Important Questions: CBSE Class 10 Mathematics Chapter 13 Statistics

Chapter 13 Statistics is part of Unit V (Statistics and Probability) in the CBSE Class 10 Mathematics syllabus. This unit carries 11 marks in the 80-mark theory paper. Statistics alone contributes approximately 10–12 marks, depending on the year. The 2025 sample paper and previous years (2023, 2024) show a consistent pattern: one or two 1-mark objective questions (MCQ or assertion-reason), one 2-mark question on formula-based computation (mean or mode), one 3-mark question involving calculation and reasoning (median, empirical formula, or graph interpretation), and one 5-mark question or case-based integrated problem requiring construction of frequency tables, calculation of all three measures of central tendency, or drawing and interpreting an ogive. The chapter builds on Class 9 Statistics (basic data presentation) and introduces grouped data formulae, making it both conceptual and computation-intensive. Topics tested include mean (direct, assumed-mean, step-deviation methods), median, mode, cumulative frequency distribution, and ogive construction. Understanding the weightage helps you allocate revision time: spend extra hours on 5-mark questions and case studies, as they fetch maximum marks and test multiple concepts together.

One-mark questions test quick recall of formulae, definitions, and basic computations. CBSE typically includes 1–2 MCQs or assertion-reason items from Statistics in Section A of the paper. These questions are designed to be solved in under a minute and require no lengthy working—just formula substitution or direct reading from a given table or graph. Common MCQ themes include identifying the correct formula for mean or median, recognizing the class with maximum frequency (modal class), reading cumulative frequency values, or applying the empirical relationship between mean, median, and mode. VSA questions may ask for the class mark of a given interval, the cumulative frequency up to a certain class, or the angle in a pie chart. Accuracy is crucial: even a small error in reading or calculation costs the full mark. Practice at least 10–12 MCQs to build speed and confidence.

Two-mark questions require one or two steps of calculation or a brief explanation. CBSE frames these to test formula application without demanding full derivation. Typical 2-mark questions include: finding the mean of a small ungrouped dataset, computing the class mark or class size for given intervals, determining the modal class and stating its frequency, or calculating cumulative frequency for a specific class. You may also be asked to find one missing frequency if the mean is given, or to convert a frequency distribution into a cumulative frequency table. Always show method clearly: write the formula, substitute values, and box the final answer. Even if the answer is obvious, examiners award marks for systematic working. Aim to complete each 2-mark question in 2–3 minutes during the exam.

Three-mark questions demand multi-step solutions, usually involving grouped data. CBSE expects you to apply the standard formulae for mean (assumed-mean or step-deviation method), median, or mode, show all substitutions, and interpret the result. Common 3-mark questions include: calculating the mean of a given frequency distribution using assumed-mean method; finding the median class, then computing median using the formula; determining mode using the mode formula; or verifying the empirical relationship Mode ≈ 3 Median − 2 Mean with given data. You may also be asked to find a missing frequency when mean or median is specified, which involves forming and solving a linear equation. Clear step-wise working is essential: define variables (l, h, f, cf), substitute into formula, simplify, and state the final answer with units. Allocate 4–5 minutes per 3-mark question and double-check arithmetic.

Five-mark questions are the foundation of Statistics scoring. They integrate multiple concepts: constructing or completing a frequency table, calculating mean (often by step-deviation to save time), finding median and mode, verifying empirical relationship, and sometimes drawing a cumulative frequency curve (ogive) to locate median graphically. A typical 5-mark question presents a grouped frequency distribution (or raw data to be grouped), asks you to compute all three measures of central tendency, and may require you to plot a 'less than' or 'more than' ogive on graph paper and mark the median point. CBSE values neat graphs: use a sharp pencil, label axes with variable and scale, plot points accurately, and draw a smooth curve. The written part should show: class intervals and frequencies clearly, cumulative frequency column, formula statement, substitution with all terms defined, arithmetic neatly laid out, and final answers underlined. Practicing 5-mark questions under timed conditions (allocate 8–10 minutes) builds exam stamina and ensures you do not lose marks for incomplete steps.

Since 2021, CBSE has introduced competency-based case studies in the Class 10 Mathematics paper. A Statistics case-based question presents a real-life scenario—daily COVID cases, rainfall data, sales figures, survey results—accompanied by a frequency table or raw data. Candidates answer 4–5 sub-questions (MCQ or short-answer), each worth 1 mark, totaling 4–5 marks per case. These questions test comprehension, data interpretation, and application of statistical formulae in context. You might be asked to identify the modal class, compute mean or median, read cumulative frequency, interpret an ogive, or draw a simple graph. The key is careful reading: underline the question requirement, refer back to the data table, and apply the correct formula. Case-based questions are scoring if you manage time well—allocate 6–7 minutes for the entire case. They also mirror real-world statistical thinking, making them valuable beyond exam scores.

Understanding CBSE question-setting patterns helps you anticipate what to expect and how to prepare. The board follows a competency-based framework: questions test conceptual understanding, procedural fluency, and application. For Statistics, this means questions are rarely rote; they require you to choose the correct formula, interpret data context, and justify steps. CBSE often embeds small twists: giving an incomplete frequency table and asking you to find the missing frequency using a given mean; providing both 'less than' and 'more than' ogives and asking you to find the median by intersection; or presenting a word problem where you must first organize raw data into a grouped table before calculating mean, median, or mode. Another common pattern is multi-part questions: part (a) asks for mean, part (b) for median, part (c) for mode, and part (d) to verify the empirical relationship—this tests whether you can apply all formulae correctly in sequence. The board also favors real-life contexts (health data, sports statistics, economic indicators) to assess application skills. Graphical questions (drawing histogram, frequency polygon, ogive) test neatness and accuracy, often carrying 1–2 marks just for correct plotting. Knowing these patterns, you can practice strategically: focus on formula derivations, multi-step problems, and graph work.

Even well-prepared students lose marks in Statistics due to recurring errors. The most frequent mistake is incorrect identification of the median class: students forget that the median class is where the cumulative frequency first equals or exceeds N/2, not merely the class with the highest frequency. Another common slip is using the wrong cf (cumulative frequency of the class before the median class) in the median formula—always double-check your cumulative frequency column. In mean calculation by assumed-mean or step-deviation method, sign errors in dᵢ or uᵢ are frequent; for instance, if xᵢ < A, then dᵢ is negative—students sometimes drop the minus sign, leading to a wrong mean. Class mark confusion also occurs: some students add the frequencies instead of the class limits when computing the class mark. In mode formula, students mix up f₁ (frequency of modal class), f₀ (frequency of class before modal class), and f₂ (frequency of class after modal class). Graphical mistakes include plotting cumulative frequency against class marks instead of upper limits in a 'less than' ogive, or forgetting to join points with a smooth curve. Units are often omitted in final answers—always state units (marks, cm, kg, ₹) as given in the question. Finally, time management errors: spending too long on a 5-mark question and rushing the rest. Practice under timed conditions to avoid this. Maintain a checklist: formula stated, all terms defined, substitution shown, arithmetic verified, answer boxed with units.

To master Chapter 13 Statistics, adopt a layered practice approach. Start with NCERT: solve all examples and exercises in Chapter 14 (NCERT Class 10 Maths Chapter 14 is Statistics). Understand the derivation of mean, median, and mode formulae—CBSE may ask you to recall or apply them with small variations. Next, memorize the three standard methods for mean (direct, assumed-mean, step-deviation) and know when to use each—step-deviation is fastest for large class intervals. Practice at least 5–6 median and mode problems until you can identify the correct class and apply the formula without hesitation. For ogives, draw 3–4 graphs on your own graph paper; measure accuracy by checking if your plotted median matches the formula-calculated median. Solve previous years' board papers (2020–2024) and CBSE sample papers; Statistics questions repeat patterns, so you will recognize familiar structures. Time yourself: 1 minute for MCQ, 2–3 minutes for 2-mark, 4–5 minutes for 3-mark, 8–10 minutes for 5-mark. Review common mistakes (listed above) before each mock test. Use CBSETUTOR.ai for instant doubt-clearing: snap a photo of any tricky frequency table or ogive question, and the AI tutor will walk you through the solution step-by-step, available 24×7 at a flat ₹999/month for all subjects and classes (6–12), with a 3-day free trial. Finally, maintain a formula sheet: write all formulae (mean, median, mode, empirical relation, class mark) on one page and revise it daily in the week before the exam. Statistics is scoring if you are systematic—organize your work, double-check arithmetic, and always write units.

Statistics can feel overwhelming when you are stuck on a cumulative frequency table at 10 p.m. and no teacher is available. CBSETUTOR.ai solves this. It is an AI-powered tutor that lets you snap a photo of any Class 10 Mathematics problem—whether a tricky ogive, a missing-frequency mean question, or a case-based data set—and receive a step-by-step solution instantly. The AI recognizes handwriting, printed text, and even graphs, so you can upload your own working and ask 'Where did I go wrong in this median calculation?' The platform covers all CBSE subjects and classes (6–12) at a single flat price of ₹999 per month, far cheaper than traditional tuition. You get unlimited question uploads, explanations aligned with NCERT terminology and CBSE marking schemes, and the freedom to learn at your own pace, any time of day. A 3-day free trial lets you test the service risk-free. For Statistics, CBSETUTOR.ai is especially valuable: it can verify your cumulative frequency column, check your formula substitutions, and even suggest faster methods (like step-deviation) if you have used a longer approach. Thousands of CBSE students across India use it to boost confidence and scores. If you are serious about mastering Chapter 13 and securing full marks in Statistics, give CBSETUTOR.ai a try—your personal AI tutor is just one photo away.