Updated NCERT Solutions for Class 11 Statistics Chapter 3: Organisation of Data
Welcome, future statisticians! This guide provides updated NCERT Solutions for Class 11 Statistics Chapter 3, "Organisation of Data." We'll break down how to classify and arrange raw data into a meaningful format. Mastering this chapter is crucial for scoring well in board exams and building a strong foundation for competitive exams.
Chapter at a Glance
Chapter 3: Organisation of Data – Quick Reference
| Chapter Name | Organisation of Data |
| Subject | Statistics (for Economics) |
| Board / Class | CBSE Class 11 |
| Target Year | 2026-27 |
| Key Topics | Classification of Data, Variables (Discrete & Continuous), Frequency Distribution, Tally Marks, Class Intervals (Exclusive & Inclusive), Frequency Arrays. |
| Difficulty Level | Easy to Medium |
| Exam Weightage | 4–6 Marks (Can be part of a longer question with Chapter 4) |
Learning Objectives
Understand the meaning and purpose of organising data.
Define and differentiate between raw data and classified data.
Distinguish between qualitative and quantitative classification.
Explain the concepts of variables, attributes, and frequency.
Differentiate between discrete and continuous variables.
Construct a frequency distribution table using tally marks.
Understand and create different types of frequency distributions like exclusive, inclusive, and open-end classes.
Key Concepts & Definitions
Understanding these terms is the first step to mastering the CBSE Class 11 Statistics Chapter 3.
2. Inclusive Method: There is a gap between the upper limit of one class and the lower limit of the next (e.g., 10-19, 20-29). Both lower and upper limits are included in the class.
Full NCERT Solutions – Chapter 3
(Note: The NCERT textbook for Class 11 Statistics provides conceptual questions and examples. The following solutions are representative of the types of numerical problems you will face based on the chapter's concepts.)
Raw Data:
41, 19, 23, 33, 46, 2, 12, 28, 48, 8, 17, 25, 35, 49, 10, 21, 31, 38, 42, 15, 20, 27, 39, 44, 11, 23, 34, 47, 5, 29To organise this data, we follow these steps:
- Identify the Range: The lowest value is 2 and the highest is 49.
- Determine Class Intervals: The question asks for an exclusive method with a class interval of 10. The classes will be 0-10, 10-20, 20-30, 30-40, and 40-50.
- Use Tally Marks: We count the number of observations falling in each class.
- Construct the Frequency Distribution Table:
| Marks (Class Interval) | Tally Marks | Frequency (No. of Students) |
|---|---|---|
| 0-10 | ||| | 3 |
| 10-20 | 5 | |
| 20-30 | 8 | |
| 30-40 | 6 | |
| 40-50 | 8 | |
| Total | 30 |
Conclusion: This table clearly shows the distribution of marks. For example, we can quickly see that the highest number of students (8 each) scored in the 20-30 and 40-50 mark ranges.
The key difference between discrete and continuous variables lies in the values they can assume.
| Basis for Comparison | Discrete Variable | Continuous Variable |
|---|---|---|
| Meaning | A variable that can only take specific, countable, and distinct values. These are often whole numbers. | A variable that can take any value (including fractions and decimals) within a given range. |
| Values | Countable (e.g., 1, 2, 3) | Uncountable / Measurable (e.g., 1.1, 1.11, 1.111) |
| How to Obtain | Values are obtained by counting. | Values are obtained by measuring. |
| Examples | 1. Number of cars in a parking lot. 2. Number of printing mistakes in a book. | 1. Height of a person (can be 175.5 cm). 2. Weight of a student (can be 60.2 kg). |
Given Inclusive Series:
| Class Interval (Inclusive) | Frequency |
|---|---|
| 10-19 | 5 |
| 20-29 | 10 |
| 30-39 | 8 |
| 40-49 | 12 |
| 50-59 | 5 |
To convert this to an exclusive series, we perform the following steps:
- Find the Gap: Find the difference between the upper limit of one class and the lower limit of the next class.
Gap = 20 - 19 = 1. - Calculate Adjustment Factor: Adjustment Factor = Gap / 2 = 1 / 2 = 0.5.
- Adjust the Class Limits: Subtract 0.5 from all lower limits and add 0.5 to all upper limits.
Resulting Exclusive Series:
| Class Interval (Exclusive) | Frequency |
|---|---|
| 9.5 - 19.5 | 5 |
| 19.5 - 29.5 | 10 |
| 29.5 - 39.5 | 8 |
| 39.5 - 49.5 | 12 |
| 49.5 - 59.5 | 5 |
Important Note: The frequencies do not change during this conversion.
Extra Important Questions (Board Exam Style)
'Loss of information' refers to the fact that when raw data is grouped into classes in a frequency distribution, the individual values of the observations are lost. We only know the number of observations that fall within a particular class interval, not their exact values. For example, if 10 students scored between 80-90, we don't know the exact score of any of those 10 students.
A frequency array is a table that shows the frequency of each value of a discrete variable. It simply lists each distinct value and its corresponding frequency.
A frequency distribution is used for continuous variables (or discrete variables with a wide range). It groups data into class intervals and shows the frequency for each interval, not for each individual value.
A Bivariate Frequency Distribution is a statistical table that summarises the relationship between two variables simultaneously. It shows the frequency of observations for each possible pair of values or class intervals of the two variables. It is also known as a two-way frequency table or a contingency table. For example, it could show the number of students based on both their height and weight classes.
Raw Data:
340, 155, 267, 480, 520, 190, 210, 370, 410, 545, 180, 290, 330, 440, 510, 160, 225, 395, 425, 530, 175, 240, 310, 490, 350- Range & Classes: Min=155, Max=545. Using inclusive method with an interval of 100, we can start the first class at 150. The classes will be 150-249, 250-349, 350-449, and 450-549.
- Tally & Count: We count the frequencies for each class.
- Create Table:
| Electricity Bill (in ₹) | Tally Marks | Frequency (No. of Households) |
|---|---|---|
| 150-249 | 8 | |
| 250-349 | 5 | |
| 350-449 | 6 | |
| 450-549 | 6 | |
| Total | 25 |
- Find Gap: Gap = Lower limit of 2nd class - Upper limit of 1st class = 250 - 249 = 1.
- Adjustment Factor: Factor = Gap / 2 = 1 / 2 = 0.5.
- Adjust Limits: Subtract 0.5 from lower limits and add 0.5 to upper limits.
| Electricity Bill (in ₹) (Exclusive) | Frequency (No. of Households) |
|---|---|
| 149.5 - 249.5 | 8 |
| 249.5 - 349.5 | 5 |
| 349.5 - 449.5 | 6 |
| 449.5 - 549.5 | 6 |
| Total | 25 |
Scenario: A new café, "Brew & Bites," tracked the age of its first 40 customers to understand its target demographic. The data collected is:
22, 18, 35, 41, 25, 28, 19, 45, 52, 23, 29, 31, 38, 48, 16, 60, 24, 26, 33, 39, 42, 21, 27, 30, 36, 55, 49, 17, 20, 24, 32, 44, 58, 28, 34, 37, 29, 43, 51, 22Based on the data, answer the following:
- What is the range of the age of customers?
- Organise the data into a frequency distribution using the exclusive method with class intervals 15-25, 25-35, etc.
- Which age group visited the café the most?
- How many customers were above the age of 45?
(i) Range of Age:
- Highest Age = 60, Lowest Age = 16
- Range = 60 - 16 = 44 years
(ii) Frequency Distribution Table (Exclusive Method):
| Age of Customers (Years) | Tally Marks | Frequency |
|---|---|---|
| 15-25 | 10 | |
| 25-35 | 14 | |
| 35-45 | 9 | |
| 45-55 | 5 | |
| 55-65 | || | 2 |
| Total | 40 |
(iii) Most Frequent Age Group:
The age group 25-35 visited the café the most, with 14 customers.
(iv) Customers Above 45:
Customers in 45-55 group + Customers in 55-65 group = 5 + 2 = 7 customers.
Common Mistakes to Avoid
Exam Preparation Tips for 2026-27
Frequently Asked Questions (FAQs)
Master Organisation of Data 📈
Well done! You have now covered the essentials of "Organisation of Data." This chapter is the bridge between collecting raw data and presenting it meaningfully. A strong grip on creating frequency distributions is fundamental for all subsequent chapters in statistics.
⚡ Practice Chapter 3 MCQs Free