NCERT  ·  Mathematics  ·  Ch.12

Statistics
MCQ Series

Data · Frequency Table · Bar Graph · Histogram · Frequency Polygon

⚡ Start Quiz 📊 Analytics
50
Questions
3
Tiers
5
Topics
Concept Check (Graphs)
36
Reasoning & Interpretation
10
HOTS / Best-choice Use
4
Question Intelligence

Quiz Analytics

A data-driven breakdown of all 50 questions by difficulty, exam origin and topic distribution.

📈 Distribution Overview

50
Total Questions
Concept Check (Graphs)
36
Reasoning & Interpretation
10
HOTS / Best-choice Use
4

🗂 Topic Coverage

Bar Graph Basics & Use
28%
Histogram Features
32%
Frequency Polygon Concepts
20%
Frequency Tables & Class Marks
12%
Shape & Interpretation
8%
36
Concept Check (Graphs)
10
Reasoning & Interpretation
4
HOTS / Best-choice Use
Conceptual Framework

Key Concept Highlights

6 foundational pillars that power every question in this quiz. Understand these, and the answers follow naturally.

📊
Bar Graphs for Discrete Data
Bar graphs represent discrete categories with separate rectangular bars where the length of each bar is proportional to the frequency or value of that category.
📈
Histograms for Continuous Data
Histograms display continuous grouped data using adjacent rectangles whose bases cover class intervals on the horizontal axis and whose heights correspond to frequencies or frequency densities.
🔹
Frequency Polygons & Class Marks
A frequency polygon is formed by plotting class marks against frequencies and joining them with straight lines, often touching the horizontal axis at the midpoints of the end intervals.
📋
Frequency Tables & Grouping
A frequency table organises raw data into classes with their frequencies, making it easier to construct bar graphs, histograms and frequency polygons accurately.
📏
Class Intervals & Midpoints
Class intervals for histograms should be continuous and preferably equal in width, while their midpoints (class marks) are used as x-coordinates when plotting frequency polygons.
🔍
Reading Shape of Distributions
The overall shape of a histogram or frequency polygon—such as a tall bar on one side or almost equal bars—gives a quick visual idea of how data are spread or concentrated.
Pedagogical Value

Why MCQs Matter

Multiple-choice questions are not mere guessing games — they are the sharpest diagnostic tool available to a competitive exam aspirant.

🎯

Precision Recall

Vague understanding doesn't survive MCQs — they force exact conceptual clarity.

⚡

Exam Format Mirror

Direct simulation of CBSE Board objective sections and JEE Main Paper 1 structure.

📊

Exam Weight

~8–10%

of Class 9 Maths weightage under “Statistics” in school exams, periodic tests and final assessments.

Learning Outcomes

What You Will Learn

By completing this quiz set you will have exercised all the following competencies.

01 Distinguish between discrete and continuous data and decide when to use a bar graph, histogram or frequency polygon.
02 Construct and interpret frequency tables with class intervals, frequencies and class marks for given raw data.
03 Draw neat bar graphs and understand that bar height represents frequency while gaps between bars show separate categories.
04 Draw histograms correctly with continuous, equal-width class intervals and axes labelled with class intervals and frequencies.
05 Plot frequency polygons using class marks and join them with straight line segments, with endpoints meeting the horizontal axis.
06 Recognise features such as very tall bars, symmetric shapes or almost equal bar heights and relate them to how data are distributed.
07 Explain why a well-organised frequency table is essential before constructing histograms or frequency polygons from raw data.
Exam Preparation

Strategy & Preparation Tips

5 evidence-based strategies to maximise your score in CBSE Boards and JEE.

Step 01
Match Graph to Data Type
Train yourself to instantly decide: discrete categories ⇒ bar graph, continuous grouped data with intervals ⇒ histogram, shape comparison ⇒ frequency polygon.
Step 02
Always Prepare a Frequency Table
Before drawing any histogram or polygon, first organise raw data into a clean frequency table with continuous intervals and class marks; this avoids plotting errors.
Step 03
Remember Axis Labels & Scales
For bar graphs and histograms, keep equal bar widths, a uniform scale on the y-axis and correct labels on both axes so scale-based MCQs do not trick you.
Step 04
Use Class Marks Consistently
For every interval like 10–20 or 25–35, compute class mark once and reuse it when plotting or checking options involving frequency polygons.
Step 05
Read Shape, Not Just Numbers
When you see a finished histogram or frequency polygon, first notice where bars peak or flatten; many questions only ask for a qualitative comment on concentration or spread.

Ready to Test Your Mastery?

50 questions  ·  Elapsed timer  ·  Instant scored results

⚡ Begin Statistics Quiz
🎯 Knowledge Check

Maths — STATISTICS

50 Questions Class 9 MCQs
1
A bar graph is best used to represent which type of data?
2
Which graph uses bars that touch each other?
3
The height of a bar in a bar graph represents:
4
A frequency polygon is drawn by joining points plotted at:
5
What is a frequency table used for?
6
Which graph is most suitable for showing continuous grouped data?
7
In a histogram, the width of each rectangle corresponds to:
8
A frequency polygon can be drawn from:
9
Bar graphs are drawn on:
10
What is the horizontal axis in a histogram usually labeled with?
11
When class intervals do not have gaps, the data is:
12
The top of each bar in a bar graph represents:
13
Which of the following is NOT used in a histogram?
14
Frequency polygons are useful because they:
15
What is the midpoint of class interval 10–20?
16
A histogram requires class intervals to be:
17
The length of a bar in a bar graph is proportional to:
18
A frequency polygon is a:
19
If a histogram has very tall bars on one side, it indicates:
20
Which of the following is essential for drawing a histogram?
21
Bar graphs compare data across:
22
The point where the frequency polygon meets the x-axis is at:
23
Gaps in bar graphs represent:
24
What do adjoining bars in histogram show?
25
Frequency tables help in:
26
The y-axis of histogram represents:
27
What must be same for all bars in a histogram?
28
What do you plot for frequency polygon?
29
A histogram with equal heights for all bars represents:
30
A bar graph is also known as:
31
The main advantage of bar graph is:
32
Frequency polygons join which type of points?
33
In bar graphs, bars may be:
34
If class intervals are unequal, histogram requires:
35
Frequency polygon without histogram is drawn using:
36
A bar graph with no scale is:
37
In a histogram, rectangles represent:
38
A broken axis is used in bar graphs to:
39
For accurate histogram, intervals must be:
40
A frequency polygon always forms a:
41
The area of histogram bars is proportional to:
42
Frequency polygons are useful to represent:
43
A bar graph compares:
44
Histogram requires:
45
The line segments in a frequency polygon are joined:
46
Class mark of 25–35 is:
47
A histogram with a single very high bar suggests:
48
A bar graph’s width of bars must be:
49
Why is frequency table important before drawing histogram?
50
A frequency polygon represents frequency using:
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Frequently Asked Questions

Statistics is the branch of mathematics concerned with collecting, organizing, presenting, analyzing, and interpreting data.

Data is a collection of numerical facts or observations used for analysis.

Data collected directly by the investigator is called primary data.

Data collected from published or already available sources is secondary data.

Unorganized numerical information collected during a study is raw data.

Data arranged into classes or intervals is grouped data.

Data presented as individual observations without grouping is ungrouped data.

The number of times a particular observation occurs is its frequency.

A table showing all observations (or class intervals) along with their frequencies.

A group between two values that defines a range, such as 10–20.

The smallest and largest values in a class interval.

The difference between upper and lower class limits.

Midpoint of a class interval: \(\dfrac{\text{(lower limit} +\text{ upper limit)}}{2}\).

Class intervals where both limits are included.

Class intervals where the upper limit is excluded.

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