Statistics — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 13
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 13, "Statistics". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
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 trains you to stay accurate under time pressure, 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. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Statistics (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.
Statistics — important questions & MCQs with answers (Class 10 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Mean of 2, 4, 6, 8, 10:
A.7B.5C.6✓ CorrectD.4Answer: C. 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.
- Q2Easy
The mean of n numbers x₁, x₂, ..., xₙ is:
A.Middle valueB.(x₁·x₂·...·xₙ)^(1/n)C.(x₁ + x₂ + ... + xₙ)/n✓ CorrectD.Most frequent valueAnswer: C. (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).
- Q3Easy
The median is:
A.The largest valueB.The most frequent valueC.The averageD.The middle value when data is arranged in order✓ CorrectAnswer: D. The middle value when data is arranged in order
Explanation: Median is the middle value once data is arranged in ascending order — for odd n a single term, for even n the average of the two middle terms.
- Q4Easy
The mode of a data set is:
A.The most frequently occurring value✓ CorrectB.The average valueC.The middle valueD.The smallest valueAnswer: A. The most frequently occurring value
Explanation: Mode is the value that occurs most frequently in the data set, unlike mean (the average) or median (the middle value).
- Q5Easy
The empirical relation among mean, median, and mode is:
A.Mode = 3 Median − 2 Mean✓ CorrectB.Mode = 2 Mean − MedianC.Median = Mean + ModeD.Mean = Mode + MedianAnswer: A. Mode = 3 Median − 2 Mean
Explanation: Empirical relation: Mode = 3 Median − 2 Mean; a common slip is swapping the coefficients to get Mode = 2 Mean − Median instead.
- Q6Easy
For class interval 10−20, the class mark (mid-point) is:
A.20B.10C.15✓ CorrectD.12Answer: C. 15
Explanation: Class mark (mid-point) = (lower limit + upper limit)/2 = (10+20)/2 = 15, the representative value used in mean and mode formulas.
- Q7Medium
Empirical relation: 3 × Median = Mode + ___ × Mean.
A.2✓ CorrectB.1C.3D.0.5Answer: A. 2
Explanation: Empirical relation Mode = 3 Median − 2 Mean rearranges to 3 Median = Mode + 2 Mean, so the missing coefficient is 2.
- Q8Medium
If the mean of 6 numbers is 7 and 5 is included, new mean is:
A.7B.6.71✓ CorrectC.6.5D.6Answer: B. 6.71
Explanation: Mean formula: sum = mean×n = 7×6 = 42. Adding the new value 5 gives sum 47 over n=7, so new mean = 47/7 ≈ 6.71. Forgetting to increase n to 7 is the common mistake.
- Q9Medium
Median class of data with cumulative frequencies 5, 13, 25, 38, 50 and class intervals 0-10, 10-20, 20-30, 30-40, 40-50 is:
A.20−30✓ CorrectB.10−20C.30−40D.0−10Answer: A. 20−30
Explanation: Median class: find where cumulative frequency first reaches n/2 = 25. That happens exactly at the top of 20−30, so it's the median class.
- Q10Medium
In a frequency distribution, modal class is the class with:
A.Lowest frequencyB.Highest frequency✓ CorrectC.Middle frequencyD.Cumulative frequency equal to n/2Answer: B. Highest frequency
Explanation: Modal class is the interval with the highest frequency — it supplies l and f₁ (its own frequency), with f₀, f₂ from its neighbours, for the mode formula.
- Q11Medium
If Mode = 24 and Mean = 18, then Median is:
A.18B.22C.20✓ CorrectD.24Answer: C. 20
Explanation: Rearranging Mode = 3 Median − 2 Mean gives Median = (Mode + 2 Mean)/3 = (24 + 36)/3 = 20 — solve for Median, don't average Mode and Mean directly.
- Q12Hard
In assumed-mean method, mean = a + (Σf·d / Σf) where d is:
A.x − a (deviation from assumed mean)✓ CorrectB.x + aC.x²D.f·xAnswer: A. x − a (deviation from assumed mean)
Explanation: In the assumed-mean method, dᵢ = xᵢ − a is each observation's deviation from the assumed mean a.
- Q13Hard
If the mean of x, x + 3, x + 5, x + 7, x + 10 is 9, then x is:
A.2B.5C.4✓ CorrectD.6Answer: C. 4
Explanation: Mean = Σx/n = (5x+25)/5 = x+5; setting x+5 = 9 gives x = 4, since these five terms form an AP centred on the middle term x+5.
- Q14Hard
Median of data: 4, 4, 5, 7, 6, 7, 7, 12, 3 (after sorting) is:
A.7B.6✓ CorrectC.5D.4Answer: B. 6
Explanation: Sort first: 3,4,4,5,6,7,7,7,12 (n=9, odd); median is the (9+1)/2 = 5th term = 6, not a value picked from the unsorted order.
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Start this chapter free →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.
What does Class 10 Mathematics Chapter 13 (Statistics) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Statistics": 30 Easy, 30 Medium and 30 Hard. Together they make 9 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 on a launch offer until 1 December 2026. 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 9 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. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" 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. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
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.