Class 9 Mathematics Exercise 11.1 – Basic Statistics (Q1 to Q4)

Exercise 11.1 from Chapter 11 (Basic Statistics) introduces students to the foundational concepts of data handling. This exercise is important because it builds the base for all advanced statistical topics in Class 9 and beyond. Students often struggle not because the concepts are difficult, but because they do not follow a clear step-by-step method. In this article, you will learn each concept in a structured and exam-focused way.

Class 9 Mathematics Basic Statistics Exercise 11.1 Q1 to Q4 showing statistical data and worked solutions for exam preparation

Understanding Basic Statistical Terms

Before solving the questions, it is important to understand the key terms used in statistics. These definitions appear repeatedly in exams.

Class Interval: A range of values used to group data, such as 1–10 or 11–20.
Frequency: The number of times a value or group appears in the data.
Lower Limit and Upper Limit: The smallest and largest values in a class interval.
Class Size: The difference between the lower limits of consecutive classes.
Class Mark (Midpoint): The center of a class interval, calculated as:
(Lower Limit + Upper Limit) ÷ 2
Cumulative Frequency: The running total of frequencies.

From experience, students who clearly understand these definitions find statistics much easier. Most mistakes in exams happen because students confuse class limits with boundaries or forget how to calculate midpoints.

Question 1 – Analyzing Grouped Data

This question usually provides grouped data, such as the number of books read by students. You are asked to interpret the table.

Step-by-step method:

Add all frequencies to find the total number of observations.
Identify the class interval with the highest frequency.
Identify the class interval with the lowest frequency.
Calculate class size by subtracting consecutive lower limits.
Find class marks using the midpoint formula.

For example, if frequencies are 5, 4, 8, 9, 2, and 2, then:

Total = 5 + 4 + 8 + 9 + 2 + 2 = 30

This type of question tests your understanding of data, not just calculations. Always write each step clearly to secure full marks.

Question 2 – Constructing Frequency Tables

In this question, raw data is given, and you must organize it into a grouped frequency table.

Correct approach:

Divide data into equal class intervals.
Count how many values fall into each class.
Create a frequency column.
Calculate cumulative frequency.

Example: If 80 students are grouped, and 7 fall below 50, then:

Percentage = (7 ÷ 80) × 100 = 8.75%

Students often lose marks here because they skip steps. Always show how you counted frequencies and how you calculated percentages.

Question 3 – Discrete Frequency Distribution

This question deals with data where values are separate numbers, such as the number of medals won.

Steps to solve:

List all possible values.
Count how many times each value appears.
Create a frequency table.
Calculate cumulative frequency.

For example:

0 medals → 5 students
1 medal → 8 students

Cumulative frequency is calculated step-by-step, such as 5, then 5 + 8 = 13, and so on.

This question checks your accuracy. Even a small counting mistake can reduce marks.

Question 4 – Frequency Polygon

This is one of the most important parts of Exercise 11.1. Students must represent data graphically.

Steps:

Calculate class marks (midpoints).
Draw axes (X-axis for midpoints, Y-axis for frequency).
Plot points carefully.
Join points with straight lines.

The result is called a frequency polygon.

From teaching experience, many students lose marks because they draw incorrect scales or plot points inaccurately. Always label axes clearly and maintain neatness.

Common Mistakes to Avoid

Confusing class limits with class boundaries
Incorrect midpoint calculation
Skipping steps in frequency tables
Wrong addition in cumulative frequency
Untidy graphs and missing labels

Examiners reward clear working. Even if your final answer is slightly incorrect, proper steps can still earn marks.

Why Exercise 11.1 Is Important

This exercise builds your foundation in statistics. Without understanding these basics, students struggle in topics like mean, median, and grouped data in later exercises.

By mastering this exercise, you will:

Understand how data is organized
Improve accuracy in calculations
Develop confidence in graphs and tables
Prepare effectively for board exams

Students Often Search For

Class 9 Mathematics Exercise 11.1 solutions
Basic Statistics FBISE notes
Frequency table examples
Class 9 statistics solved questions
How to draw frequency polygon

This article covers all these topics in a clear and structured way to support exam preparation.

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Explore more Class 9 Mathematics lectures, solved exercises, and revision material on the STEMBridge Learning Blog. Consistent practice and clear understanding will help you perform better in exams and build a strong mathematical foundation.