CBSE Class 10 Mathematics Chapter 13 Statistics Worksheet with Answers

Before you dive into the questions, refresh the essentials. Statistics in Class 10 builds on your Class 9 foundation but zooms into grouped data — data organized into class intervals like 0–10, 10–20, and so on. You will calculate the mean using the direct, assumed-mean, or step-deviation method; find the median by locating the middle class and applying the formula; determine the mode by identifying the class with the highest frequency. Cumulative frequency (the running total of frequencies) leads you to construct ogives — smooth curves that help you read off medians and quartiles graphically. Bar graphs, histograms, and frequency polygons turn raw numbers into visual stories. The CBSE board loves to test formula recall, stepwise calculation, and interpretation of graphs, so keep your formula sheet handy and practice converting word problems into frequency tables. Remember: class mark equals (lower limit plus upper limit) divided by two, and cumulative frequency is cumulative frequency of the previous class plus frequency of the current class. With these tools, every question in this worksheet becomes manageable.

This worksheet is pitched at medium difficulty — it mirrors the standard CBSE Class 10 board paper in structure and rigor. Section A and Section B are straightforward, testing definitions and direct formula application. Section C checks your conceptual clarity through matching or true-false. Section D steps up with three-mark short-answer questions requiring two to three calculation steps and proper mathematical notation. Section E contains five-mark HOTS (Higher Order Thinking Skills) problems that may ask you to construct an ogive from scratch, compare mean-median-mode for the same dataset, or solve a two-part grouped-data question. The case-study integrates Statistics with a real-world scenario — sports, health surveys, or market data. Allocate roughly ninety minutes: fifteen minutes for Sections A through C combined, thirty minutes for Section D, and forty minutes for Section E plus the case study, leaving five minutes to review. Work in a quiet space, keep your calculator, ruler, and graph paper ready, and resist the urge to peek at answers until you have attempted every question. Treat this as your board-exam dress rehearsal.

This section tests quick recall and conceptual understanding. Each MCQ has four options; choose the single best answer. No negative marking, so never leave a question blank — educated guessing is part of exam strategy. Read each question twice, underline keywords like 'cumulative frequency,' 'modal class,' or 'ogive,' and eliminate obviously wrong options first. Watch out for traps: sometimes two options look similar but differ in a formula sign or boundary condition. If a question asks for the median class, remember it is the class where cumulative frequency first crosses n/2, not necessarily the class with the highest frequency. If the question shows a histogram, check bar heights carefully — they represent frequency, not class marks. These six MCQs cover mean, median, mode, cumulative frequency, and graphical interpretation, giving you a quick six marks if you have revised your formulae. Time limit for Section A: about six minutes, one minute per question. Mark your answers clearly — A, B, C, or D — and move on without second-guessing unless you spot an obvious mistake during final review.

Fill-in-the-blank questions demand precise terminology and formula components. Write your answers neatly in the space provided; spelling matters because CBSE examiners look for exact terms like 'cumulative frequency' or 'step-deviation method,' not casual phrases like 'running total' or 'shortcut way.' Read the sentence fully before filling in — sometimes the grammar or article ('a,' 'an,' 'the') gives you a clue about the expected word. If a blank asks for a numerical value, double-check your mental math or jot workings in the margin. These five blanks test your grasp of definitions, formula structure, and the relationship between mean, median, and mode. For instance, you should know that for a symmetric distribution, mean equals median equals mode, but for a positively skewed distribution, mode is less than median is less than mean. Time allocation: about five minutes total. If you are stuck, leave it blank and return after finishing Section C; sometimes later questions trigger your memory. Remember, every mark counts, and fill-in-the-blanks are often easier than MCQs because you don't have to choose between similar-looking options.

This section checks whether you can pair concepts correctly or identify the truth value of statements. For matching, draw clear lines or write pairs like A–3, B–1, etc., in the answer space. Read all items in both columns before you start matching; sometimes the last option in Column B clarifies an earlier ambiguous match. For true/false, write 'True' or 'False' in full — avoid T/F abbreviations that might be misread. If a statement says 'The mode is always greater than the mean,' recall that this is only true for negatively skewed distributions, so mark it False. If it says 'A histogram is used for continuous data,' that is True. These questions are quick wins if you have learned definitions properly. Budget four minutes for this section. Because each is worth one mark, do not overthink; trust your first instinct unless you spot an obvious error. Section C often includes a statement about ogives, class intervals, or the relationship between mean and median — core NCERT concepts that appear verbatim in your textbook. Revising the 'Important Definitions' section from your notes the night before the exam pays off handsomely here.

Section D is the backbone of your score. Each question carries three marks and expects you to show clear working: write the formula, substitute values, perform arithmetic step-by-step, and box or underline the final answer. Marks are awarded for method even if your final answer is wrong due to a calculation slip, so never skip steps. A typical three-mark question might ask: 'Find the mean of the following frequency distribution using the step-deviation method,' or 'Calculate the median from the given grouped data,' or 'Construct a cumulative frequency table and identify the median class.' Start by reading the question carefully and noting what is given and what is required. Write 'Given' and 'To find' if it helps you organize your thoughts. Use a ruler to draw neat tables; examiners appreciate tidy presentation. If the question provides a frequency table, rewrite it in your answer sheet rather than referring back, because that forces you to engage with the data and spot patterns. Allocate roughly six minutes per question — thirty minutes total for five questions. If you get stuck on one, move to the next and return later; sometimes a fresh look solves it. These questions directly mirror NCERT exercise problems, so practicing those is the best preparation.

Section E separates the average student from the high-scorer. Each question is worth five marks and demands multi-step reasoning, accurate graph construction, or comparison across measures of central tendency. A typical long-answer question might say: 'Draw a 'less than' ogive and a 'more than' ogive on the same graph for the given data, and use them to estimate the median,' or 'The mean of a distribution is 53 and the mode is 50; using the empirical relationship, find the median,' or 'Compare the suitability of mean, median, and mode for the given dataset and justify your choice.' For graph-based questions, use graph paper, label axes with units, plot points carefully with a sharp pencil, and draw smooth curves with a steady hand. For formula-heavy questions, write every intermediate step: state the formula, show substitution, simplify algebraically, compute numerically, and state the final answer in a sentence. If the question has two parts — part (a) and part (b) — allocate marks and time proportionally; a five-mark question typically means part (a) is two or three marks and part (b) is the rest. These three questions will take you about thirty-five to forty minutes; do not rush. Quality over speed — one perfectly solved long answer is better than three half-done attempts. HOTS questions test whether you can apply formulas in unfamiliar contexts, so read the scenario carefully and identify which statistical tool fits.

The case-study question is a recent CBSE innovation, introduced to test your ability to extract and analyze statistical information from a real-world paragraph or table. You will read a short scenario — for example, a survey on smartphone usage among teenagers, rainfall data across five cities, or sales figures for a product over six months — and answer three or four sub-questions based on that data. Sub-questions typically include one MCQ (one mark), one or two short calculations (one or two marks each), and one interpretation or reasoning question (one mark). Read the passage slowly and underline numbers, keywords, and any given frequency table. Convert the narrative into a structured frequency distribution if it is not already presented as a table. Then tackle each sub-question in order; they are usually sequential, with part (a) helping you answer part (b). Because the case study is contextual, it feels less abstract than a pure formula question — think of it as a mini real-life statistics project. Allocate ten to twelve minutes. Write clearly, show any necessary working for calculations, and use proper units (₹, kg, km, etc.) in your final answers. This question is scoring-friendly if you stay calm and organized; even if you are unsure about one sub-question, attempt the others to grab partial marks.

Below is the answer key for every question in this worksheet, complete with brief explanations and key steps. Use this section to self-assess after you have attempted all questions. Award yourself one mark per correct MCQ or fill-in-the-blank, three marks for each correctly worked short answer (deduct one mark for missing steps or wrong final answer), and five marks for long answers (allocate partial marks if method is correct but arithmetic slips occur). If your total is above seventy-two out of ninety (eighty percent), you are board-ready for Chapter 13. If you score sixty to seventy-two, revisit the questions you got wrong and practice similar NCERT problems. Below sixty means you need to go back to the theory, rewrite formulae, and solve at least ten more problems before attempting another worksheet. Remember, mistakes are learning gold — analyze each error, understand why your approach failed, and note the correct method in your revision notebook. Statistics is a chapter where practice truly makes perfect; every solved question strengthens your pattern-recognition and calculation speed. Keep this answer key handy during revision week, and use it to double-check your own solutions rather than passively reading through.

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