Statistics — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 13
108 practice questions · 31 Easy · 39 Medium · 38 Hard · Updated
Jump to the 6 solved questions
Practise the most important Class 10 CBSE Mathematics questions from Chapter 13, "Statistics". You get 11 timed quizzes made from 108 NCERT-based MCQs, with answers and explanations. The questions are split into 31 Easy, 39 Medium and 38 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
To score well in "Statistics", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Statistics, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.
Statistics — important questions & MCQs with answers (Class 10 Mathematics)
6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.
0 of 6 answered
- Q1 of 6Easy
Mean of 2, 4, 6, 8, 10:
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Answer: 6
Explanation: Mean = Σx ÷ n = (2+4+6+8+10)/5 = 30/5 = 6; a common mistake is dividing by the wrong count of terms.
- Q2 of 6Easy
The mean of n numbers x₁, x₂, ..., xₙ is:
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Answer: (x₁ + x₂ + ... + xₙ)/n
Explanation: Arithmetic mean = (x₁+x₂+...+xₙ)/n, sum of all values divided by their count — distinct from the middle value (median) or most frequent value (mode).
- Q3 of 6Medium
Median class of data with cumulative frequencies 5, 13, 28, 38, 50 and class intervals 0-10, 10-20, 20-30, 30-40, 40-50 is:
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Answer: 20−30
Explanation: Median class: n = 50, so n/2 = 25; the first cumulative frequency greater than 25 is 28, for the class 20−30, so that is the median class.
- Q4 of 6Medium
Assertion (A): When the data has extreme values, as for the average wage in a country, the median is a better measure of central tendency than the mean. Reason (R): Extreme values in the data do not affect the mean.
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Answer: A is true but R is false
Explanation: A is true: the chapter prefers the median when extreme values are present. R is false: extreme values do affect the mean, which is exactly why the median is preferred.
- Q5 of 6Hard
An ogive is the graph of:
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Answer: Cumulative frequency vs class boundaries
Explanation: An ogive plots cumulative frequency against class boundaries; it's the standard tool for reading off the median graphically.
- Q6 of 6Hard
Assertion (A): If the mode of a set of data is 24 and its mean is 60, then by the empirical relationship its median is 48. Reason (R): 3 Median = Mode + 2 Mean.
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Answer: Both A and R are true and R is the correct explanation of A
Explanation: Both are true. Using R, 3 × Median = 24 + 2 × 60 = 144, so the median is 48. R is the relation that gives A, so it explains A.
Statistics notes: key concepts (Class 10 Mathematics)
Grouped data is summarised by its mean, median and mode, each answering a different question about the centre. This chapter computes all three from frequency tables — including the assumed-mean and step-deviation shortcuts — and draws the ogive that locates the median graphically.
- Grouped frequency distribution
- Data organised into class intervals with their frequencies, used when individual values are too numerous to list.
- Class mark
- The midpoint of a class interval, (lower limit + upper limit)/2, which represents the whole class in mean calculations.
- Mean by direct method
- The sum of each class mark times its frequency, divided by the total frequency.
- Assumed mean method
- Choosing a convenient value a and working with deviations d = x − a, which keeps the arithmetic small.
- Step-deviation method
- Dividing the deviations by the class width h to give u = (x − a)/h, the quickest route when classes are equally wide.
- Median of grouped data
- The value splitting the distribution into two equal halves, found from the class containing the n/2-th observation.
- Median class
- The class in which the cumulative frequency first reaches or exceeds n/2 — identifying it correctly is the crux of the calculation.
- Cumulative frequency
- A running total of frequencies, needed for both the median calculation and the ogive.
- Mode of grouped data
- The most frequently occurring value, computed from the modal class and its neighbouring frequencies.
- Modal class
- The class interval with the highest frequency, from which the modal formula is applied.
- Empirical relationship
- 3 Median = Mode + 2 Mean, which lets any one of the three be estimated when the other two are known.
- Ogive (cumulative frequency curve)
- A graph of cumulative frequency against class boundaries; the less-than and more-than ogives cross at the median.
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Statistics — FAQs
What are the key concepts in Class 10 Mathematics Statistics?+
Grouped data is summarised by its mean, median and mode, each answering a different question about the centre. This chapter computes all three from frequency tables — including the assumed-mean and step-deviation shortcuts — and draws the ogive that locates the median graphically. Key ideas include Grouped frequency distribution, Class mark, Mean by direct method, Assumed mean method, Step-deviation method, Median of grouped data.
What does Class 10 Mathematics Chapter 13 (Statistics) cover on XamBaaz?+
It has 108 NCERT-based MCQs on "Statistics": 31 Easy, 39 Medium and 38 Hard. Together they make 11 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Statistics" questions free to practise?+
Yes. Sign in with Google to practise "Statistics" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 10 till 31 March; on 1 April your account moves up to Class 11 and the rest of your year carries over. No chapter is charged separately.
How should I revise "Statistics" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 11 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Statistics" MCQs available with answers?+
Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Statistics" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Statistics (Class 10 Mathematics)?+
The questions that matter most test Grouped frequency distribution, Class mark, Mean by direct method, Assumed mean method, Step-deviation method, Median of grouped data. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 108 questions on the chapter as timed quizzes.
Is there an online quiz for Statistics?+
Yes — Class 10 Mathematics Statistics has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.
Are there question answers and extra questions for Statistics (Class 10 Mathematics)?+
Yes. This page has 6 solved questions on Statistics, each with the correct answer and a short explanation. Sign in to practise all 108 questions on the chapter as timed quizzes.
Are there assertion–reason and case study questions for Statistics (Class 10 Mathematics)?+
Yes. The Statistics question bank has 6 assertion–reason questions and 12 case-based (case study) questions in the CBSE board format, alongside the regular MCQs. Each comes with the answer and a worked explanation. Sign in to practise them in timed quizzes.