Median N/2 Mean / Mode / Median Mode=3Median−2Mean
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Chapter 13  ·  Class X Mathematics  ·  MCQ Practice

MCQ Practice Arena

Statistics

Mean, Median, Mode — Three Formulae, Predictable Patterns, Full Marks

📋 50 MCQs ⭐ 30 PYQs ⏱ 65 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
22Medium
8Hard
30PYQs
65 secAvg Time/Q
7Topics
Easy 40% Medium 44% Hard 16%

Why Practise These MCQs?

CBSE Class XNTSEState Boards

Statistics MCQs follow extremely predictable patterns — CBSE has asked almost the same question types for 10+ consecutive years. Mean by direct, assumed mean, and step deviation methods each appear as 3-mark questions. Mode and Median from grouped data each yield 3 marks. Ogive-based MCQs test graphical interpretation. This is a chapter where MCQ drill converts directly to Board marks.

Topic-wise MCQ Breakdown

Mean — Direct Method8 Q
Mean — Assumed Mean Method8 Q
Mean — Step Deviation Method7 Q
Mode of Grouped Data9 Q
Median of Grouped Data9 Q
Cumulative Frequency & Ogive5 Q
Empirical Relation (Mean, Median, Mode)4 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\bar{x} = \sum f_ix_i / \sum f_i\ (\text{Direct})$
$\bar{x} = a + \sum f_id_i / \sum f_i\ (\text{Assumed Mean})$
$\bar{x} = a + h\cdot\sum f_iu_i / \sum f_i\ (\text{Step Dev.})$
$\text{Mode} = l + \dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h$
$\text{Median} = l + \dfrac{N/2-cf}{f}\times h$
$\text{Mode} = 3\,\text{Median} - 2\,\text{Mean}$

MCQ Solving Strategy

For mean MCQs, build the frequency table carefully — label columns fᵢ, xᵢ, fᵢxᵢ (direct) or fᵢ, dᵢ, fᵢdᵢ (assumed mean). For mode, identify the MODAL CLASS (highest frequency), then substitute into the formula — never just read the highest value. For median, find N/2 first, then locate the median class where cumulative frequency first exceeds N/2. The empirical relation (Mode = 3 Median − 2 Mean) is a quick 1-mark formula substitute.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Direct method mean, identify modal class, basic cumulative frequency

② Medium

Assumed mean and step deviation, mode and median full calculation

③ Hard

Combined mean+median+mode from one table, ogive-based median

★ PYQ

CBSE — all three methods + ogive; NTSE — data interpretation

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Probability
🎯 Knowledge Check

Maths — STATISTICS

50 Questions Class 10 MCQs
1
What is the main purpose of Statistics?
2
Which of the following is an example of raw data?
3
What is grouped data?
4
What is the class mark of the class interval \(20-30\)?
5
What does frequency represent?
6
Which measure represents the average value of data?
7
The formula for mean by direct method is:
8
Which method of finding mean is best when class intervals are equal?
9
What is assumed mean?
10
Median is the value which:
11
The median class is the class:
12
The formula for median of grouped data is:
13
In the median formula, \(cf\) represents:
14
What is mode?
15
The modal class is the class:
16
The formula for mode of grouped data is:
17
In the mode formula, \(f_1\) denotes:
18
What is cumulative frequency?
19
An ogive is a graph of:
20
A less-than ogive is drawn using:
21
A more-than ogive uses:
22
Median can be found graphically by:
23
Which measure is most affected by extreme values?
24
Which measure is suitable for skewed data?
25
Which measure helps identify the most common item?
26
What is class width?
27
Total frequency is denoted by:
28
Statistics helps mainly in:
29
Which chapter concept helps compare two distributions?
30
What should be calculated first while finding median?
31
Which representation is most suitable for cumulative data?
32
Which of the following is not a measure of central tendency?
33
In step deviation method, \(u_i\) represents:
34
Statistics is useful in which field?
35
Which graph shows frequency distribution?
36
The lower limit of median class is denoted by:
37
Which quantity represents class interval size?
38
Which value divides cumulative frequency into two equal parts?
39
Which method of mean is shortest?
40
Statistics mainly deals with:
41
In board exams, clarity of steps is important because:
42
Which value is always present in a data set?
43
What happens if frequencies are incorrect?
44
Statistics encourages which type of thinking?
45
Which measure is easiest to calculate?
46
The intersection point of ogives gives:
47
Which term describes most repeated observation?
48
Which chapter skill is most scoring?
49
Which value summarises the entire data?
50
The key objective of Statistics is to:
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Can You Solve These 50 MCQs? Class 10 Statistics Challenge
Can You Solve These 50 MCQs? Class 10 Statistics Challenge — Complete Notes & Solutions · academia-aeternum.com
Multiple Choice Questions in Statistics are designed to test not only a student’s ability to recall formulas, but also their understanding of data interpretation, logical reasoning, and correct method selection. This MCQ set for NCERT Class X Mathematics Chapter “Statistics” systematically covers every essential concept prescribed in the syllabus, including grouped data, measures of central tendency, cumulative frequency, and graphical analysis through ogives. These questions are carefully…
🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    STATISTICS-Exercise 13.1 STATISTICS-Exercise 13.2 STATISTICS-Exercise 13.3
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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    Can You Solve These 50 MCQs? Class 10 Statistics Challenge
    Can You Solve These 50 MCQs? Class 10 Statistics Challenge — Complete Notes & Solutions · academia-aeternum.com
    Multiple Choice Questions in Statistics are designed to test not only a student’s ability to recall formulas, but also their understanding of data interpretation, logical reasoning, and correct method selection. This MCQ set for NCERT Class X Mathematics Chapter “Statistics” systematically covers every essential concept prescribed in the syllabus, including grouped data, measures of central tendency, cumulative frequency, and graphical analysis through ogives. These questions are carefully…
    🎓 Class 10 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
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    Telegram
    X / Twitter
    Facebook
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    Threads
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    LinkedIn
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    Email
    academia-aeternum.com/class-10/mathematics/statistics/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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