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Important Questions: CBSE Class 11 Mathematics Chapter 13 Statistics

Q: How many marks does Chapter 13 Statistics carry in CBSE Class 11 annual exam?

Statistics contributes 10-12 marks out of 80 in the CBSE Class 11 Mathematics annual exam, distributed across 1-mark MCQs, 2-mark VSA, 3-mark short answer, and one 5-mark long answer question.

Q: Which method for calculating mean is fastest in the exam—direct, assumed mean, or step-deviation?

Step-deviation method is fastest when class intervals are uniform and frequencies are large, because you work with small integers (uᵢ) instead of large deviations. Choose assumed mean when intervals are non-uniform, and direct method only for very simple datasets.

Q: What is the difference between variance and standard deviation, and when do I use each?

Variance is the average of squared deviations (unit²), used in intermediate calculations. Standard deviation is the square root of variance (same unit as data), used for interpretation and reporting. Always compute variance first, then take √ to get SD for the final answer.

Q: Why is coefficient of variation better than standard deviation for comparing two datasets?

Coefficient of variation (CV) is a relative measure (percentage), so it allows fair comparison between datasets with different units or vastly different means. For example, comparing consistency of cricket scores (runs) and ages (years) requires CV, because their units differ. SD alone does not account for scale.

Q: How do I avoid arithmetic mistakes in grouped data variance calculations?

Construct a full table with labeled columns: fᵢ, xᵢ, dᵢ, fᵢ dᵢ, dᵢ², fᵢ dᵢ². Fill row by row, write each product carefully, sum each column separately, and double-check sums before substituting into the variance formula. Use a calculator if allowed, and always verify that variance is non-negative.

Q: What should I do if I forget a formula during the exam?

At the start of the exam, write all key formulas (mean, variance, SD, CV) on the top of your rough page or answer sheet margin. If you still forget, try to derive it logically: variance is average of squared deviations, SD is √variance, CV is (SD/mean)×100. Showing logical reasoning earns partial marks.

Q: Are case-based questions in Statistics difficult, and how should I approach them?

Case-based questions present a real-world scenario with data embedded in a paragraph. They are not inherently harder—just read carefully, underline the data, organize it into a table or list, then solve sub-questions one by one. Each sub-question is straightforward (calculate mean, find SD, compare using CV). Practice 3-4 case studies from sample papers to build confidence.

Q: Can I score full marks in Statistics if I am weak in arithmetic?

Yes, if you master the method and show clear working. CBSE awards method marks generously—if your formula, table setup, and approach are correct, you earn 60-70% marks even if arithmetic is wrong. Use a calculator (if allowed), double-check sums, and write neatly. Consider using CBSETUTOR.ai to practice and catch arithmetic patterns before the exam.

Q: How important is it to practice previous years' CBSE questions for Statistics?

Extremely important. CBSE repeats question patterns—grouped frequency distribution with mean and variance, comparison using CV, case-based multi-part questions. Solving 2022-2024 papers shows you exactly what to expect, which methods are preferred, and how mark distribution works. Aim to solve at least 5 previous papers under timed conditions.

Q: What are the most common mistakes in Statistics questions and how can I avoid them?

Top mistakes: confusing inclusive/exclusive class limits, forgetting to multiply deviations by frequency (fᵢ dᵢ), not taking √ for standard deviation, omitting units, and skipping interpretation in comparison questions. Avoid these by constructing labeled tables, double-checking every step, always stating units, and writing a one-line conclusion for CV comparisons.

Chapter 13 Statistics in CBSE Class 11 Mathematics moves beyond the basic bar graphs and pie charts of Class 9 into rigorous numerical analysis. You will learn to compute mean, median, mode for grouped data, and quantify how scattered or consistent a dataset is through variance, standard deviation, and coefficient of variation. This chapter is critical—it accounts for 10-12 marks in your annual exam and builds the statistical foundation for Class 12 Probability. Below are 18 important questions, spanning 1-mark MCQs to 5-mark application problems, each with model answers so you can self-check and refine your technique before exam day.

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Key takeaways

✓Chapter 13 Statistics contributes 10-12 marks in CBSE Class 11 Mathematics annual exams, distributed across MCQs, short answers, and long answers.
✓Core topics include measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation, coefficient of variation), and frequency distributions.
✓Mean of grouped data can be calculated by three methods: direct, assumed mean (shortcut), and step-deviation—know when to use each for fast calculation.
✓Variance and standard deviation quantify data spread; coefficient of variation allows comparison between datasets with different units or scales.
✓CBSE often asks application-based questions: given a frequency table, calculate mean and standard deviation, or compare two datasets using coefficient of variation.
✓Common mistakes include mixing inclusive and exclusive class boundaries, arithmetic errors in deviation methods, and forgetting to take the square root for standard deviation.
✓Practice all three question types—conceptual MCQs, numerical short answers, and multi-step long answers—to cover the full marks spectrum.

Chapter Overview and Marks Weightage in CBSE Class 11 Exam

Statistics appears in Unit VI: Statistics and Probability, carrying a combined weightage of approximately 20 marks across both chapters. Chapter 13 Statistics alone is worth 10-12 marks in the CBSE Class 11 annual exam. The question paper typically includes one or two MCQs (1 mark each), one or two very short answer questions (2 marks), one short answer question (3 marks), and at least one long answer question (5 marks) from this chapter. The three big pillars are: measures of central tendency (mean, median, mode for grouped data), measures of dispersion (range, variance, standard deviation), and coefficient of variation for comparing datasets. NCERT exercises 13.1 and 13.2 cover these exhaustively. CBSE usually sets one numerical problem asking you to calculate mean and standard deviation from a frequency distribution, and one application question comparing two datasets using coefficient of variation. In recent years, case-based questions have also appeared, presenting real-world data (exam scores, rainfall, sales) and asking multi-part statistics questions worth 4-5 marks. Mastering the shortcut methods—assumed mean and step-deviation—saves precious minutes in the exam. Given that each mark counts, thorough practice of all question types is non-negotiable for scoring full marks in Statistics.

Unit VI (Statistics and Probability) = 20 marks; Chapter 13 Statistics = 10-12 marks standalone
1-2 MCQs (1 mark each): definitions, properties, or quick calculations
1-2 VSA (2 marks): simple mean, median, or range from small datasets
1 short answer (3 marks): compute mean by assumed-mean method or find variance
1 long answer (5 marks): full frequency distribution analysis—mean, variance, standard deviation, coefficient of variation

1-Mark Questions: Multiple Choice and Very Short Answer

One-mark questions test definitions, properties, and quick recall. CBSE often asks which measure of central tendency is most affected by extreme values (mean), the formula for coefficient of variation, or the unit of variance (square of original unit). MCQs may present a small dataset and ask you to identify the correct mean or median. These questions reward conceptual clarity and formula recall. Below are six representative 1-mark questions with concise answers. Practice these until you can answer each in under 30 seconds—that is the exam reality. Remember, every mark lost here is a mark you must make up elsewhere, so accuracy is paramount. Use NCERT definitions verbatim: for instance, 'Range is the difference between the maximum and minimum observations in the dataset.' CBSE mark schemes are strict on terminology, so precise language matters even in 1-mark answers.

2-Mark Questions: Short Numerical Problems

Two-mark questions require one or two calculation steps and a brief explanation. Typical examples: find the mean of a small frequency distribution, calculate range or variance of five observations, or determine the class mark and frequency when given grouped data boundaries. CBSE expects clear working—write the formula, substitute values, compute the answer, and state the unit if applicable. Skipping steps may cost you a mark even if the final answer is correct. Below are four 2-mark questions with model solutions. Notice the structure: state the formula, show substitution, simplify, box or underline the final answer. This discipline not only earns full marks but also helps you catch arithmetic errors before finalizing your answer. In the exam, allocate roughly 2-3 minutes per 2-mark question, leaving time to review your working before moving to the next section.

3-Mark Questions: Application and Short Derivations

Three-mark questions test your ability to apply formulas to slightly more complex scenarios, often involving grouped data or multi-step reasoning. CBSE may ask you to calculate mean using the assumed-mean method, find variance from a frequency table, or compare two small datasets. These questions reward methodical working: construct a working table (columns for xᵢ, fᵢ, dᵢ, fᵢdᵢ, etc.), show each step of substitution, compute intermediate sums, and arrive at the final answer with proper units. Partial marks are awarded for correct method even if arithmetic goes wrong, so never skip the formula statement. Below are three representative 3-mark questions with full model answers. Study the layout—examiners appreciate clean tabular working and clearly labeled steps. In the exam, budget 4-5 minutes per 3-mark question and use the margin or rough space for trial calculations before writing the final solution.

5-Mark Questions: Long Answer and Case-Based Problems

Five-mark questions are the crown jewels of Statistics—they test your full command of the chapter. CBSE typically presents a frequency distribution with 5-7 classes and asks you to compute mean (using step-deviation or assumed mean), variance, standard deviation, and coefficient of variation. Marks are distributed: 1 mark for correct class marks or deviations table, 1 mark for mean, 1.5 marks for variance calculation, 1 mark for standard deviation, 0.5 mark for coefficient of variation and interpretation. Another common 5-mark format is a case study: a paragraph describes rainfall in two cities or exam scores of two batches, followed by sub-questions (a) find mean and standard deviation for each, (b) which is more consistent, (c) interpret the result. These questions reward organized working—use tables, label every column, show all intermediate sums, and box final answers. Below are three full 5-mark questions with step-by-step model solutions. Practice these under timed conditions (10-12 minutes each) to build speed and accuracy. In the exam, if you run short on time, prioritize showing your method and writing formulas—partial marks can save your grade even if you don't reach the final number.

How CBSE Frames Questions from Statistics

Understanding CBSE's question design strategy helps you anticipate what will be asked and prepare targeted answers. First, CBSE loves grouped data in frequency distributions—almost every year, at least one 5-mark question presents a table of classes and frequencies. You must compute mean (often by assumed mean or step-deviation to test shortcut skills), then variance and standard deviation. Second, coefficient of variation appears regularly, especially in comparison questions: 'Which dataset is more variable?' or 'Which group is more consistent?' These test your ability to interpret CV as a relative measure. Third, CBSE increasingly uses real-world contexts—exam marks, wages, rainfall, ages—wrapped in a short paragraph (case study). You extract data, form a frequency table if needed, and solve sub-questions worth 4-5 marks total. Fourth, MCQs test definitions and properties: 'Variance is always non-negative,' 'Mean is affected by extreme values,' 'Median is a positional average.' These require conceptual clarity, not computation. Fifth, CBSE occasionally asks for the empirical relationship between mean, median, and mode (Mode ≈ 3Median − 2Mean for moderately skewed data), though this is more common in Class 10. Sixth, CBSE mark schemes reward method marks—if your formula and approach are correct but arithmetic is wrong, you still earn 60-70% of the marks. Therefore, always write the formula, show substitution, construct tables neatly, and label steps. Finally, CBSE has started including assertion-reason questions (2 statements; choose if both true, first true second false, etc.)—practice these from sample papers. In summary, CBSE tests three things: recall (definitions, formulas), computation (apply formulas accurately), and interpretation (what does CV=20% mean for consistency?).

5-mark question almost always involves a grouped frequency distribution and asks for mean, variance, SD, and CV—practice the step-deviation method for speed.
Case-based questions (4-5 marks) present a real scenario with data; you must extract, organize, compute, and interpret.
MCQs test properties and definitions—know which measure is resistant to outliers, units of variance, and definition of range.
Comparison questions using coefficient of variation are common: 'Which batch is more consistent?'—always calculate CV for both, then interpret.
CBSE awards method marks generously—state formulas, show working, construct tables even if final answer is wrong.
Recent papers include assertion-reason MCQs and integrated questions linking Statistics with Probability or Sets—practice sample papers from 2023-2025.

Common Mistakes Students Make in Statistics Questions

Mistakes in Statistics are often avoidable—awareness is half the battle. First, confusing inclusive and exclusive class boundaries: if the question says 'Class: 10-20, 20-30,' students sometimes count 20 twice. Always check the question's convention; NCERT typically uses 10-20 meaning 10 ≤ x < 20 (upper limit exclusive). Second, arithmetic errors in deviation methods: forgetting to multiply deviations by frequency (fᵢ dᵢ instead of just dᵢ), or summing dᵢ² instead of fᵢ dᵢ². Use a table with labeled columns—fᵢ, xᵢ, dᵢ, fᵢ dᵢ, fᵢ dᵢ²—and fill row by row; this minimizes errors. Third, forgetting to take the square root: variance is in squared units, standard deviation is the square root of variance. Many students write variance value as SD and lose a full mark. Fourth, incorrect choice of assumed mean: while any value works mathematically, choosing the middle class mark (or a value close to it) keeps deviations small and reduces arithmetic load. Fifth, mixing up formulas: writing mean formula when asked for median, or using population variance formula (÷n) instead of sample variance (÷(n−1)) if specified. CBSE Class 11 uses population formulas (÷n), so stick to NCERT. Sixth, not checking units: if data is in ₹, variance is in ₹², standard deviation is in ₹, and CV is unitless (%). State units in your final answer. Seventh, omitting the interpretation in comparison questions: if asked 'Which dataset is more variable?' don't just compute CV—write a one-line conclusion: 'Dataset A has lower CV, hence more consistent.' Finally, poor time management: spending 15 minutes on a 5-mark question leaves no time to review. Practice under timed conditions to build speed. Learn from your mistakes: keep an error log and review it before the exam.

Confusing inclusive/exclusive class boundaries—always confirm the convention (NCERT uses lower-inclusive, upper-exclusive).
Arithmetic slips in deviation methods—construct a full table with all columns labeled; double-check sums before final calculation.
Forgetting to take √ for standard deviation—variance is intermediate, SD is the final answer; don't mix them up.
Poor choice of assumed mean—pick the middle class mark to keep deviations small and arithmetic simple.
Mixing population (÷n) and sample (÷(n−1)) formulas—CBSE Class 11 uses population formulas, follow NCERT exactly.
Omitting units—variance has squared units, SD has original units, CV is %; always state units in answers.
Skipping interpretation—when asked 'Which is more consistent?' compute CV for both, then write a conclusion sentence.
Time mismanagement—allocate 2 min for 1-mark, 3 min for 2-mark, 5 min for 3-mark, 10 min for 5-mark; stick to it.

Quick Revision Formulas for Last-Minute Prep

Before walking into the exam hall, revise these core formulas—they are your toolkit for every Statistics question. Mean (ungrouped) = Σxᵢ / n. Mean (grouped) direct method = Σ(fᵢ xᵢ) / Σfᵢ. Mean by assumed mean method: x̄ = A + (Σfᵢ dᵢ / Σfᵢ), where dᵢ = xᵢ − A. Mean by step-deviation: x̄ = A + h(Σfᵢ uᵢ / Σfᵢ), where uᵢ = (xᵢ − A)/h and h is class width. Variance (ungrouped) = Σ(xᵢ − x̄)² / n. Variance (grouped) = [Σfᵢ(xᵢ − x̄)²] / Σfᵢ. Alternatively, σ² = (Σfᵢ xᵢ²) / Σfᵢ − x̄². For step-deviation, σ² = h² [(Σfᵢ uᵢ² / Σfᵢ) − (Σfᵢ uᵢ / Σfᵢ)²]. Standard deviation σ = √(variance). Coefficient of variation CV = (σ / x̄) × 100 (expressed as percentage). Range = Maximum observation − Minimum observation. Class mark xᵢ = (Lower limit + Upper limit) / 2. These formulas appear in every exam; write them on your formula sheet or rough page at the start, so you don't waste time recalling mid-question. Also memorize the empirical relation for moderately skewed distributions: Mode ≈ 3Median − 2Mean (useful if a question asks to estimate mode given mean and median). Finally, remember that standard deviation is the most commonly used measure of dispersion because it has the same unit as the data and is sensitive to every observation, while range is easy to compute but ignores the entire dataset between min and max. Coefficient of variation is the go-to for comparing datasets with different units or vastly different means.

Mean (grouped, assumed-mean): x̄ = A + (Σfᵢ dᵢ / Σfᵢ), dᵢ = xᵢ − A
Mean (step-deviation): x̄ = A + h(Σfᵢ uᵢ / Σfᵢ), uᵢ = (xᵢ−A)/h
Variance (grouped): σ² = (Σfᵢ xᵢ²)/Σfᵢ − x̄² or σ²= [Σfᵢ(xᵢ−x̄)²]/Σfᵢ
Variance (step-deviation): σ² = h²[(Σfᵢ uᵢ²/Σfᵢ) − (Σfᵢ uᵢ/Σfᵢ)²]
Standard deviation: σ = √(variance)
Coefficient of variation: CV = (σ/x̄)×100%
Range = Max − Min; Class mark = (Lower+Upper)/2

How CBSETUTOR.ai Helps You Master Statistics (and Every Chapter)

Statistics is a calculation-heavy chapter—one arithmetic slip, one formula mix-up, and marks slip away. That is where CBSETUTOR.ai becomes your 24×7 study partner. Imagine you are practicing Question 14 above (the 5-mark wages problem) at 11 p.m. and get stuck on the variance calculation—just snap a photo of your working and upload it to CBSETUTOR.ai. Within seconds, the AI tutor identifies your error (perhaps you forgot to multiply by h² in the step-deviation formula), explains the correct method, and shows you the right working step-by-step. No waiting for tomorrow's tuition class, no hunting for solutions online. CBSETUTOR.ai covers every NCERT chapter for Classes 6 to 12, so whether you need help with Statistics, Trigonometry, Coordinate Geometry, or Probability, one platform does it all. The AI asks you questions to check understanding, generates similar practice problems, and tracks which topics you have mastered and which need more work. Parents love the flat ₹999/month fee—one price for every class, every subject—and the 3-day free trial means your child can test drive the platform risk-free. For Statistics specifically, CBSETUTOR.ai has solved thousands of CBSE previous-year questions, so it knows exactly how examiners frame variance problems, what common mistakes look like, and how to guide you to full marks. Think of it as having a patient, expert tutor in your pocket, available anytime, anywhere—perfect for last-minute doubts the night before your exam or methodical chapter-by-chapter preparation throughout the year.

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Aligned with NCERT and CBSE: every explanation uses official terminology and formulas, so exam answers match marking schemes.

Exam-Day Strategy for Statistics Questions

Walk into the exam with a plan. First 5 minutes: skim the entire paper, identify the Statistics questions (likely one MCQ, one 2-mark, one 3-mark, one 5-mark). Decide your order—many students tackle the 5-mark question first while mind is fresh, because it carries the most weight. Or, if you prefer confidence-building, start with MCQs and short answers, then dive into the long answer. Either way, allocate time strictly: 1 mark = ~2 minutes, 2 marks = 3 minutes, 3 marks = 5 minutes, 5 marks = 10 minutes. Stick to it—don't let one question eat up 20 minutes. For grouped data questions, immediately write the formula sheet (mean, variance, SD, CV) at the top of your rough work; this prevents mid-question panic. Construct the working table neatly: columns for xᵢ, fᵢ, dᵢ, fᵢ dᵢ, dᵢ², fᵢ dᵢ²—label each column, fill row by row, double-check sums before substituting into formulas. Show every step: examiners award method marks generously. If you make an arithmetic error but the method is right, you still get 60-70% of marks. Always state the unit in your final answer (₹, cm, years, etc.). For MCQs, if unsure, use elimination: scratch out obviously wrong options, guess from the remaining. Never leave MCQs blank—no negative marking. In case-based questions, underline or highlight the data given in the paragraph, then organize it into a table or list before attempting sub-questions. Finally, reserve the last 10 minutes for review: re-check your arithmetic (especially sums in tables), ensure you took √ for standard deviation, verify that CV is expressed as a percentage, and confirm that you answered every part of multi-part questions. A calm, methodical approach beats speed without accuracy every time.

Skim the paper first 5 min, identify Statistics questions, decide your order of attempt.
Allocate time strictly: 1 mark ~2 min, 2 marks ~3 min, 3 marks ~5 min, 5 marks ~10 min; move on if stuck.
Write the formula sheet (mean, variance, SD, CV) at the top of rough work before starting calculations.
Construct neat working tables with labeled columns—fᵢ, xᵢ, dᵢ, fᵢ dᵢ, dᵢ², fᵢ dᵢ²; fill row-by-row, sum carefully.
Show every step and state formulas—method marks are generous; even if arithmetic is wrong, you earn partial credit.
State units in final answers (₹, cm, %, etc.)—marks can be deducted for omitting units.
For MCQs, use elimination; never leave blank—no negative marking in CBSE.
Reserve last 10 min for review: re-check arithmetic, verify √ for SD, confirm CV as %, ensure all parts answered.

Frequently asked questions

How many marks does Chapter 13 Statistics carry in CBSE Class 11 annual exam?+

Statistics contributes 10-12 marks out of 80 in the CBSE Class 11 Mathematics annual exam, distributed across 1-mark MCQs, 2-mark VSA, 3-mark short answer, and one 5-mark long answer question.

Which method for calculating mean is fastest in the exam—direct, assumed mean, or step-deviation?+

Step-deviation method is fastest when class intervals are uniform and frequencies are large, because you work with small integers (uᵢ) instead of large deviations. Choose assumed mean when intervals are non-uniform, and direct method only for very simple datasets.

What is the difference between variance and standard deviation, and when do I use each?+

Variance is the average of squared deviations (unit²), used in intermediate calculations. Standard deviation is the square root of variance (same unit as data), used for interpretation and reporting. Always compute variance first, then take √ to get SD for the final answer.

Why is coefficient of variation better than standard deviation for comparing two datasets?+

Coefficient of variation (CV) is a relative measure (percentage), so it allows fair comparison between datasets with different units or vastly different means. For example, comparing consistency of cricket scores (runs) and ages (years) requires CV, because their units differ. SD alone does not account for scale.

How do I avoid arithmetic mistakes in grouped data variance calculations?+

Construct a full table with labeled columns: fᵢ, xᵢ, dᵢ, fᵢ dᵢ, dᵢ², fᵢ dᵢ². Fill row by row, write each product carefully, sum each column separately, and double-check sums before substituting into the variance formula. Use a calculator if allowed, and always verify that variance is non-negative.

What should I do if I forget a formula during the exam?+

At the start of the exam, write all key formulas (mean, variance, SD, CV) on the top of your rough page or answer sheet margin. If you still forget, try to derive it logically: variance is average of squared deviations, SD is √variance, CV is (SD/mean)×100. Showing logical reasoning earns partial marks.

Are case-based questions in Statistics difficult, and how should I approach them?+

Case-based questions present a real-world scenario with data embedded in a paragraph. They are not inherently harder—just read carefully, underline the data, organize it into a table or list, then solve sub-questions one by one. Each sub-question is straightforward (calculate mean, find SD, compare using CV). Practice 3-4 case studies from sample papers to build confidence.

Can I score full marks in Statistics if I am weak in arithmetic?+

Yes, if you master the method and show clear working. CBSE awards method marks generously—if your formula, table setup, and approach are correct, you earn 60-70% marks even if arithmetic is wrong. Use a calculator (if allowed), double-check sums, and write neatly. Consider using CBSETUTOR.ai to practice and catch arithmetic patterns before the exam.

How important is it to practice previous years' CBSE questions for Statistics?+

Extremely important. CBSE repeats question patterns—grouped frequency distribution with mean and variance, comparison using CV, case-based multi-part questions. Solving 2022-2024 papers shows you exactly what to expect, which methods are preferred, and how mark distribution works. Aim to solve at least 5 previous papers under timed conditions.

What are the most common mistakes in Statistics questions and how can I avoid them?+

Top mistakes: confusing inclusive/exclusive class limits, forgetting to multiply deviations by frequency (fᵢ dᵢ), not taking √ for standard deviation, omitting units, and skipping interpretation in comparison questions. Avoid these by constructing labeled tables, double-checking every step, always stating units, and writing a one-line conclusion for CV comparisons.

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