Statistics Class 9 Important Questions Free PDF Download

Statistics is one of the most practical and interesting chapters in the Class 9 Mathematics syllabus. It introduces students to the world of data analysis and equips them with essential tools to interpret information effectively. Whether it’s analyzing cricket scores, studying weather patterns, or understanding survey results, statistics play a vital role in our everyday lives.

This chapter focuses on organizing and interpreting raw data, presenting it graphically, and calculating measures of central tendency like mean, median, and mode. To ace your exams, it’s crucial to practice a variety of questions that cover both the theoretical and practical aspects of the chapter.

In this blog, we’ll highlight Chapter 12 Statistics Important Questions that will help you prepare effectively for your exams. From constructing frequency tables to solving problems on mean, median, and mode, these questions are carefully chosen to give you a complete understanding of the concepts.

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Chapter 12 Statistics Important Questions

A charity surveys the people of a village for their haemoglobin counts. 25 out of 100 adult females in the village were tested. The result is given in this table

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1. A haemoglobin count below 12 is considered deficient.

What proportion of females in the survey can be considered deficient? 

a. 3/25

b. 4/25

c. 18/25

d. 22/25

Solution:

(c) 18/25

Explanation:

Number of females below 12= 18

Total females= 25

Proportion of females below 12= Number of females below 12/Total females

=18/25

2. What are the median haemoglobin counts (mg/dl) of the females in the survey?

a. 8

b. 9

c. 9.5

d. 12.5

Solution:

(d) 12.5

Explanation:

Median = N/2

Median = 25/2

Median = 12.5

3. Divya said that 8 and 12 are the most observed haemoglobin counts (mg/dl) among 25 females. Krishna said that 8 and 12 are the most observed haemoglobin counts (mg/dl) among 100 females in the village. Who is correct? Explain your answer

Solution: 

Divya is correct

Since,

In the above data, the total number of females = 3+3+2+5+1+1+3+4+2+1

    = 25

Among 25 females, 8 and 12 are the most observed haemoglobin counts (mg/dl)

Five friends Anchal, Amisha, Mahi, Vaishu and Sahar are living in a hostel. At the end of every month, they calculate the expenses for food and shopping. The table given below shows their monthly expenses for November. 

4. Which graphical representation method would best represent the data given?

Solution:

‍Bar

GraphBar graphs are good for showing how something changes over time, especially when the changes are large.

5. What is the average expense of the friends for November?

Solution:

‍Average= Total Expense/ No. of friends

Average= (3000+5000+6000+4500+7000)/ 5

Average= (25500)/ 5

Average= 5100

6. Anchal says, “The difference between the median expenditures for October and November amounts to 10% of the November expense, and we have been able to reduce our median expense for November.” What was their median expense for October?

a. 12π

b. 15π

c. 19π

d. 20π

Solution:

(c) 19π

Explanation: 

To calculate the median expenditure for November, we first arrange the expenditures in ascending order:

• 3000, 4500, 5000, 6000, 7000

The median is the middle value in this ordered list. Here, the median for November is Rs. 5000.

As per Aanchal

Difference=10%×5000

=500

Median for October=Median for November+Difference

=5000+500

=5500

The options are expressed as multiples of π. To match:

5500=kπ

Assume π=3.14

k=5500/3.14≈1751.6

Now consider the options:

• 12π=12×3.14=37.68 (too small)
• 15π=15×3.14=47.1 (too small)
• 19π=19×3.14=59.66 (matches closely)
• 20π=20×3.14=62.8 (too large)

Thus, the correct option is 19π.

Chapter 12 Statistics Important Questions: Concepts

Statistics is the branch of mathematics that deals with collecting, organizing, analyzing, and interpreting data. In this chapter, you’ll learn how to handle data systematically.

Key Topics Covered:

What is Data?

Data refers to the information collected for analysis. It can be in raw form or organized in a way that makes it easier to understand.

Types of Data

Primary Data: Information collected directly by the researcher.

Secondary Data: Information gathered from existing sources like books or reports.

Presentation of Data

Data can be represented in various forms:

Ungrouped Data: Data listed without being categorized.

Grouped Data: Data is organized into intervals or classes to make it easier to interpret.

Frequency Distribution Table

A table that shows how often each value or range of values occurs in the data.

Graphical Representation of Data

Data can be visualized using:

Bar Graphs: Used for comparing different categories of data.

Histograms: A graphical representation of grouped data, where bars are adjacent to each other.

Frequency Polygons: A line graph that represents the frequencies of data points.

Measures of Central Tendency

These are values that represent the centre or average of a data set:

Mean: The average value, is calculated by adding all observations and dividing by the total number of observations.

Median: The middle value when the data is arranged in ascending or descending order.

Mode: The value that appears most frequently in the data set.

Uses of Statistics

Statistics are used in fields like economics, sports, weather forecasting, and more to make informed decisions.

Chapter 12 Statistics Important Questions: Formulas

Mean (Average)

The mean is the sum of all observations divided by the total number of observations.

For Ungrouped Data (Raw Data): 

Mean= Sum of all observations​/Number of observations

For Grouped Data (Direct Method):

Mean= ∑f_i​x_i​​/∑f_i

For Grouped Data (Assumed Mean Method):

Mean=A+ ∑f_i​d_i​​/∑f_i

d_i​=x_i​−A (deviation from the assumed mean)

Median

For Grouped Data: 

Median=L+((N/2−CF)/f)⋅h

Mode

Mode=L+ ((f_m - f₁)/(f_m - f₁)+(f_m - f₂)

Cumulative Frequency

Cumulative frequency is the sum of the frequencies of all classes up to a given class. It is used to calculate the median.

Chapter 12 Statistics Important Questions: Why

Statistics is a chapter that forms the foundation for understanding data in real life. Whether you're planning to pursue advanced studies in mathematics, economics, or even social sciences, the concepts from this chapter are invaluable. Here’s why practicing important questions from Chapter 12: Statistics is essential:

Strengthens Conceptual Understanding

• Solving a variety of questions helps you understand the core concepts of statistics, such as data organization, graphical representation, and measures of central tendency (mean, median, and mode).
• It clarifies the practical applications of formulas and how they work in real-world scenarios.

Improves Problem-Solving Skills

• Statistics involves calculations, formula application, and logical reasoning.
• Practising important questions boosts your ability to solve problems accurately and quickly during exams.

Exam-Focused Preparation

• CBSE exams often follow a pattern, and certain types of questions (like constructing frequency tables, and calculating mean, median, and mode) are frequently asked.
• Practising important questions ensures you cover all possible variations and stay exam-ready.

Enhances Graphical Representation Skills

• Questions on histograms, bar graphs, and frequency polygons test your ability to present data visually.
• Regular practice makes these graphical representations easier and more accurate.

Builds Confidence for Higher Studies

• Statistics is not just a school subject—it’s widely used in higher studies and professional fields like data science, economics, and research.
• Solving important questions at this stage lays the groundwork for more advanced statistical concepts.

Prepares for Real-Life Applications

• The skills you gain from studying statistics are highly practical. For instance, analyzing trends, interpreting survey results, or making predictions based on data are all rooted in the principles of statistics.

Practising important questions from Chapter 12: Statistics helps you master the concepts, build confidence, and prepare effectively for exams and future applications. It’s not just about scoring marks—it’s about developing a skill set that will serve you for life! We hope that you practice the above Statistics Class 9 Important Questions and achieve your dream marks.

All the Best!