Wrong shortcode initialized

I. Chapter Summary

The chapter Statistics introduces students to the process of collecting, organizing, presenting, and analyzing numerical data. It emphasizes techniques to find measures of central tendency such as mean, median, and mode. Students also learn to represent data using frequency tables and bar graphs and interpret data from visual formats. This chapter builds a strong foundation for higher statistical concepts used in fields such as economics, science, data analysis, and social sciences.

II. Key Concepts Covered

Concept	Explanation
Data	Collection of numerical facts or information.
Ungrouped Data	Raw data not organized into groups or intervals.
Frequency	Number of times a particular value appears in the data.
Mean	Average of data = (Sum of observations) ÷ (Number of observations).
Median	Middlemost observation when data is arranged in ascending or descending order.
Mode	Observation that occurs most frequently.
Frequency Distribution Table	A way to organize data showing frequency of each observation.
Bar Graph	A graphical representation of categorical data with rectangular bars.

III. Important Questions

(A) Multiple Choice Questions (1 Mark)

1. The average of first five natural numbers is:
   a) 3 ✔️
   b) 5
   c) 2
   d) 4
2. The mode of the data 3, 5, 3, 2, 3, 4, 5 is:
   a) 5
   b) 3 ✔️
   c) 4
   d) 2
3. Median of the data 5, 7, 9, 10, 12 is:
   a) 7
   b) 9 ✔️
   c) 10
   d) 8
4. In a frequency table, the number of times a particular value occurs is called:
   a) Class
   b) Frequency ✔️
   c) Mode
   d) Median

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

1. Find the mean of the data: 6, 8, 10, 12, 14.
2. The marks obtained by 10 students are: 12, 15, 17, 13, 15, 18, 15, 14, 15, 16. Find the mode. (PYQ 2019)
3. Find the median of the data: 9, 7, 8, 5, 6, 10, 4. (PYQ 2020)
4. Prepare a frequency table for the following data:
   4, 5, 6, 4, 4, 5, 6, 6, 4, 5, 5, 6.

(C) Long Answer Questions (5 Marks)

1. The marks (out of 10) obtained by 20 students are:
   5, 7, 8, 5, 6, 9, 7, 8, 6, 10, 6, 5, 9, 8, 7, 6, 10, 9, 8, 6
   • Prepare a frequency table,
   • Find mean, median, and mode.
2. Represent the following data using a bar graph:
   Favorite Fruits of Students: Apple – 10, Banana – 15, Mango – 20, Orange – 5.
3. A student scored the following marks in 5 tests: 78, 82, 85, 80, 75.
   • Find the mean, median, and mode.
   • Which of the three best represents his performance? Justify.
4. The heights (in cm) of 9 students are: 145, 150, 152, 153, 155, 157, 160, 162, 165.
   • Calculate mean, median, and mode of the data.
   • Interpret the central tendency of the data.

(D) HOTS (Higher Order Thinking Skills)

1. If the mean of 8 observations is 12, and 7 of them are 10, 13, 14, 9, 11, 15, 13, find the 8th observation.
2. If the mean and median of 5 numbers are the same but mode is different, give an example and explain how this is possible.

IV. Key Formulas/Concepts

Measure	Formula
Mean (Average)	Mean=Sum of observations Number of $observationstext{Mean} = frac{text{Sum of observations}}{text{Number of observations}}Mean=Number of observations Sum of observations​$
Median

• Arrange in ascending order.
• If n is odd: Middle term.
• If n is even: Average of two middle terms. |
  | Mode | The value that appears most frequently in the data. |

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)

Chapter	Estimated Marks	Types of Questions Typically Asked
Statistics	6–8 Marks	1 MCQ, 1 Short Calculation, 1 Long Data-Based Problem

VII. Previous Year Questions (PYQs)

Marks	Question	Year
2 marks	Find the mode of 12, 15, 17, 13, 15, 18, 15, 14, 15, 16.	PYQ 2019
2 marks	Find the median of: 9, 7, 8, 5, 6, 10, 4.	PYQ 2020
3 marks	Prepare a frequency table and find mean.	PYQ 2018
5 marks	Frequency table with mean, median, and mode.	PYQ 2020

VIII. Real-World Application Examples to Connect with Topics

• Education: Analyzing student marks to determine class average, topper, and most common score.
• Business: Survey data analysis to understand customer preferences.
• Healthcare: Calculating average patient wait times in hospitals.
• Sports: Analyzing scores of players to determine consistency and peak performance.
• Weather Forecasting: Average temperature, rainfall data.

IX. Student Tips & Strategies for Success

 Time Management

• Day 1: Understand mean, median, and mode through simple examples.
• Day 2: Solve problems involving frequency tables.
• Day 3: Work on HOTS and PYQs for full preparation.

 Exam Preparation

• Use step-by-step solutions to avoid errors.
• Show working for ascending order and calculations clearly.
• Label Mean, Median, and Mode clearly in final answers.

 Stress Management

• Practice on personal data (e.g., family ages, daily expenses).
• Use graphs or visual aids for better understanding.

X. Career Guidance & Exploration (Class-Specific)

• For Classes 9–10:
  ➤ Statistics strengthens logical reasoning, essential for NTSE, Olympiads, and Data Science foundations.
• For Classes 11–12 & Beyond:
  ➤ Used in:
  • Economics & Commerce
  • Data Analytics
  • Business Management
  • Social Sciences
  • Artificial Intelligence
• Exams Where Useful:
  ➤ CUET
  ➤ JEE (Math Statistics in Class 11)
  ➤ NEET (Data interpretation)
  ➤ UCEED / NID (Data-based reasoning)

XI. Important Notes

 Always arrange data correctly before finding median.
 Use accurate frequency counts when working with tables.
 Mean ≠ Median ≠ Mode in all cases—understand the difference.
 Apply concepts to daily life examples to reinforce understanding.