I. Chapter Summary:

This chapter focuses on the collection, organization, and interpretation of data. It introduces various methods of representing data, such as bar graphs, histograms, and pie charts. It emphasizes the importance of data handling in daily life and how different forms of data presentation can provide insights into real-world situations.

II. Key Concepts Covered:

1. Data Collection:

   • Understanding different types of data: discrete and continuous.

   • Collecting data through surveys, experiments, or observation.

2. Data Representation:

   • Bar Graphs: Used for comparing different categories of data.

   • Histograms: Used for continuous data and for showing frequency distributions.

   • Pie Charts: Represent data in a circular graph, showing proportions.

3. Measures of Central Tendency:

   • Mean: The average of all data points.

   • Median: The middle value in a data set.

   • Mode: The value that appears most frequently.

4. Probability:

   • Basic understanding of probability and its real-world applications.

   • How to calculate simple probabilities.

III. Important Questions:

(A) Multiple Choice Questions (1 Mark):

1. Which of the following is used to represent data that is divided into categories?

   • a) Bar graph

   • b) Histogram

   • c) Pie chart

   • d) All of the above
     Answer: a) Bar graph
     PYQ: 2019, 1 Mark

2. What is the mode of the following data set: 2, 3, 3, 5, 7, 7, 7, 8?

   • a) 3

   • b) 5

   • c) 7

   • d) 8
     Answer: c) 7
     PYQ: 2020, 1 Mark

3. The median of the data set {12, 7, 15, 5, 9} is:

   • a) 7

   • b) 9

   • c) 12

   • d) 15
     Answer: b) 9
     PYQ: 2018, 1 Mark

4. Which of the following is true about a histogram?

   • a) It uses bars of equal width.

   • b) It represents discrete data.

   • c) The bars are not connected.

   • d) It is used for representing data in percentages.
     Answer: a) It uses bars of equal width
     PYQ: 2021, 1 Mark

(B) Short Answer Questions (2/3 Marks):

1. Explain how data can be represented using a bar graph.
   PYQ: 2019, 2 Marks

2. What is the difference between a histogram and a bar graph?
   PYQ: 2020, 3 Marks

3. Calculate the mean of the following data set: 3, 5, 7, 8, 10.
   PYQ: 2021, 3 Marks

4. What is the importance of probability in real life? Give one example.
   PYQ: 2020, 2 Marks

(C) Long Answer Questions (5 Marks):

1. Discuss the different types of data representation with suitable examples.
   PYQ: 2019, 5 Marks

2. Define and explain the concept of probability with an example.
   PYQ: 2021, 5 Marks

3. Explain how to calculate the mean, median, and mode of a given data set.
   PYQ: 2020, 5 Marks

4. Describe the steps involved in collecting data for a survey. How is this data useful?
   PYQ: 2021, 5 Marks

(D) HOTS (Higher Order Thinking Skills) Questions:

1. A school conducted a survey of student preferences regarding the use of technology in learning. The data was collected and presented using various graphs. Based on the given data, identify which graph would be most appropriate for representing preferences and why.
   PYQ: 2021, HOTS

2. How can data presentation techniques, such as histograms and pie charts, be used to make informed decisions in a business setting?
   PYQ: 2020, HOTS

IV. Key Formulas/Concepts:

1. Mean:

   Mean=∑data pointsN\text{Mean} = \frac{\sum \text{data points}}{N}Mean=N∑data points​

2. Median:

   • Arrange the data in ascending order.

   • If the number of data points is odd, the median is the middle value.

   • If even, the median is the average of the two middle values.

3. Mode: The value that appears most frequently.

4. Probability:

   P(event)=number of favorable outcomestotal number of outcomesP(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}P(event)=total number of outcomesnumber of favorable outcomes​

V. Deleted Portions (CBSE 2025–2026):

No portions have been deleted from this chapter as per the rationalized NCERT textbooks.

VI. Chapter-Wise Marks Bifurcation (Estimated – CBSE 2025–2026):

VII. Previous Year Questions (PYQs):

1. 1 Mark Questions:

   • 2018: MCQs on types of graphs

   • 2019: Probability and mean calculation

2. 2/3 Mark Questions:

   • 2020: Data interpretation using pie charts and histograms

3. 5 Mark Questions:

   • 2021: Importance of data handling and real-life applications

VIII. Real-World Application Examples to Connect with Topics:

• Bar Graphs: Used by market analysts to compare sales data over a period.

• Histograms: Applied in quality control to measure manufacturing processes.

• Pie Charts: Used in elections to show vote percentages for different parties.

• Probability: Used by insurance companies to calculate risks and premiums.

IX. Student Tips & Strategies for Success (Class-Specific):

• Time Management: Prioritize subjects and topics, setting specific time slots for revision.

• Exam Preparation: Practice sample papers, work on past year questions, and focus on areas with higher marks weight.

• Stress Management: Engage in physical activities, take regular breaks, and maintain a balanced diet.

X. Career Guidance & Exploration (Class-Specific):

For Classes 9–10:

• Academic Streams: Science (Physics, Chemistry, Biology), Commerce (Accountancy, Economics, Business Studies), Arts (History, Geography, Political Science).

• Career paths: Data Scientist, Statistician, Researcher, Software Engineer, etc.

• Entrance Exams: NTSE, Olympiads, JEE (for Science), and other foundational exams.

For Classes 11–12:

• Specific Careers: Data Analyst, Mathematician, Statistician, and Software Engineer.

• Entrance Exams: JEE, NEET, CUET, etc.

• Top Institutions: IITs, AIIMS, Delhi University, and prestigious engineering and medical colleges.

XI. Important Notes:

• Always refer to the official CBSE website for the latest updates.

• Consistent revision and practice are key to success.

• Conceptual clarity is more important than rote memorization. Focus on understanding the application of concepts.