Class 9 Maths Exercise 11.2: Basic Statistics

Class 9 Mathematics – Exercise 11.2 (Basic Statistics) Complete Explanation

Exercise 11.2 of Class 9 Mathematics introduces one of the most important concepts in statistics: measures of central tendency. These measures help us understand how data behaves and where its central value lies. In exams, students often lose marks not because the concept is difficult, but because they do not apply formulas correctly or present their work properly.

In this article, you will learn how to solve Exercise 11.2 step by step, with clear explanations, correct formulas, and practical examples. This approach will help you build strong concepts and improve your exam performance.

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1. Arithmetic Mean (Average)

The arithmetic mean represents the average value of a data set. It is the most commonly used measure of central tendency.

Formula (Ungrouped Data):

x̄ = (Σx) / n

• Σx = Sum of all values
• n = Total number of observations

Example:

Find the mean of 2, 4, 6, 8, 10

Solution:

Sum = 2 + 4 + 6 + 8 + 10 = 30

n = 5

Mean = 30 / 5 = 6

In exams, always write each step clearly. Do not jump directly to the answer.

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2. Mean for Grouped Data

When data is given in the form of a frequency table, you must use a different formula.

Formula:

x̄ = (Σfx) / (Σf)

• f = Frequency
• x = Midpoint of class interval

Midpoint Formula:

x = (Lower Limit + Upper Limit) / 2

From experience, many students forget to calculate midpoints correctly. This leads to incorrect answers even if the method is correct. Always calculate midpoints carefully before proceeding.

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3. Weighted Mean

Weighted mean is used when some values have more importance than others. This concept is especially useful in real-life situations like grading systems.

Formula:

x̄ = (Σwx) / (Σw)

• w = Weight of each value

Example:

If Mathematics has more importance than other subjects, its marks will carry a higher weight in calculating the average.

Students often ignore weights in questions and apply the simple mean formula. This is a common mistake and should be avoided.

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4. Median

The median is the middle value of a data set after arranging it in ascending order.

Steps:

• Arrange data in ascending order
• Find position using (n + 1) / 2
• Locate the value at that position

Example:

Data: 3, 7, 9, 12, 15

n = 5

Position = (5 + 1) / 2 = 3rd term

Median = 9

For even values of n, take the average of the two middle values.

In exams, students often forget to arrange the data first. This leads to incorrect answers even if the formula is correct.

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5. Mode

The mode is the value that appears most frequently in a data set.

Example:

Data: 2, 5, 5, 8, 9

Mode = 5

Types of Mode:

• Unimodal: One mode
• Bimodal: Two modes
• Multimodal: More than two modes

Mode is especially useful when identifying the most common value in real-life data, such as survey results.

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6. Comparison of Mean, Median, and Mode

• Mean: Best for balanced data but affected by extreme values
• Median: Best for skewed data
• Mode: Best for identifying the most frequent value

Understanding when to use each measure is important for solving exam questions correctly.

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Why Exercise 11.2 Is Important

Exercise 11.2 builds your foundation in statistics. These concepts are not only important for exams but also for higher-level mathematics.

• Improves accuracy in calculations
• Develops logical thinking
• Strengthens data interpretation skills
• Prepares you for advanced statistics topics

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Exam Tips

• Always write formulas before solving
• Show complete working steps
• Organize data clearly in tables
• Double-check calculations
• Maintain neat presentation

Based on teaching experience, students who present their work clearly score significantly higher marks, even if minor mistakes occur.

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Related Lessons – Class 9 Mathematics

• Exercise 11.1 – Introduction to Statistics
• Exercise 11.2 – Complete Solutions
• Chapter 11 – Statistics Notes

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Conclusion

Exercise 11.2 is not difficult if you understand the concepts and follow the correct steps. Focus on clarity, accuracy, and presentation. With consistent practice, you can solve all statistics questions confidently in exams.