Class 11 Statistics for Economics – Chapter 3: Organisation of Data

Introduction

After collecting data, the next step is to organize it properly. Raw data are often large, unorganized, and difficult to understand. Classification helps arrange data into groups so that analysis becomes easier and more meaningful.

1. Meaning of Organisation of Data

Organisation of Data means arranging collected data into systematic groups or classes according to common characteristics.

Need for Organising Data

Makes data easy to understand.
Helps in comparison.
Saves time and effort.
Makes statistical analysis possible.
Helps in drawing conclusions.

2. Raw Data

Raw Data are data collected in their original form before classification or arrangement.

Features of Raw Data

Unorganized
Difficult to interpret
Time-consuming to analyze
Large datasets become confusing

Example

Marks of students written randomly:
45, 62, 38, 51, 72, 40, 56, 49

This is raw data because it is not arranged or grouped.

3. Classification of Data

Classification is the process of arranging data into different groups or categories based on common characteristics.

Objectives of Classification

Simplify data
Highlight similarities
Facilitate comparison
Make analysis easier

4. Types of Classification

A. Chronological Classification

Data arranged according to time.

Example

Year	Population (Crores)
1951	35.7
1961	43.8
1971	54.6
1981	68.4

Key Point

Uses years, months, weeks, days, etc.

B. Spatial Classification

Data arranged according to geographical locations.

Example

Country	Wheat Yield
India	3154
China	5055
Germany	7998

Key Point

Based on countries, states, districts, cities, etc.

C. Qualitative Classification

Classification based on qualities or attributes that cannot be measured numerically.

Examples

Gender
Religion
Marital Status
Literacy

Example

Population

Male
Female

Further classification:

Married Male
Unmarried Male
Married Female
Unmarried Female

D. Quantitative Classification

Classification based on numerical values.

Examples

Marks
Income
Height
Weight
Age

Example

Marks	Frequency
0–10	1
10–20	8
20–30	6

5. Variables

A Variable is a characteristic that can take different values.

Examples

Income
Age
Marks
Height

6. Types of Variables

A. Continuous Variable

A variable that can take any value within a given range.

Examples

Height
Weight
Temperature
Distance
Time

Characteristics

Can take whole numbers and fractions.
Infinite possible values.

Example:
Height = 150.5 cm, 150.75 cm, 150.88 cm

B. Discrete Variable

A variable that takes only specific values.

Examples

Number of students
Number of cars
Number of family members

Characteristics

Values change by jumps.
Fractions usually not possible.

Example:
1, 2, 3, 4, 5 students

Not 2.5 students.

7. Frequency Distribution

A Frequency Distribution is a table showing different classes and the number of observations in each class.

Example

Marks	Frequency
0–10	1
10–20	8
20–30	6
30–40	7

Advantages

Summarizes large data.
Easy interpretation.
Helps statistical calculations.

8. Important Terms in Frequency Distribution

Class

A group of observations.

Example:
20–30

Class Frequency

Number of observations in a class.

Example:
If 6 students scored between 20–30 marks,
Frequency = 6

Class Limits

Lower Class Limit

Smallest value of the class.

Example:
20–30

Lower Limit = 20

Upper Class Limit

Largest value of the class.

Example:
20–30

Upper Limit = 30

Class Interval (Class Width)

Difference between upper and lower class limits.

Formula:

Class Interval = Upper Limit − Lower Limit

Example:

30 − 20 = 10

Class Mark (Midpoint)

Middle value of a class.

Formula:

Class Mark = (Upper Limit + Lower Limit) ÷ 2

Example:

20–30

Class Mark = (20 + 30) ÷ 2 = 25

9. Frequency Curve

A graphical presentation of a frequency distribution.

Construction

Class marks on X-axis.
Frequencies on Y-axis.
Join plotted points smoothly.

Uses

Visual representation of data.
Easy comparison.

10. Range

Range shows the spread of data.

Formula

Range = Largest Value − Smallest Value

Example

Largest = 100

Smallest = 10

Range = 100 − 10 = 90

11. Class Intervals

A. Inclusive Method

Both upper and lower limits belong to the same class.

Example

Class
0–10
11–20
21–30

Suitable for:

Discrete variables

B. Exclusive Method

Upper limit excluded from the class.

Example

Class
0–10
10–20
20–30

Suitable for:

Continuous variables

12. Tally Marks

Tally marks are used to count frequencies easily.

Example

Class	Tally	Frequency
0–10
10–20

Rule

Every fifth tally crosses the previous four.

13. Frequency Array

Used for discrete variables.

Example

Family Size	Frequency
1	5
2	15
3	25
4	35

14. Unequal Class Intervals

Sometimes classes are not of equal width.

Example

40–45

45–50

50–55

55–60

Used When

Data are concentrated in a particular range.
More detailed analysis is required.

15. Loss of Information

When raw data are grouped into classes, individual observations are lost.

Example

Class 20–30 contains:

20, 22, 25, 25, 28

After classification, only frequency is known.

Frequency = 5

Exact values disappear.

Advantage

Although some details are lost, data become easier to analyze.

16. Bivariate Frequency Distribution

Shows frequency distribution of two variables simultaneously.

Example

Advertisement Expenditure	Sales
Low	Low
Medium	High
High	High

Uses

Study relationship between two variables.
Useful in correlation analysis.

Key Formulae

Range

Range = Largest Value − Smallest Value

Class Interval

Class Interval = Upper Limit − Lower Limit

Class Mark

Class Mark = (Upper Limit + Lower Limit) ÷ 2

Important Questions with Answers

A. Multiple Choice Questions (MCQs)

1. Raw data are:

a) Classified data
b) Organized data
c) Unclassified data
d) Tabulated data

Answer: c) Unclassified data

2. Classification helps in:

a) Creating confusion
b) Making data difficult
c) Organizing data
d) Destroying data

Answer: c) Organizing data

3. Classification according to years, months, and days is called:

a) Spatial classification
b) Qualitative classification
c) Chronological classification
d) Quantitative classification

Answer: c) Chronological classification

4. Classification according to states and countries is:

a) Spatial classification
b) Quantitative classification
c) Chronological classification
d) Frequency classification

Answer: a) Spatial classification

5. Gender is an example of:

a) Quantitative classification
b) Qualitative classification
c) Numerical classification
d) Frequency distribution

Answer: b) Qualitative classification

6. Marks obtained by students are:

a) Qualitative data
b) Spatial data
c) Quantitative data
d) Chronological data

Answer: c) Quantitative data

7. A variable that can take any value is called:

a) Discrete variable
b) Continuous variable
c) Qualitative variable
d) Attribute

Answer: b) Continuous variable

8. Which of the following is a continuous variable?

a) Number of students
b) Number of cars
c) Height
d) Number of books

Answer: c) Height

9. Which of the following is a discrete variable?

a) Weight
b) Height
c) Temperature
d) Number of students

Answer: d) Number of students

10. Frequency distribution shows:

a) Class intervals only
b) Frequencies only
c) Classes and frequencies
d) Class marks only

Answer: c) Classes and frequencies

11. The number of observations in a class is called:

a) Class mark
b) Frequency
c) Range
d) Interval

Answer: b) Frequency

12. Range is:

a) Largest value + Smallest value
b) Largest value ÷ Smallest value
c) Largest value – Smallest value
d) Smallest value – Largest value

Answer: c) Largest value – Smallest value

13. Class mark is:

a) Upper limit
b) Lower limit
c) Midpoint of a class
d) Frequency

Answer: c) Midpoint of a class

14. Class interval is:

a) Frequency
b) Difference between class limits
c) Class mark
d) Observation

Answer: b) Difference between class limits

15. A frequency distribution of two variables is called:

a) Univariate distribution
b) Bivariate distribution
c) Frequency array
d) Time series

Answer: b) Bivariate distribution

B. Fill in the Blanks

Raw data are __________ data.

Answer: unclassified

Classification brings __________ in data.

Answer: order

Data arranged according to time is called __________ classification.

Answer: chronological

Data arranged according to location is called __________ classification.

Answer: spatial

Gender is a __________ characteristic.

Answer: qualitative

Income is a __________ characteristic.

Answer: quantitative

Height is a __________ variable.

Answer: continuous

Number of students is a __________ variable.

Answer: discrete

Class frequency means the number of __________ in a class.

Answer: observations

The middle value of a class is called __________.

Answer: class mark

Range = Largest Value – __________.

Answer: Smallest Value

Tally marks help in finding __________.

Answer: frequency

Inclusive method includes both class __________.

Answer: limits

Frequency array is used for __________ variables.

Answer: discrete

Frequency distribution of two variables is called __________ distribution.

Answer: bivariate

C. True or False

Raw data are organized data.

Answer: False

Classification simplifies data.

Answer: True

Height is a continuous variable.

Answer: True

Number of students is a continuous variable.

Answer: False

Frequency distribution summarizes data.

Answer: True

Class mark is the midpoint of a class.

Answer: True

Range is obtained by adding largest and smallest values.

Answer: False

Inclusive method includes both limits.

Answer: True

Frequency array is used for continuous variables.

Answer: False

Bivariate distribution involves two variables.

Answer: True

D. Match the Following

Column A	Column B
Raw Data	Unclassified Data
Height	Continuous Variable
Number of Students	Discrete Variable
Gender	Qualitative Classification
Income	Quantitative Classification
Range	Largest – Smallest
Class Mark	Midpoint
Frequency	Number of Observations
Time Series	Chronological Classification
Country-wise Data	Spatial Classification

E. One Word Answer Questions

Data in original form are called ________.

Answer: Raw Data

Arrangement of data into groups is called ________.

Answer: Classification

Classification according to years is called ________.

Answer: Chronological Classification

Classification according to places is called ________.

Answer: Spatial Classification

Middle value of a class is called ________.

Answer: Class Mark

Number of observations in a class is called ________.

Answer: Frequency

Difference between largest and smallest value is ________.

Answer: Range

A variable that takes any value is ________.

Answer: Continuous Variable

A variable that takes specific values only is ________.

Answer: Discrete Variable

Distribution of two variables is ________.

Answer: Bivariate Distribution

F. Very Short Answer Questions

1. What is raw data?

Answer: Data collected in its original and unorganized form is called raw data.

2. What is classification?

Answer: Classification is the process of arranging data into groups based on common characteristics.

3. What is frequency?

Answer: The number of observations in a class is called frequency.

4. What is class mark?

Answer: The midpoint of a class interval is called class mark.

5. What is range?

Answer: Range is the difference between the largest and smallest observations.

6. What is a frequency distribution?

Answer: A table showing class intervals and their frequencies.

7. What is a variable?

Answer: A characteristic that can take different values.

8. What is a continuous variable?

Answer: A variable that can take any numerical value within a range.

9. What is a discrete variable?

Answer: A variable that takes only specific values.

10. What is a frequency array?

Answer: A frequency distribution of a discrete variable.

G. Short Answer Questions

1. Why is classification necessary?

Answer:

Organizes data
Simplifies analysis
Facilitates comparison
Helps draw conclusions

2. Distinguish between raw data and classified data.

Raw Data	Classified Data
Unorganized	Organized
Difficult to understand	Easy to understand
Difficult to analyze	Easy to analyze

3. Distinguish between continuous and discrete variables.

Continuous Variable	Discrete Variable
Takes any value	Takes specific values
Example: Height	Example: Number of students

4. Explain qualitative classification.

Answer: Classification based on qualities or attributes such as gender, religion, literacy, and marital status.

5. Explain quantitative classification.

Answer: Classification based on numerical values such as income, age, marks, and height.

H. Long Answer Questions

1. Explain the different types of classification.

Answer:

Chronological Classification
Spatial Classification
Qualitative Classification
Quantitative Classification

(Explain each with examples.)

2. Explain frequency distribution and its advantages.

Answer:
Frequency distribution is a table showing class intervals and frequencies.

Advantages:

Simplifies data
Easy interpretation
Facilitates statistical analysis
Saves time

3. Explain inclusive and exclusive methods.

Inclusive Method:
Both limits included.
Example: 0–10, 11–20, 21–30

Exclusive Method:
Upper limit excluded.
Example: 0–10, 10–20, 20–30

Important Formula-Based Questions

1. Formula of Range

Answer:
Range = Largest Value − Smallest Value

2. Formula of Class Mark

Answer:
Class Mark = (Upper Limit + Lower Limit) ÷ 2

3. Formula of Class Interval

Answer:
Class Interval = Upper Limit − Lower Limit