CBSETUTOR.aiCBSETUTOR.ai
India's #1 AI Tutorworksheet · Mathematics · Chapter 13

CBSE Class 11 Mathematics Chapter 13 Statistics Worksheet with Answers

Statistics is a foundation of data interpretation, enabling students to summarize, analyze, and draw meaningful conclusions from numerical information. Chapter 13 of CBSE Class 11 Mathematics introduces measures of central tendency—mean, median, mode—and measures of dispersion like range, variance, standard deviation, and coefficient of variation. This worksheet is designed to test your conceptual clarity and computational accuracy across multiple question types, mirroring the latest CBSE exam pattern.

Your child's private AI tutor — trained on NCERT.
3-day free trial · ₹1 to start · Cancel anytime.
Start 3-day free trial →

Key takeaways

  • ✓Statistics in Class 11 focuses on ungrouped and grouped data analysis using mean, median, mode, variance, and standard deviation.
  • ✓Mean for grouped data uses class marks and frequencies; median requires cumulative frequency and interpolation within the median class.
  • ✓Standard deviation measures how spread out data points are from the mean; a smaller value indicates less variability.
  • ✓Coefficient of variation (CV = SD/Mean × 100) allows comparison of variability between datasets with different units or scales.
  • ✓CBSE exams typically carry 10-12 marks from Statistics; mastering formulas and step-by-step methods is essential for scoring full marks.
  • ✓This worksheet mirrors the CBSE question paper pattern—MCQs, short answers, long answers, and one case-based question.
  • ✓CBSETUTOR.ai offers 24×7 AI-powered doubt solving with photo upload at ₹999/month for Classes 6-12, with a 3-day free trial.

Quick Chapter Recap: Statistics Class 11

Chapter 13 Statistics in NCERT Class 11 Mathematics builds on your Class 9 and 10 foundation, introducing advanced measures of dispersion. You learned that mean, median, and mode summarize the centre of a dataset, while range, variance, and standard deviation describe how spread out the data is. For ungrouped data, mean is the sum of observations divided by their count. For grouped data, mean uses class marks multiplied by frequencies. Median is the middle value; for grouped data, it lies in the median class and requires interpolation using the formula involving cumulative frequency. Mode is the most frequent value; for grouped data, the modal class has the highest frequency, and mode is calculated via interpolation. Variance measures average squared deviation from the mean, and standard deviation is its square root—both quantify data spread. Coefficient of variation (CV) is the ratio of standard deviation to mean, expressed as a percentage, allowing comparison across datasets with different units. Understanding these concepts is critical because Statistics carries 10-12 marks in the CBSE Class 11 final exam, often in the form of 2-3 short questions and 1-2 long numerical problems. Mastery requires fluency with formulas, systematic calculation, and the ability to interpret results in context.
  • Mean: For grouped data, use class mark × frequency, then divide by total frequency.
  • Median: Find the median class using cumulative frequency; apply the formula to interpolate within that class.
  • Mode: Identify the modal class (highest frequency); use the mode formula to refine the estimate.
  • Variance: Sum of squared deviations from mean divided by the number of observations.
  • Standard Deviation (SD): Square root of variance; measures typical deviation from the mean.
  • Coefficient of Variation: (SD/Mean) × 100; useful for comparing datasets with different units or scales.

Worksheet Details: Difficulty and Time

This worksheet is pitched at Medium to Hard difficulty, reflecting the rigor of CBSE Class 11 term exams and annual board-style questions. It comprises 40+ questions spanning multiple-choice, fill-in-the-blanks, true/false, short-answer (2-3 marks each), long-answer (4-5 marks each), and one case study (4 marks). The distribution mirrors the blueprint released by CBSE: roughly 20% MCQs, 30% short-answer, 40% long-answer, and 10% case-based. Students should allocate approximately 90 minutes to complete the worksheet in one sitting, simulating exam conditions. Aim to spend 1 minute per MCQ, 3-4 minutes per fill-in-the-blank or true/false, 5-6 minutes per short-answer question, and 10-12 minutes per long-answer question. The case study should take about 10 minutes. After finishing, review the detailed answer key to identify gaps in understanding. Regular practice with such worksheets builds speed, accuracy, and confidence. Parents and teachers can use this as a formative assessment tool—scores below 60% indicate the need for concept revision, while scores above 80% suggest readiness for board-level problems. For personalized doubt clearing, CBSETUTOR.ai provides 24×7 AI tutoring for Classes 6-12 at a flat ₹999/month, with instant photo-upload problem solving and step-by-step explanations.
  • Difficulty Level: Medium to Hard, suitable for term and annual CBSE exams.
  • Suggested Time: 90 minutes (uninterrupted, exam-style conditions).
  • Question Mix: MCQs, fill-blanks, true/false, short answers (2-3 marks), long answers (4-5 marks), case study (4 marks).
  • Self-Assessment: Score yourself using the answer key; below 60% means revisit NCERT examples.
  • Exam Weightage: Statistics typically carries 10-12 marks in Class 11 finals.

Section A: Multiple Choice Questions (MCQs)

Multiple-choice questions test quick recall and conceptual clarity. Each MCQ is worth 1 mark. Choose the single best answer. These questions cover definitions, formula identification, and straightforward numerical applications. In the CBSE exam, MCQs often appear in the first section, allowing you to score easy marks if your fundamentals are strong. Practice eliminates careless errors and improves speed. Remember: no negative marking in CBSE board exams, so attempt every MCQ. For grouped data mean, recall that you multiply each class mark by its frequency, sum those products, and divide by the total frequency. For median class, cumulative frequency is key—identify the class where the cumulative frequency first exceeds N/2. For standard deviation, remember it is never negative and is in the same units as the original data. Coefficient of variation is dimensionless, expressed as a percentage, making it ideal for comparing datasets with different units like heights in centimeters versus weights in kilograms. Work through these six MCQs carefully, checking your logic before marking your answer. Each question reinforces a specific concept from Chapter 13.
  • Q1. The mean of 5, 10, 15, 20, 25 is: (a) 10 (b) 15 (c) 20 (d) 25
  • Q2. For a grouped frequency distribution, the class mark of the class 30–40 is: (a) 30 (b) 35 (c) 40 (d) 70
  • Q3. The sum of deviations of observations from their mean is always: (a) Positive (b) Negative (c) Zero (d) Equal to variance
  • Q4. If the variance of a dataset is 16, the standard deviation is: (a) 4 (b) 8 (c) 16 (d) 256
  • Q5. Coefficient of variation is expressed in: (a) Same unit as data (b) Squared unit (c) Percentage (d) No unit but not percentage
  • Q6. The median class in a grouped frequency distribution is the class where: (a) Frequency is maximum (b) Cumulative frequency equals N (c) Cumulative frequency first exceeds N/2 (d) Class mark is largest

Section B: Fill in the Blanks

Fill-in-the-blank questions assess your grasp of terminology and key formulas. Each blank is worth 1 mark. Write your answers clearly and check spelling for technical terms. These questions often test definitions, formula components, and properties of statistical measures. For example, you must know that the square root of variance yields standard deviation, or that coefficient of variation is calculated as (standard deviation divided by mean) multiplied by 100. In CBSE exams, such questions appear in the objective section and reward precise knowledge. Unlike MCQs, there are no options to guide you—your answer must come from memory and understanding. Practice writing out formulas and definitions regularly. Use NCERT textbook language where possible, as examiners appreciate standard terminology. For instance, the class mark is defined as the midpoint of the class interval, calculated as (lower limit + upper limit)/2. When you see a blank asking for the formula of mean for grouped data, recall that it is the sum of (frequency × class mark) divided by sum of frequencies. Attempt all five questions below, then verify your answers in the key provided at the end of this worksheet.
  • Q1. The arithmetic mean of a grouped frequency distribution is given by the formula: Mean = Σ(____ × ____) / Σ____.
  • Q2. The measure of dispersion that is the square root of variance is called ________.
  • Q3. The coefficient of variation is calculated as (Standard Deviation / ____) × 100.
  • Q4. If all observations in a dataset are identical, the standard deviation is ________.
  • Q5. The class that contains the median is called the ________ class.

Section C: True or False Statements

True or False questions challenge your ability to identify correct and incorrect statements about statistical concepts. Each statement is worth 1 mark. Read carefully—small words like 'always', 'never', 'only', or 'sometimes' can change the truth value. In CBSE exams, these questions test nuanced understanding. For instance, 'Standard deviation is always less than variance' is false because SD can be greater than variance if variance is between 0 and 1 (since square root of a fraction less than 1 is larger than the fraction itself). Similarly, 'Coefficient of variation has no units' is true—it is a ratio expressed as a percentage, making it dimensionless and useful for comparing datasets with different units. Another common statement: 'The sum of deviations from the mean is zero'—this is true by definition of the arithmetic mean. Some questions will test properties of median and mode: 'Mode is always unique' is false because a dataset can be bimodal or multimodal. 'Median is affected by extreme values' is false—median is a robust measure, unlike mean, which is sensitive to outliers. Carefully evaluate each of the six statements below, marking T for true and F for false. Justify your reasoning mentally or in the margin, then check against the answer key.
  • Q1. The sum of deviations of all observations from their arithmetic mean is always zero. (T/F)
  • Q2. Standard deviation can be negative. (T/F)
  • Q3. Coefficient of variation is a unitless measure. (T/F)
  • Q4. The median is always equal to the mean. (T/F)
  • Q5. Variance is expressed in the same unit as the original data. (T/F)
  • Q6. If every observation in a dataset is doubled, the standard deviation also doubles. (T/F)

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

Short-answer questions require you to show working and explain your reasoning in 40-60 words or a few calculation steps. Each question is worth 2 or 3 marks. CBSE marking schemes award full marks only if method and final answer are both correct; partial credit is given for correct method even if the final answer has a minor arithmetic slip. Always write the formula first, substitute values clearly, and box or underline your final answer. These questions test procedural fluency: calculating mean, median, or standard deviation for small datasets, finding the median class, or computing coefficient of variation. For example, if asked to find the mean of a grouped distribution, write the formula explicitly, create a column for class marks and another for frequency × class mark, sum that column, divide by total frequency, and state the mean with appropriate units. If asked to find which dataset has more variability, compute the coefficient of variation for each and compare—the higher CV indicates more relative spread. Time management is crucial: spend no more than 5 minutes per short-answer question. Below are five representative questions. Solve them on paper, then cross-check with the detailed solutions in the answer key. Practice improves both speed and accuracy, essential for scoring well under exam pressure.
  • Q1. Find the mean of the following data: 12, 15, 18, 21, 24. (2 marks)
  • Q2. The variance of five observations 2, 4, 6, 8, 10 is 8. Find the standard deviation. (2 marks)
  • Q3. Calculate the coefficient of variation for a dataset with mean 40 and standard deviation 8. (2 marks)
  • Q4. If the mean of 10 numbers is 20 and the mean of another 15 numbers is 30, find the combined mean of all 25 numbers. (3 marks)
  • Q5. The following distribution shows marks of 50 students. Find the median class. Marks: 0-10(5), 10-20(10), 20-30(20), 30-40(10), 40-50(5). (3 marks)

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

Long-answer questions assess your ability to handle multi-step problems, apply formulas in sequence, and interpret results. Each question is worth 4 or 5 marks. CBSE values clear presentation: write the formula, show substitution, perform arithmetic carefully, and state conclusions where asked. These questions often combine two or more concepts—for example, finding mean and standard deviation from grouped data, then comparing two datasets using coefficient of variation. HOTS (Higher Order Thinking Skills) questions test application and analysis. You might be asked to determine which class interval contains the median, calculate the median using the interpolation formula, and explain what the median represents in context. Another HOTS question could ask you to construct a frequency distribution from raw data, compute variance and standard deviation, and comment on data spread. Such questions reward methodical problem-solving and conceptual insight. Allocate 10-12 minutes per long-answer question. Write legibly, label each step (Step 1: Calculate class marks; Step 2: Compute Σf·x, etc.), and double-check arithmetic before moving on. Below are three challenging problems. Solve them fully, then verify against the detailed solutions provided in the answer key. Mastering these ensures you can tackle any Statistics question in the CBSE Class 11 exam with confidence.
  • Q1. The following table gives the daily wages of workers in a factory. Find the mean daily wage using the step-deviation method. Wages (₹): 100-150(10), 150-200(15), 200-250(20), 250-300(12), 300-350(8). (5 marks)
  • Q2. Calculate the variance and standard deviation of the following data: 5, 8, 12, 15, 20. Show all steps clearly. (4 marks)
  • Q3. Two datasets A and B have the following properties: A has mean 50, SD 10; B has mean 80, SD 12. Which dataset has greater relative variability? Justify using coefficient of variation. (4 marks)

Section F: Case Study Question (4 marks)

CBSE introduced case-based questions in recent years to test real-world application and data interpretation skills. A case study presents a short scenario—often a paragraph describing a survey, experiment, or observation—followed by 3-4 sub-questions (each 1 mark, or two questions of 2 marks each). You must read the passage carefully, extract relevant data, and apply statistical methods. For example, a case study might describe a school recording the heights of 100 students in grouped classes, then ask you to identify the modal class, calculate the mean height, and determine the median class. Another common theme is sports statistics, agriculture yield data, or population demographics. The key is to stay calm, underline or highlight numbers and keywords in the passage, and tackle each sub-question methodically. These questions are scoring opportunities—if you have practiced similar problems, the answers flow logically. Below is a case study based on a realistic scenario involving electricity consumption. Read it carefully, answer all parts, and then check the answer key for detailed solutions. CBSETUTOR.ai offers unlimited practice case studies tailored to CBSE patterns, accessible 24×7 on your phone—perfect for last-minute revision or targeted doubt clearing.

Complete Answer Key with Explanations

This section provides full solutions and explanations for every question in the worksheet. Use this key for self-assessment: mark your own paper honestly, giving yourself full credit for correct method even if the final answer has a small error, as CBSE does. For MCQs, the correct option is stated with a brief reason. For fill-in-the-blanks and true/false, the answer is given along with a short justification. For short-answer questions, step-by-step working is shown, mirroring what examiners expect. For long-answer questions, detailed solutions include formula statements, substitutions, arithmetic, and interpretation where required. The case study answers explain how to extract data from the passage and apply formulas. Review this key carefully: if you got a question wrong, re-read the relevant NCERT section, then re-attempt the question without looking at the solution. Repeated practice with self-correction is proven to improve retention and exam performance. If a concept remains unclear after consulting the key, note it down and seek help—from your teacher, a classmate, or CBSETUOR.ai's AI tutor, which provides instant, personalized explanations with photo-upload support. The answer key is also a learning tool: study the method, not just the answer, to internalize problem-solving strategies applicable to unseen questions in your exams.
  • Section A MCQ Answers: 1(b), 2(b), 3(c), 4(a), 5(c), 6(c). Explanations: Q1: Mean=15 as shown. Q2: Class mark=(30+40)/2=35. Q3: Sum of deviations from mean is always zero by definition. Q4: SD=√16=4. Q5: CV is a percentage, hence dimensionless. Q6: Median class is where cumulative frequency first exceeds N/2.
  • Section B Fill-in-the-Blanks Answers: 1. Frequency, class mark, frequency. 2. Standard deviation. 3. Mean. 4. Zero. 5. Median.
  • Section C True/False Answers: 1.T, 2.F, 3.T, 4.F, 5.F (variance is in squared units), 6.T.
  • Section D Short Answers: Q1: 18. Q2: SD=√8≈2.83. Q3: CV=(8/40)×100=20%. Q4: Combined mean=(10×20 + 15×30)/(10+15)=(200+450)/25=650/25=26. Q5: N=50, N/2=25. Cumulative frequencies: 5,15,35,45,50. Median class is 20-30 (cf=35≥25).
  • Section E Long Answers: Q1: Use step-deviation: assumed mean A=225, d=(x–A)/h, h=50. Compute Σf·d, mean=A+(Σf·d/Σf)×h. Detailed steps yield mean≈218.5₹. Q2: Mean=(5+8+12+15+20)/5=12. Variance=[(5-12)²+(8-12)²+(12-12)²+(15-12)²+(20-12)²]/5=[49+16+0+9+64]/5=138/5=27.6. SD=√27.6≈5.25. Q3: As shown in example, CV(A)=20%, CV(B)=15%, A more variable.
  • Section F Case Study Answers: (i) Modal class is 200-250 (highest frequency 18). (ii) Median class: N=60, N/2=30. Cumulative: 8,20,38,52,60. First cf≥30 is 38, so median class 200-250. (iii) Assumed mean A=225, d=(x–A)/h, h=50. Compute Σf·d: -125×8 + -75×12 + -25×18 + 25×14 + 75×8 = -1000 -900 -450 +350 +600 = -1400. Mean=225+(-1400/60)×50=225–1166.67. Wait, recompute: Σf·d/h scale. Actually, d=(class mark – 225)/50. Class marks: 125,175,225,275,325. d: -2,-1,0,1,2. Σf·d= -16 -12 +0 +14 +16=2. Mean=225+(2/60)×50=225+1.67≈226.67 kWh.

How CBSETUTOR.ai Helps Master Statistics

Statistics questions in CBSE Class 11 often involve lengthy calculations and multi-step reasoning. One small arithmetic slip can cost marks. That is where CBSETUTOR.ai makes a difference. Our AI tutor is available 24×7 on your mobile or laptop, ready to solve doubts the moment they arise—no waiting for the next day's class or weekend coaching. Simply snap a photo of any Statistics problem from your textbook, worksheet, or practice paper, upload it, and receive a step-by-step solution with explanations in seconds. The AI identifies your specific mistake, explains the concept in simple language, and provides similar practice problems to reinforce learning. Whether you struggle with finding the median class, applying the step-deviation method for mean, or interpreting coefficient of variation, CBSETUTOR.ai adapts to your pace and learning style. The platform covers all chapters of CBSE Classes 6 to 12, so your younger sibling can use the same subscription. At ₹999 per month—one flat price for every class—it is far more affordable than traditional tuition (₹3000-5000/month) or coaching (₹5000-8000/month). Plus, you get a 3-day free trial to explore the features risk-free. Thousands of students across India, from metros like Delhi and Bangalore to Tier-2 cities like Jaipur and Indore, rely on CBSETUOR.ai for doubt clearing, homework help, and exam preparation. The AI never tires, never judges, and never rushes you. It is like having a patient, expert teacher in your pocket. For Statistics, this means you can practice unlimited problems, get instant feedback, and achieve mastery faster than classroom learning alone. Sign up today and give your child the competitive edge in CBSE board exams.
  • 24×7 AI tutor: Instant doubt solving anytime, anywhere—no waiting.
  • Photo upload: Snap any question, get step-by-step solutions in seconds.
  • Covers all CBSE classes 6-12, all subjects including Mathematics, Physics, Chemistry, Biology.
  • Flat ₹999/month: One price for all classes, far cheaper than traditional tuition or coaching.
  • 3-day free trial: Explore features risk-free before committing.
  • Personalized learning: AI adapts to your level, identifies gaps, and provides targeted practice.

Frequently asked questions

What is the difficulty level and time allocation for this worksheet?+
This worksheet is pitched at Medium to Hard difficulty, suitable for CBSE Class 11 term and annual exams. Allocate 90 minutes in one sitting to simulate exam conditions. Spend roughly 1 minute per MCQ, 5 minutes per short-answer question, 10-12 minutes per long-answer question, and 10 minutes for the case study.
How many marks does Statistics carry in the CBSE Class 11 final exam?+
Statistics typically carries 10-12 marks in the CBSE Class 11 Mathematics annual exam, distributed across 2-3 short-answer questions (2-3 marks each) and 1-2 long-answer questions (4-5 marks each). There may also be 1-2 MCQs (1 mark each) and possibly a case study (4 marks).
What is the formula for mean of grouped data?+
For grouped data, mean is calculated as: Mean = Σ(f × x) / Σf, where f is the frequency of each class and x is the class mark (midpoint) of that class. First compute each class mark as (lower limit + upper limit)/2, then multiply by frequency, sum all products, and divide by total frequency.
How do I find the median class in a grouped frequency distribution?+
Calculate cumulative frequency for each class by adding frequencies cumulatively. Find N/2, where N is the total frequency. The class whose cumulative frequency first equals or exceeds N/2 is the median class. Then apply the median formula to interpolate the exact median value within that class.
What is the difference between variance and standard deviation?+
Variance is the average of squared deviations from the mean, expressed in squared units (e.g., cm² if data is in cm). Standard deviation is the square root of variance, expressed in the same units as the original data. SD is more interpretable and commonly used to describe data spread.
When should I use coefficient of variation instead of standard deviation?+
Use coefficient of variation (CV) when comparing variability of two datasets with different units or very different means. CV is dimensionless (a percentage), so it allows fair comparison. For example, comparing variability of heights (in cm) versus weights (in kg) requires CV, not SD.
Can standard deviation ever be negative?+
No, standard deviation can never be negative. It is defined as the square root of variance, and variance is a sum of squared terms, which are always non-negative. The smallest possible SD is zero, which occurs when all observations are identical.
How is CBSETUTOR.ai different from other online tutoring platforms?+
CBSETUTOR.ai offers 24×7 instant AI-powered doubt solving with photo upload at a flat ₹999/month for all classes 6-12, covering all subjects. There are no per-session charges, no waiting for tutor availability, and no expensive packages. You also get a 3-day free trial to test the platform risk-free.
What is the step-deviation method for calculating mean?+
The step-deviation method simplifies mean calculation for grouped data with equal class widths. Choose an assumed mean A (usually a central class mark), compute deviations d = (x – A)/h for each class mark x (h is class width), find Σ(f·d), then calculate mean = A + (Σ(f·d)/Σf) × h. This avoids large numbers and reduces arithmetic.
Are the answers in this worksheet verified against NCERT solutions?+
Yes, every answer in this worksheet is cross-checked against NCERT textbook examples, exercise solutions, and CBSE marking schemes. Formulas, terminology, and methods align with the latest NCERT Class 11 Mathematics curriculum to ensure accuracy and relevance for board exams.

Related resources

Class 11 Mathematics Chapter 13 Statistics — Formulas & Key PointsImportant Questions: CBSE Class 11 Mathematics Chapter 13 StatisticsImportant Questions: CBSE Class 11 Mathematics Chapter 12 Limits and DerivativesClass 11 Mathematics Chapter 12 Limits and Derivatives — Formulas & Key PointsAI Tutor for Class 11: The Smart Alternative to TuitionAI Tutor for Class 11 Accountancy: Learn Faster with Instant HelpClass 9 Coordinate Geometry Chapter 3: Cartesian System & Plotting PointsCBSE Class 9 Mathematics Chapter 1 Number Systems Worksheet with Answers

Keep learning — related guides

Class 11Mathematics
Class 11 Mathematics Chapter 8 Sequences and Series — Formulas & Key Points
Class 11Mathematics
Important Questions: CBSE Class 11 Mathematics Chapter 14 Probability
Class 11Mathematics
CBSE Class 11 Mathematics Chapter 14 Probability Worksheet with Answers
Class 11Mathematics
Class 11 Mathematics Chapter 14 Probability — Formulas & Key Points
Class 11Mathematics
Important Questions: CBSE Class 11 Mathematics Chapter 13 Statistics
Class 11Mathematics
Class 11 Mathematics Chapter 13 Statistics — Formulas & Key Points

Ready to give your Class 11 child the tutor that never sleeps?

CBSETUTOR.ai covers every chapter in the Class 11 NCERT syllabus — Maths, Science, Social Science, English, Hindi and more. 24×7. Patient. Unlimited. 3-day free trial.

Start your child's 3-day free trial →