What is the difference between exclusive and inclusive class intervals?

In exclusive class intervals, the upper limit of one class is the lower limit of the next (e.g., 0-10, 10-20). In inclusive class intervals, the upper limit is included in the class (e.g., 0-9, 10-19). Exclusive intervals are preferred for continuous data.

How is cumulative frequency calculated?

Cumulative frequency is obtained by adding each frequency to the sum of all previous frequencies. There are two types: 'less than' (running total from top) and 'more than' (running total from bottom).

Organisation of Data — NCERT Class 11 Economics

How to Use This Page

This page provides complete NCERT exercise solutions for CBSE Class 11 Economics Chapter 3 — Organisation of Data. Start with the Key Concepts recap, then attempt the intext and chapter-end exercises. For numerical questions involving frequency distribution tables, follow the step-by-step working shown. Use these solutions to verify your own answers and build confidence for exams.

Key Concepts (Quick Recap)

Raw Data: unorganised data in its original form as collected
Classification of Data: arranging data into groups/classes based on common characteristics
Types of Classification: (a) Chronological (time-based), (b) Geographical (region-based), (c) Qualitative (attribute-based), (d) Quantitative (variable-based)
Variable: a characteristic that can take different values; types — Discrete (whole numbers) and Continuous (fractional values)
Frequency: the number of times a value (or class) repeats in the data
Frequency Distribution: a table showing classes and their corresponding frequencies
Class Interval: the range of values in each class (e.g., 0-10, 10-20)
Class Limits: the lowest and highest values of a class interval
Class Width (h): Upper limit − Lower limit
Class Mid-point: (Upper limit + Lower limit) / 2
Exclusive Series: upper limit of one class = lower limit of next (0-10, 10-20)
Inclusive Series: upper limit included in the class (0-9, 10-19)
Open-ended Classes: classes without a specified lower or upper limit (e.g., Below 10, Above 80)
Cumulative Frequency: running total of frequencies; less-than and more-than types
Bivariate Frequency Distribution: distribution of two variables simultaneously

Intext Questions

Section 3.1 — Classification

Q1. What is meant by classification of data?

AnswerClassification of data is the process of arranging raw data into groups or classes based on common characteristics. It makes the data more meaningful, simplifies it, and facilitates comparison and analysis.

Q2. Classify the following as discrete or continuous variables:

Answer

(a) Number of students in a class (b) Height of students (c) Number of cars in a parking lot (d) Weight of rice bags

Answer

(a) Discrete — number of students is always a whole number (b) Continuous — height can take any fractional value (c) Discrete — number of cars is always a whole number (d) Continuous — weight can take any fractional value

Section 3.2 — Frequency Distribution

Q3. What is a class interval?

AnswerA class interval is the range of values within which the data is grouped. For example, in the class 10-20, the class interval is 10 (20 − 10 = 10). Each class has a lower limit and an upper limit.

Chapter-End Exercise

Question 1

Define classification. Why is it necessary?

AnswerClassification is the process of arranging data into groups or classes on the basis of common characteristics. It is necessary because:

1. It simplifies complex and unorganised data. 2. It highlights the essential features of the data. 3. It facilitates comparison between groups. 4. It helps in identifying patterns and trends. 5. It is the basis for further statistical analysis like tabulation and frequency distribution. 6. It eliminates unnecessary details and presents data in a condensed form.

Question 2

What is a variable? Distinguish between discrete and continuous variables.

AnswerA variable is a characteristic or property that can take different values. It is of two types:

Basis	Discrete Variable	Continuous Variable
Values	Takes only whole numbers	Takes any value including fractions
Examples	Number of students, number of books	Height, weight, temperature
Gap	Gaps between values	No gaps — values form a continuum
Frequency distribution	Individual values listed	Class intervals required

Question 3

What is a frequency distribution? What are its types?

AnswerA frequency distribution is a tabular presentation of data showing the values (or classes) of a variable along with their corresponding frequencies.

Types:

1. Discrete Frequency Distribution: Lists individual values and their frequencies. Used for discrete variables. Example: Number of children (0, 1, 2, 3) and their frequencies.

2. Continuous Frequency Distribution: Data is grouped into class intervals and frequencies are shown for each class. Used for continuous variables. Example: Heights of students grouped as 140-150, 150-160, 160-170 cm.

3. Cumulative Frequency Distribution: Shows running totals of frequencies — less-than type (cumulative from top) and more-than type (cumulative from bottom).

4. Bivariate Frequency Distribution: Shows frequencies for two variables simultaneously.

Question 4

Distinguish between exclusive and inclusive class intervals.

Answer

Basis	Exclusive Class Intervals	Inclusive Class Intervals
Upper limit	Upper limit is excluded from the class	Upper limit is included in the class
Format	0-10, 10-20, 20-30	0-9, 10-19, 20-29
Gap between limits	No gap — upper of one = lower of next	Gap of 1 between upper and next lower
Used for	Continuous variables	Discrete variables
Example	Height: 150-160, 160-170 cm	Marks: 0-9, 10-19, 20-29

Question 5

Convert the following inclusive series into exclusive series: 0-9, 10-19, 20-29, 30-39, 40-49

AnswerTo convert inclusive to exclusive series, adjust the class limits by half the gap between the upper limit of one class and the lower limit of the next.

Gap between upper limit of first class (9) and lower limit of next class (10) = 10 − 9 = 1. Adjustment = 1/2 = 0.5.

Inclusive	Exclusive
0-9	-0.5 to 9.5
10-19	9.5 to 19.5
20-29	19.5 to 29.5
30-39	29.5 to 39.5
40-49	39.5 to 49.5

Question 6

Prepare a frequency distribution table from the following data (marks of 20 students):

12, 15, 18, 12, 20, 15, 18, 12, 15, 20, 25, 18, 15, 12, 20, 25, 30, 18, 20, 25

Answer

Marks	Frequency
12			4
15			4
18				4
20				4
25			3
30		1
Total	20

Question 7

Prepare a continuous frequency distribution with class interval 10 from the following data:

15, 22, 8, 12, 18, 25, 35, 42, 5, 28, 33, 19, 14, 38, 45, 10, 32, 20, 27, 40

Answer

Range = Highest value − Lowest value = 45 − 5 = 40. Number of classes = 40/10 = 4 (approximately). Taking class interval of 10:

Class Interval	Frequency
0-10			2
10-20					7
20-30				6
30-40				4
40-50		1
Total	20

Question 8

What is a cumulative frequency distribution? Prepare a 'less than' cumulative frequency table from the following:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	4	6	8	5	3

AnswerA cumulative frequency distribution shows the running total of frequencies. In a 'less than' type, we add frequencies from the top.

Class (Less than)	Cumulative Frequency
Less than 10	4
Less than 20	4 + 6 = 10
Less than 30	10 + 8 = 18
Less than 40	18 + 5 = 23
Less than 50	23 + 3 = 26

Total frequency (N) = 26

Question 9

Prepare a 'more than' cumulative frequency distribution from the data in Question 8.

AnswerIn a 'more than' type, we start from the bottom and add frequencies upward.

Class (More than)	Cumulative Frequency
More than 0	4 + 6 + 8 + 5 + 3 = 26
More than 10	6 + 8 + 5 + 3 = 22
More than 20	8 + 5 + 3 = 16
More than 30	5 + 3 = 8
More than 40	3

Question 10

What are open-ended class intervals? Give an example.

AnswerOpen-ended class intervals are classes that do not have a specified lower or upper limit. They occur at the extremes of a distribution. For example:

Class	Frequency
Below 10	5
10-20	12
20-30	18
30-40	10
Above 40	4

"Below 10" and "Above 40" are open-ended classes. They create difficulty in calculating mid-points, mean, and other statistical measures.

Question 11

What is a bivariate frequency distribution?

AnswerA bivariate frequency distribution is a table that shows the distribution of two variables simultaneously. It presents frequencies for each combination of values (or classes) of two variables. For example, a table showing marks in Mathematics and marks in Economics for a group of students, with each cell showing the number of students with a particular combination, is a bivariate frequency distribution.

Question 12

Explain the concept of class mid-point. How is it calculated?

AnswerThe class mid-point (or class mark) is the value that lies at the centre of a class interval. It represents the entire class in calculations.

FormulaClass Mid-point = (Lower Limit + Upper Limit) / 2

Example: For the class 20-30, Mid-point = (20 + 30) / 2 = 50 / 2 = 25

Class mid-points are used in calculating the mean of a grouped frequency distribution, in constructing frequency polygons, and in other statistical computations.

Internal Links

[Chapter 3 Guide — Organisation of Data](/school/cbse/class/11/economics/cbse-organisation-of-data)
[All Class 11 Economics Solutions](/school/cbse/class/11/economics/solutions)
[Class 11 Economics Subject Guide](/school/cbse/class/11/economics)

Frequently Asked Questions

A frequency distribution is a table that shows how the values of a variable are distributed across different classes along with their corresponding frequencies (number of observations in each class).

Organisation of Data — NCERT Class 11 Economics

How to Use This Page

Key Concepts (Quick Recap)

Intext Questions

Section 3.1 — Classification

Section 3.2 — Frequency Distribution

Chapter-End Exercise

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Internal Links

Frequently Asked Questions

Other question types — same chapter

CBSE Class 11 Economics Chapter 3 Notes: Organisation of Data

Collection of Data — NCERT Class 11 Economics

Correlation — NCERT Class 11 Economics