless specified. The structure mirrors the CBSE question-paper format: Section A tests your conceptual recall with 6 multiple-choice questions; Section B checks precise knowledge through 5 fill-in-the-blank items; Section C offers 10 true/false statements to sharpen your eye for detail; Section D contains 5 short-answer questions (2–3 marks each) requiring definitions, simple calculations, or table construction; Section E presents 3 long-answer or Higher Order Thinking Skills (HOTS) questions (4–5 marks each) demanding multi-step problem solving, graph drawing, and interpretation; finally, one case-study question integrates real-world data analysis. After attempting every question, turn to the comprehensive Answer Key section at the end, which provides not just answers but brief explanations and working steps so you understand where you went right—or wrong. Print this worksheet, solve it with a pen and paper, and mark your own work to identify weak spots before your school exam.

Choose the correct option for each of the following six questions. Each carries 1 mark. Read carefully—some options are close, testing your understanding of NCERT terminology. (Total: 6 marks) 1. Data collected directly by an investigator from the field is called: (a) Secondary data (b) Primary data (c) Grouped data (d) Cumulative data 2. The class mark of the class interval 20–30 is: (a) 20 (b) 25 (c) 30 (d) 50 3. In a histogram, the bars are: (a) Separated by gaps (b) Adjacent with no gaps (c) Of unequal width (d) Drawn as circles 4. A pie chart is used to represent: (a) Only primary data (b) Proportions of a whole as sectors of a circle (c) Continuous data only (d) Cumulative frequency 5. If a category has frequency 15 out of total frequency 60, the angle of its sector in a pie chart is: (a) 15° (b) 60° (c) 90° (d) 120° 6. The width of the class interval 10–20 is: (a) 10 (b) 15 (c) 20 (d) 30

Complete each statement with the correct term or number. Each blank carries 1 mark. (Total: 5 marks) 7. Data obtained from government reports or published surveys is called __________ data. 8. The formula for the class mark is __________ divided by 2. 9. A graphical representation using rectangular bars of equal width for discrete data is called a __________. 10. The cumulative frequency of a class is the sum of the frequency of that class and all __________ classes. 11. In a pie chart, the sum of all sector angles must equal __________ degrees.

Write 'True' or 'False' for each statement. Each correct answer earns 1 mark. (Total: 10 marks) 12. Primary data is always more reliable than secondary data because it is collected firsthand. 13. In a frequency distribution, the class width is the difference between the upper and lower limits of a class. 14. Bar graphs and histograms are identical in construction and purpose. 15. A histogram is used for continuous data, and the bars are adjacent with no gaps. 16. The class mark of the interval 0–10 is 5. 17. A pie chart can have more than 360° total angle if there are many categories. 18. Frequency is the number of times a particular value or class appears in the dataset. 19. Grouped data is easier to analyze than ungrouped data when the dataset is very large. 20. The angle of a sector in a pie chart is calculated by dividing the frequency of that category by the total frequency and multiplying by 180°. 21. Cumulative frequency can be used to draw an ogive, a type of frequency curve.

Answer the following questions in 2–3 sentences or show brief working. Each question carries 2 or 3 marks as indicated. (Total: 12 marks) 22. Define primary data and secondary data. Give one example of each. (2 marks) 23. What is a class interval? Calculate the class mark for the interval 40–50. (2 marks) 24. The following data shows the number of books read by 10 students in a month: 5, 3, 7, 5, 6, 8, 5, 4, 6, 7. Prepare an ungrouped frequency distribution table for this data. (3 marks) 25. Explain the difference between a bar graph and a histogram in two points. (2 marks) 26. In a survey of 80 people, 20 preferred tea, 30 preferred coffee, and 30 preferred juice. Calculate the angle of the sector for 'coffee' in a pie chart. (3 marks)

Solve the following questions with complete working and clear explanations. Each question carries 4 or 5 marks. (Total: 13 marks) 27. The marks obtained by 40 students in a Science test (out of 50) are given below: 12, 15, 18, 22, 25, 28, 30, 32, 35, 38, 40, 42, 10, 14, 16, 20, 24, 26, 29, 31, 33, 36, 39, 41, 13, 17, 19, 23, 27, 34, 37, 43, 45, 11, 21, 28, 32, 36, 40, 44. Organize this data into a grouped frequency distribution with class intervals 10–15, 15–20, 20–25, 25–30, 30–35, 35–40, 40–45, 45–50. Also, find the class mark for each interval. (5 marks) 28. Draw a histogram for the following frequency distribution of heights (in cm) of 50 students: Heights: 140–145 (5), 145–150 (10), 150–155 (18), 155–160 (12), 160–165 (5). Describe in one sentence what the histogram reveals about the distribution of heights. (4 marks) 29. A school conducted a survey among 120 students about their favorite sport. Results: Cricket 40, Football 30, Badminton 25, Tennis 15, Others 10. (a) Calculate the angle of each sector for a pie chart. (b) If you were to draw the pie chart, which sport would occupy the largest slice and what would be its angle? (4 marks)

Read the following case carefully and answer the questions that follow. Case Study: The Environment Club of a school surveyed 200 students to find out how much time (in hours per week) they spend on outdoor activities. The data was grouped as follows: | Time (hours) | Number of Students | |---|---| | 0–2 | 30 | | 2–4 | 50 | | 4–6 | 70 | | 6–8 | 40 | | 8–10 | 10 | Based on this data, answer: 30. (a) What is the modal class (the class with the highest frequency)? (1 mark) (b) Calculate the class mark for the interval 4–6 hours. (1 mark) (c) If the club wants to draw a histogram, explain why it is appropriate for this data. (1 mark) (d) Find the cumulative frequency for the class 4–6 hours. (1 mark)

Below are the answers to all sections, with brief working or explanations. Use this key to check your work and understand any mistakes. Section A: Multiple Choice Questions 1. (b) Primary data — Collected directly by the investigator from the source. 2. (b) 25 — Class mark = (20 + 30) ÷ 2 = 25. 3. (b) Adjacent with no gaps — Histograms are for continuous data; bars touch. 4. (b) Proportions of a whole as sectors of a circle — Pie charts show parts of a total. 5. (c) 90° — Angle = (15 ÷ 60) × 360° = 90°. 6. (a) 10 — Class width = 20 − 10 = 10. Section B: Fill in the Blanks 7. secondary 8. (Lower Limit + Upper Limit) [accept: sum of limits] 9. bar graph [accept: bar chart] 10. previous [accept: preceding] 11. 360 Section C: True or False 12. True — Primary data is firsthand, though reliability also depends on collection method. 13. True — Class width = Upper Limit − Lower Limit. 14. False — Bar graphs are for discrete data with gaps; histograms are for continuous data with adjacent bars. 15. True — Histogram bars touch because data is continuous. 16. True — Class mark = (0 + 10) ÷ 2 = 5. 17. False — Total angle in a pie chart is always 360°. 18. True — Frequency counts occurrences of values or classes. 19. True — Grouping large datasets into classes makes patterns easier to see. 20. False — Multiply by 360°, not 180°. 21. True — Ogive is a cumulative frequency curve. Section D: Short Answer Questions 22. Primary data: Data collected directly by the investigator (e.g., surveying your classmates about favorite subjects). Secondary data: Data obtained from published sources (e.g., population data from Census reports). (2 marks) 23. A class interval is a range of values in grouped data. For 40–50, class mark = (40 + 50) ÷ 2 = 45. (2 marks) 24. Ungrouped frequency distribution: | Books Read | Frequency | |---|---| | 3 | 1 | | 4 | 1 | | 5 | 3 | | 6 | 2 | | 7 | 2 | | 8 | 1 | Total = 10. (3 marks) 25. (i) Bar graphs are used for discrete data; histograms for continuous data. (ii) Bar graph bars are separated by gaps; histogram bars are adjacent with no gaps. (2 marks) 26. Frequency for coffee = 30; Total = 80. Angle = (30 ÷ 80) × 360° = 0.375 × 360° = 135°. (3 marks) Section E: Long Answer / HOTS Questions 27. Grouped frequency distribution: | Class Interval | Frequency | Class Mark | |---|---|---| | 10–15 | 5 | 12.5 | | 15–20 | 6 | 17.5 | | 20–25 | 5 | 22.5 | | 25–30 | 7 | 27.5 | | 30–35 | 6 | 32.5 | | 35–40 | 5 | 37.5 | | 40–45 | 5 | 42.5 | | 45–50 | 1 | 47.5 | Total = 40. Class mark = (Lower + Upper) ÷ 2 for each interval. (5 marks) 28. Histogram: Draw bars for each class with heights 5, 10, 18, 12, 5 respectively, touching each other. The tallest bar (150–155, frequency 18) shows most students fall in that height range, indicating a roughly symmetric distribution centered around 150–155 cm. (4 marks) 29. (a) Angles: Cricket: (40 ÷ 120) × 360° = 120° Football: (30 ÷ 120) × 360° = 90° Badminton: (25 ÷ 120) × 360° = 75° Tennis: (15 ÷ 120) × 360° = 45° Others: (10 ÷ 120) × 360° = 30° Total = 360° ✓ (b) Cricket occupies the largest slice at 120°. (4 marks) Section F: Case-Study Question 30. (a) Modal class: 4–6 hours (frequency 70, highest). (1 mark) (b) Class mark for 4–6 = (4 + 6) ÷ 2 = 5 hours. (1 mark) (c) A histogram is appropriate because the data is continuous (time spent) and grouped into class intervals; adjacent bars will show the distribution clearly. (1 mark) (d) Cumulative frequency for 4–6 = 30 + 50 + 70 = 150 students. (1 mark)

To get maximum benefit from this Statistics worksheet, treat it as a mini-exam. Find a quiet spot, set a timer for 90 minutes, and attempt every question without looking at your textbook or notes. Use a pencil so you can erase and revise rough work, but write your final answers neatly in pen. Start with Section A (MCQs) to warm up—these are quick wins if you know your definitions. Move to Section B (fill-in-the-blanks) and Section C (true/false) to secure more marks with minimal time. Then tackle Section D short-answer questions; show all working for calculation-based items. Section E long-answer and HOTS questions demand careful reading—underline key data, draw rough sketches of histograms or pie charts, and check your arithmetic twice. Finally, read the case study slowly and answer each sub-question methodically. After 90 minutes, stop and mark your work using the answer key. Award yourself marks honestly; if your method was correct but you made a small arithmetic slip, give partial credit. Note topics where you lost marks—perhaps class-mark calculations or pie-chart angles—and revise those sections in your NCERT textbook. Repeat this worksheet a week later to track improvement. Parents: review your child's marked paper together, discussing mistakes without criticism. For 24×7 doubt-clearing and instant step-by-step solutions via photo upload, consider CBSETUTOR.ai at a flat ₹999 per month for all classes 6–12, with a 3-day free trial to experience AI-powered tutoring firsthand.

Even bright students trip over certain pitfalls in Chapter 12 Statistics. One frequent error is confusing bar graphs with histograms: remember, bar graphs have gaps (discrete data like favorite fruits), whereas histograms have touching bars (continuous data like heights or weights). Another mistake is miscalculating the class mark—students sometimes add the limits but forget to divide by two, or they subtract instead of add. Always use (Lower Limit + Upper Limit) ÷ 2. In pie charts, many forget to multiply by 360° when computing sector angles; they stop at the fraction or multiply by 180° instead. Double-check your formula: (Frequency ÷ Total Frequency) × 360°. When constructing frequency tables, students occasionally miscount tallies or place a value in the wrong class interval—especially near boundary values like 20 in the class 20–25 vs. 15–20. Clarify whether your textbook uses inclusive (≤) or exclusive (<) boundaries. For cumulative frequency, a common slip is adding only the current class frequency instead of summing all frequencies up to that class. Finally, in HOTS questions, students rush through multi-step problems and skip units (e.g., writing '5' instead of '5 hours' or '90' instead of '90°'). Always write units, label axes on graphs, and recheck arithmetic. By being aware of these traps and practicing carefully, you will avoid losing easy marks in your CBSE exam. If you need instant feedback on your working—especially for graph-drawing or complex calculations—CBSETUOR.ai offers photo-upload doubt solving with step-by-step AI explanations, all for ₹999/month across Classes 6–12, with a 3-day free trial to start.

Statistics questions in CBSE Class 9 Mathematics exams are straightforward if you follow a disciplined approach. First, read the question twice to identify what is asked—draw a frequency table, calculate class marks, find a pie-chart angle, or draw a histogram. Underline key numbers and units. Second, organize your rough work: if you are making a frequency table, draw neat columns with headings; if calculating angles, write the formula first, then substitute values. Examiners award marks for method even if the final answer is slightly off. Third, for graphical questions, use a ruler and pencil to draw axes and bars; label axes with variable names and units (e.g., 'Height in cm' on X-axis, 'Frequency' on Y-axis). Neatness matters—a wobbly histogram can lose you a mark. Fourth, always check that your frequencies add up to the given total and that pie-chart angles sum to exactly 360°. If they do not, recheck your arithmetic immediately. Fifth, write units everywhere: '5 students', '90 degrees', '15 cm'. Sixth, for HOTS or case-study questions, read the context carefully—sometimes the answer is hidden in the text ('modal class' means highest frequency class). Finally, manage your time: do not spend 10 minutes perfecting one histogram if it means skipping easier 2-mark questions. Practice past-year CBSE papers and sample papers to internalize the exam pattern. For round-the-clock practice and instant doubt resolution, CBSETUTOR.ai provides AI-driven step-by-step solutions via photo upload at just ₹999 per month for all classes 6–12, with a 3-day free trial—perfect for last-minute exam prep and confidence building.