CBSE Class 10 Mathematics Chapter 13 Statistics — 20 MCQs with Answers

Before diving into calculations, you must be crystal-clear on terminology. Class mark is the midpoint of a class interval, calculated as (Lower Limit + Upper Limit)/2. Frequency is the count of observations in a class. Cumulative frequency is the running total of frequencies from the first class up to the current class. The median class is identified by locating N/2 in the cumulative frequency column, where N is the total number of observations. Understanding these definitions prevents silly mistakes in formula substitution.

The mean (arithmetic average) for grouped data is calculated using the formula: Mean = Σ(fᵢ × xᵢ) / Σfᵢ, where xᵢ is the class mark and fᵢ is the frequency. For large numbers, the assumed mean (A) method simplifies calculation: Mean = A + [Σ(fᵢ × dᵢ) / Σfᵢ], where dᵢ = xᵢ − A. The step-deviation method further scales dᵢ by dividing by class size h. Recognizing which method to apply and substituting correctly is a common MCQ trap. Always check units and whether the question asks for the final mean or an intermediate sum.

The median is the middle value when data is ordered. For grouped data, the formula is: Median = L + [(N/2 − cf) / f] × h, where L is the lower boundary of the median class, N is total frequency, cf is the cumulative frequency of the class before the median class, f is the frequency of the median class, and h is the class size. First, find N/2 and locate the median class in the cumulative frequency column. Then substitute carefully—most errors come from using the wrong cf or mixing up L with the upper limit. The 2024 CBSE Class 10 Maths board paper had a 4-mark median question; expect at least one MCQ on this formula.

The mode is the value (or class) with the highest frequency. For grouped data, the modal class is identified first. The mode formula is: Mode = L + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h, where L is the lower boundary of the modal class, f₁ is the frequency of the modal class, f₀ is the frequency of the class before, f₂ is the frequency of the class after, and h is the class size. The empirical relationship connecting mean, median, and mode is: 3 Median = Mode + 2 Mean. This relationship is useful for quick checks and appears in assertion-reason MCQs. CBSE loves testing whether you can identify the modal class and apply the formula without mixing up f₀, f₁, and f₂.

Cumulative frequency is the running total of frequencies. A 'less than' cumulative frequency table lists upper class boundaries and cumulative frequencies; a 'more than' table lists lower boundaries and frequencies greater than or equal to that boundary. An ogive is a smooth curve plotting cumulative frequency against class boundaries. The 'less than' ogive is rising; the 'more than' ogive is falling. The two ogives intersect at the median value on the x-axis. CBSE often asks you to read the median from an ogive graph or to identify which type of ogive is drawn. Knowing how to construct these tables and interpret graphs is critical for 2- or 3-mark questions, and MCQs test your conceptual clarity.

Assertion-Reason questions present two statements: an assertion (A) and a reason (R). You must decide if both are true, if both are true and R correctly explains A, if only one is true, or if both are false. These MCQs test conceptual depth—can you distinguish a correct statement from a correct explanation? Higher-order thinking questions require you to apply multiple concepts or work backwards from an answer. For example, given the mean and mode, can you find the median using the empirical relation? Or, can you deduce the modal class from a verbal description? Practise these carefully; they carry the same 1 mark as easier questions but demand more reasoning.

CBSE Class 10 Mathematics papers typically include 20 MCQs (Section A) worth 20 marks, with 1 mark each. You have roughly 60 minutes for the entire paper, so allocate no more than 20–25 minutes to MCQs—about one minute per question. Here is a proven strategy used by toppers across Delhi, Mumbai, and Bengaluru coaching centres: (1) Read the question stem completely before looking at options; underline keywords like 'not,' 'except,' 'maximum,' or 'minimum.' (2) For formula-based questions (mean, median, mode), jot down the formula in the margin, substitute values, and solve on paper—do not guess. Mental math errors cost marks. (3) In assertion-reason questions, evaluate the assertion first. If it is false, eliminate options stating A is true. Then check the reason independently. Finally, decide if R explains A. (4) Mark answers directly on the OMR sheet as you go; do not plan a second round unless you have spare time—OMR marking errors are common under pressure. (5) If stuck, skip and return; never spend more than 90 seconds on one MCQ. (6) For questions involving tables or graphs, cover the options with your hand, read the data, predict the answer, then match—it prevents option-induced confusion. (7) Negative marking does not apply in CBSE Maths MCQs as of 2025, but blind guessing wastes time better spent on 2- or 3-mark questions. Practise 20-MCQ sets weekly using NCERT Exemplar, previous year papers (2022–2024), and platforms like CBSETUTOR.ai, which offers unlimited AI-generated MCQ quizzes tailored to Chapter 13 Statistics and instant feedback on your phone. During revision, time yourself strictly—speed improves with repetition. Finally, double-check OMR bubbling in the last two minutes; a correctly solved question marked in the wrong row earns zero. Statistics MCQs are scoring if you stay calm, apply formulae accurately, and manage time ruthlessly.

Even strong students lose marks on Statistics MCQs due to avoidable errors. The most frequent mistake is using the cumulative frequency of the median class instead of the cumulative frequency before the median class in the median formula—this single slip changes the entire answer. Another trap is confusing class boundaries with class limits; for example, the class 10–20 has lower boundary 10 and upper boundary 20, but if the data uses inclusive intervals (like 10–19), adjust boundaries accordingly (9.5–19.5 for continuous data). In mode problems, students often forget to identify f₀ and f₂ correctly, especially when the modal class is the first or last class (in those cases, take f₀ or f₂ as zero). Calculation errors in the step-deviation method arise when you forget to multiply the final result by h—always write the full formula before plugging numbers. In pie-chart or ogive interpretation questions, misreading the scale on the y-axis or x-axis leads to wrong answers; use a ruler or finger to trace the grid line carefully. Finally, many students skip reading the question twice, missing keywords like 'class mark of the preceding class' or 'more than type ogive,' and choose the first plausible-looking option. Slow down on the first read, underline key terms, and verify your answer matches the question asked. Regular self-assessment with CBSETUTOR.ai's instant feedback feature highlights your specific error patterns—upload a photo of your working, and the AI tutor points out exactly where you went wrong, whether it is a formula mix-up or an arithmetic slip.

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