a lim f(x)=L x→a L sinx/x → 1
σ
Chapter 13  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Statistics

Visualize Data — Analyze Variation — Score with Precision

📋 50 MCQs ⭐ 22 PYQs ⏱ 60–75 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
20Medium
10Hard
22PYQs
60–75 secAvg Time/Q
6Topics
Easy 40% Medium 40% Hard 20%

Why Practise These MCQs?

JEE MainCBSENEETBITSAT

Statistics MCQs in JEE Main and CBSE are largely concept-based involving graphs (histogram, bar graph, frequency polygon) and formulas like mean, variance, and deviation. Questions often test interpretation rather than calculation. Graph-based questions are highly scoring and predictable.

Topic-wise MCQ Breakdown

Bar Graphs8 Q
Histograms10 Q
Frequency Polygon8 Q
Frequency Distribution8 Q
Measures of Dispersion10 Q
Mean/Variance/SD6 Q

Must-Know Formulae Before You Start

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

$\mathrm{Mean = Σfᵢxᵢ / Σfᵢ}$
$\mathrm{Variance σ² = Σ(x−x̄)² / }N$
$\mathrm{σ² = (Σfᵢxᵢ² / N) − (x̄)}²$
$\mathrm{Standard Deviation σ = √σ²}$
$\mathrm{Class Mark = (Upper + Lower)/2}$
$\mathrm{Mean Deviation = (1/N) Σ|x−A|}$

MCQ Solving Strategy

Focus heavily on graphs: histogram vs bar graph vs polygon. Most MCQs are conceptual. Practice identifying graph types quickly. Use shortcut variance formula for speed. Revise class mark and frequency table basics. Solve at least 50 MCQs for pattern recognition.

⚠ Common Traps & Errors

Difficulty Ladder

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

① Easy

Identify graph type, basic definitions, class mark

② Medium

Interpret histogram/polygon, frequency relations

③ Hard

Mixed graph + dispersion concept MCQs

★ PYQ

JEE Main — identify graph/data type; CBSE — interpret diagrams

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Probability MCQs
🎯 Knowledge Check

Maths — STATISTICS

50 Questions Class 11 MCQs
1
The arithmetic mean of \(2,4,6\) is
(Basic)
2
If each observation of a data set is increased by 5, the mean will
(Basic)
3
The mean of first 10 natural numbers is
(Basic)
4
The class mark of class interval \(10–20\) is
(Basic)
5
The mean of \(3,3,3,3\) is
(Basic)
6
Median of \(1,3,5,7,9\) is
(Basic)
7
Mode of \(2,4,4,6,8\) is
(Basic)
8
Mean deviation is always
(Basic)
9
For ungrouped data, variance is
(Basic)
10
Standard deviation is
(Basic)
11
If variance is \(16\), standard deviation equals
(Moderate)
12
If all observations are multiplied by 3, variance becomes
(Moderate)
13
Combined mean formula is
(Moderate)
14
Median class is the class containing
(Moderate)
15
The modal class is the class with
(Moderate)
16
Mean deviation about mean is minimum for
(Moderate)
17
Range of data \(5,10,15\) is
(Moderate)
18
If mean is \(20\) and deviations sum to zero, then
(Moderate)
19
Step deviation method simplifies calculation by using
(Moderate)
20
For grouped data, mean is calculated using
(Moderate)
21
If standard deviation is zero, data are
(Moderate)
22
Coefficient of variation \(=\)
(Moderate)
23
Smaller C.V. indicates
(Moderate)
24
Mean of \(x,x,x\) is
(Moderate)
25
Variance has unit
(Moderate)
26
If mean is \(10\) and variance \(4\), standard deviation is
(Hard)
27
The median of even number of observations is
(Hard)
28
If every observation is divided by 2, standard deviation becomes
(Hard)
29
Mean deviation is based on
(Hard)
30
Dispersion measures
(Hard)
31
The most stable series has
(Hard)
32
If variance is \(25\), coefficient of variation for mean \(20\) is
(Hard)
33
The sum of deviations from mean is always
(Hard)
34
Which is least affected by extreme values?
(Hard)
35
Mean deviation about median is minimum because
(Hard)
36
If \(x\) is replaced by \(x+3\), variance
(Hard)
37
Standard deviation of \(a,a,a\) is
(Hard)
38
Combined mean depends on
(Hard)
39
Median for grouped data uses
(Hard)
40
Mode formula uses
(Hard)
41
If data is symmetric, mean = median = mode
(Very Hard)
42
Standard deviation is a measure of
(Very Hard)
43
Mean deviation is less than standard deviation because
(Very Hard)
44
If CV of A < CV of B, then
(Very Hard)
45
Variance of first \(n\) natural numbers increases as
(Very Hard)
46
Mean of deviations from any point is zero only when point is
(Very Hard)
47
Mean deviation about mean is
(Very Hard)
48
Which is most sensitive to extreme values?
(Very Hard)
49
Dispersion is zero when
(Very Hard)
50
Statistics mainly deals with
(Very Hard)
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Frequently Asked Questions

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting numerical data.

Raw data is ungrouped data collected directly from observations without classification.

Frequency is the number of times a particular observation occurs.

Data arranged in class intervals with corresponding frequencies is called grouped data.

A class interval is the range between lower and upper class limits.

Class mark is the midpoint of a class: \(x=\frac{l+u}{2}\).

\(\bar{x}=\frac{\sum f_ix_i}{\sum f_i}\).

A shortcut method using an assumed mean \(a\): \(\bar{x}=a+\frac{\sum f_id_i}{\sum f_i}\).

A refined method using \(u_i=\frac{x_i-a}{h}\): \(\bar{x}=a+h\frac{\sum f_iu_i}{\sum f_i}\).

\(h\) is the common class width.

Mean is the arithmetic average of observations.

Median \(=l+\frac{\left(\frac{N}{2}-cf\right)}{f}\times h\).

\(l\) is the lower boundary of the median class.

It is the running total of frequencies.

Median is the middle value when data is arranged in order.

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