Class 11 Statistics for Economics Chapter 4: Presentation of Data

Introduction

After collecting and organizing data, it must be presented in a clear and understandable form. Proper presentation makes data easy to read, compare, analyze, and interpret.

Objectives of Data Presentation

Simplify large amounts of data.
Make information easy to understand.
Help in analysis and decision-making.
Improve communication of facts.

Forms of Data Presentation

There are three main methods of presenting data:

Textual (Descriptive) Presentation
Tabular Presentation
Diagrammatic Presentation

1. Textual Presentation of Data

In textual presentation, data are presented through words and sentences.

Example

A school has 500 students, out of which 280 are boys and 220 are girls.

Advantages

Simple to prepare.
Suitable for small data.
Easy explanation of facts.

Disadvantages

Difficult to understand large data.
Comparisons become difficult.
Time-consuming to read.

2. Tabular Presentation of Data

Tabular presentation means presenting data in rows and columns.

Definition

A table is a systematic arrangement of data in rows and columns.

Advantages

Organizes large data.
Easy comparison.
Saves time.
Useful for statistical analysis.

Types of Classification Used in Tables

A. Qualitative Classification

Classification based on qualities or attributes.

Examples

Gender
Religion
Literacy
Marital status

Example Table

Gender	Number of Students
Boys	30
Girls	25

B. Quantitative Classification

Classification based on numerical values.

Examples

Age
Income
Height
Weight

Example

Age Group	Persons
20–30	50
30–40	80

C. Temporal Classification

Classification according to time.

Examples

Years
Months
Weeks
Days

Example

Year	Sales (₹ lakh)
2021	50
2022	60
2023	75

D. Spatial Classification

Classification according to place or location.

Examples

Village
City
State
Country

Example

State	Literacy Rate
Kerala	96%
Bihar	63%

Parts of a Statistical Table

A good table consists of the following parts:

1. Table Number

Used for identification.

Example:
Table 4.1

2. Title

Describes the contents of the table.

Example:
“Population of India by Gender”

3. Captions (Column Headings)

Names given to columns.

Example:

| Boys | Girls |

4. Stubs (Row Headings)

Names given to rows.

Example:

| Class 11 |
| Class 12 |

5. Body of Table

Contains actual data values.

6. Unit of Measurement

Indicates the unit used.

Examples:

Rupees
Kilograms
Crores
Percentage

7. Source

Shows where data were obtained.

Example:
Source: Census Report

8. Note

Provides additional information or explanations.

Diagrammatic Presentation of Data

Diagrammatic presentation uses diagrams and graphs to represent data visually.

Advantages

Attractive presentation.
Easy understanding.
Quick comparison.
Saves time.

Limitation

Less accurate than tables.

Types of Diagrams

1. Geometric Diagrams

Include:

Bar Diagrams
Pie Diagrams

Bar Diagram

A bar diagram uses rectangular bars of equal width.

Features

Equal width bars.
Height represents magnitude.
Space left between bars.

Types of Bar Diagrams

A. Simple Bar Diagram

Used to represent a single set of data.

Example

State	Literacy
Kerala	96
Bihar	63

Each state is represented by one bar.

B. Multiple Bar Diagram

Used to compare two or more related series.

Example

Comparison of:

Boys and Girls
Exports and Imports
Income and Expenditure

Advantages

Easy comparison of multiple variables.

C. Component Bar Diagram

Shows total value and its components.

Example

Total Students

Boys
Girls

Each component forms part of the total bar.

Uses

Population composition
Budget expenditure
Family expenditure

Pie Diagram (Pie Chart)

A circular diagram divided into sectors.

Features

Circle represents total.
Sectors represent components.
Area proportional to value.

Formula

Angle = Percentage × 3.6°

Example

If Food = 25%

Angle = 25 × 3.6 = 90°

Advantages

Attractive presentation.
Shows composition clearly.

Limitation

Difficult when many categories exist.

Frequency Diagrams

Used for frequency distributions.

Main types:

Histogram
Frequency Polygon
Frequency Curve
Ogive

Histogram

A histogram consists of adjoining rectangles.

Features

Used for continuous data.
No gaps between bars.
Area represents frequency.

Important Point

Histogram differs from bar diagram because:

Histogram	Bar Diagram
No gaps	Gaps present
Continuous data	Any data
Area important	Height important

Uses

Shows frequency distribution.
Helps locate mode graphically.

Frequency Polygon

A graph formed by joining the midpoints of histogram bars.

Features

Alternative to histogram.
Useful for comparison.

Construction

Plot class marks.
Plot frequencies.
Join points with straight lines.

Frequency Curve

A smooth curve obtained from a frequency polygon.

Features

Smooth line.
Shows shape of distribution.

Ogive (Cumulative Frequency Curve)

An ogive is a cumulative frequency graph.

Types

Less Than Ogive

Uses cumulative frequencies.
Plots upper class limits.

More Than Ogive

Uses cumulative frequencies.
Plots lower class limits.

Importance

The point where:

Less than ogive
More than ogive

intersect gives the Median.

Arithmetic Line Graph (Time Series Graph)

A graph showing changes over time.

Features

Time on X-axis.
Values on Y-axis.
Points joined by lines.

Uses

Shows trend.
Shows growth or decline.
Useful in time-series analysis.

Examples

Population growth
Export-import trends
Rainfall changes

Difference Between Bar Diagram and Histogram

Bar Diagram	Histogram
Used for discrete data	Used for continuous data
Bars separated by gaps	No gaps
Width not important	Width important
Height shows magnitude	Area shows frequency

Difference Between Frequency Polygon and Frequency Curve

Frequency Polygon	Frequency Curve
Straight lines	Smooth curve
Joins plotted points	Passes close to points
Easier to draw	More refined

Important Formula

Pie Chart Angle

Angle = (Value ÷ Total) × 360°

Angle = Percentage × 3.6°

Quick Revision Points

✔ Data can be presented in textual, tabular, and diagrammatic forms.

✔ Tables organize data into rows and columns.

✔ Types of classification:

Qualitative
Quantitative
Temporal
Spatial

✔ Parts of a table:

Table Number
Title
Captions
Stubs
Body
Unit
Source
Note

✔ Bar diagrams:

Simple
Multiple
Component

✔ Pie chart is a circular diagram.

✔ Histogram is used for continuous data.

✔ Frequency polygon joins class midpoint frequencies.

✔ Frequency curve is a smooth frequency polygon.

✔ Ogive is a cumulative frequency curve.

✔ Intersection of two ogives gives the median.

✔ Arithmetic line graph is used for time-series data.

Important Questions and Answers

A. Multiple Choice Questions (MCQs)

1. Which of the following is a method of presenting data?

a) Textual Presentation
b) Tabular Presentation
c) Diagrammatic Presentation
d) All of these

Answer: d) All of these

2. Which presentation method is most suitable for small amounts of data?

a) Tabular
b) Diagrammatic
c) Textual
d) Graphical

Answer: c) Textual

3. Data arranged in rows and columns is called:

a) Diagrammatic Presentation
b) Textual Presentation
c) Tabular Presentation
d) Frequency Distribution

Answer: c) Tabular Presentation

4. Classification based on gender is:

a) Quantitative
b) Temporal
c) Qualitative
d) Spatial

Answer: c) Qualitative

5. Classification based on income is:

a) Qualitative
b) Quantitative
c) Temporal
d) Spatial

Answer: b) Quantitative

6. Classification according to time is called:

a) Spatial
b) Quantitative
c) Temporal
d) Qualitative

Answer: c) Temporal

7. Classification according to place is called:

a) Temporal
b) Spatial
c) Quantitative
d) Qualitative

Answer: b) Spatial

8. The actual figures in a table are found in:

a) Title
b) Source
c) Body
d) Note

Answer: c) Body

9. Column headings are called:

a) Stubs
b) Captions
c) Notes
d) Sources

Answer: b) Captions

10. Row headings are called:

a) Captions
b) Notes
c) Stubs
d) Titles

Answer: c) Stubs

11. Which diagram is used to compare two or more data series?

a) Pie Diagram
b) Simple Bar Diagram
c) Multiple Bar Diagram
d) Histogram

Answer: c) Multiple Bar Diagram

12. Pie diagram is also called:

a) Circle Graph
b) Pie Chart
c) Frequency Chart
d) Component Graph

Answer: b) Pie Chart

13. Histogram is used for:

a) Continuous Data
b) Qualitative Data
c) Temporal Data
d) Spatial Data

Answer: a) Continuous Data

14. Which graph helps in locating the median?

a) Histogram
b) Pie Chart
c) Ogive
d) Bar Diagram

Answer: c) Ogive

15. Arithmetic Line Graph is also called:

a) Frequency Graph
b) Time Series Graph
c) Pie Graph
d) Histogram

Answer: b) Time Series Graph

16. Histogram helps in finding:

a) Mean
b) Median
c) Mode
d) Average

Answer: c) Mode

17. Frequency polygon is formed by joining:

a) Class limits
b) Midpoints
c) Frequencies
d) Angles

Answer: b) Midpoints

18. A frequency curve is:

a) Straight line graph
b) Pie chart
c) Smooth frequency polygon
d) Histogram

Answer: c) Smooth frequency polygon

19. Component bar diagram shows:

a) Only total values
b) Components of a total
c) Frequency only
d) Time trend

Answer: b) Components of a total

20. In a pie chart, total angle equals:

a) 90°
b) 180°
c) 270°
d) 360°

Answer: d) 360°

B. Fill in the Blanks

Data presented through words and sentences is called __________ presentation.

Answer: Textual

Data arranged in rows and columns is called __________ presentation.

Answer: Tabular

Classification based on attributes is called __________ classification.

Answer: Qualitative

Income is an example of __________ classification.

Answer: Quantitative

Classification according to years is called __________ classification.

Answer: Temporal

Classification according to location is called __________ classification.

Answer: Spatial

Column headings are called __________.

Answer: Captions

Row headings are called __________.

Answer: Stubs

The actual data in a table is called the __________.

Answer: Body

The source of data is mentioned at the __________ of a table.

Answer: Bottom

A pie chart is a __________ diagram.

Answer: Circular

A histogram is used for __________ data.

Answer: Continuous

In a histogram there are no __________ between rectangles.

Answer: Gaps

Frequency polygon is obtained by joining __________.

Answer: Midpoints

Ogive is also called a __________ frequency curve.

Answer: Cumulative

Arithmetic line graph is also called __________ graph.

Answer: Time Series

The intersection of two ogives gives the __________.

Answer: Median

Histogram helps locate the __________ graphically.

Answer: Mode

Pie chart represents data through __________.

Answer: Sectors

Total angle of a pie chart is __________ degrees.

Answer: 360

C. True or False

Textual presentation is suitable for large volumes of data.

Answer: False

Tabular presentation uses rows and columns.

Answer: True

Qualitative classification is based on numerical values.

Answer: False

Income is a quantitative characteristic.

Answer: True

Spatial classification is based on place.

Answer: True

Histogram is used for continuous data.

Answer: True

Gaps are left between histogram rectangles.

Answer: False

Pie chart is a circular diagram.

Answer: True

Frequency polygon is derived from a histogram.

Answer: True

Ogive helps locate the median.

Answer: True

Arithmetic line graph shows trends over time.

Answer: True

Component bar diagram shows components of a total.

Answer: True

Histogram and bar diagram are exactly the same.

Answer: False

Total angle in a pie chart is 360°.

Answer: True

Frequency curve is smoother than frequency polygon.

Answer: True

D. Match the Following

Column A	Column B
Textual Presentation	Data in Words
Tabular Presentation	Rows and Columns
Pie Chart	Circular Diagram
Histogram	Continuous Data
Ogive	Median
Frequency Polygon	Midpoints Joined
Arithmetic Line Graph	Time Series
Captions	Column Headings
Stubs	Row Headings
Spatial Classification	Place-wise Classification

E. One Word Answer Questions

Data presented through words is called ________.

Answer: Textual Presentation

Data arranged in rows and columns is called ________.

Answer: Tabulation

Column headings are called ________.

Answer: Captions

Row headings are called ________.

Answer: Stubs

Circular diagram is called ________.

Answer: Pie Chart

Graph used for continuous data is ________.

Answer: Histogram

Smooth frequency polygon is ________.

Answer: Frequency Curve

Cumulative frequency curve is ________.

Answer: Ogive

Time series graph is ________.

Answer: Arithmetic Line Graph

Intersection of two ogives gives ________.

Answer: Median

F. Very Short Answer Questions

1. What is textual presentation?

Answer: Presentation of data through words and sentences.

2. What is tabular presentation?

Answer: Presentation of data in rows and columns.

3. What is a table?

Answer: A systematic arrangement of data in rows and columns.

4. What is a caption?

Answer: Heading of a column in a table.

5. What is a stub?

Answer: Heading of a row in a table.

6. What is a histogram?

Answer: A graphical representation of continuous frequency distribution using adjacent rectangles.

7. What is a frequency polygon?

Answer: A graph formed by joining class midpoint frequencies with straight lines.

8. What is an ogive?

Answer: A cumulative frequency curve.

9. What is a pie chart?

Answer: A circular diagram showing parts of a whole.

10. What is an arithmetic line graph?

Answer: A graph showing changes in values over time.

G. Short Answer Questions

1. What are the three methods of data presentation?

Answer:

Textual Presentation
Tabular Presentation
Diagrammatic Presentation

2. State any four advantages of tabular presentation.

Answer:

Organizes data
Saves time
Easy comparison
Facilitates analysis

3. What are the four types of classification used in tabulation?

Answer:

Qualitative
Quantitative
Temporal
Spatial

4. State any four parts of a table.

Answer:

Table Number
Title
Captions
Stubs
Body
Source
Note

5. Why are pie diagrams useful?

Answer:

Attractive presentation
Easy comparison
Shows composition clearly
Easy understanding

H. Long Answer Questions

1. Explain the parts of a statistical table.

Answer:

Table Number
Title
Captions
Stubs
Body
Unit of Measurement
Source
Note

(Explain each part with examples.)

2. Explain the different types of bar diagrams.

Answer:

Simple Bar Diagram
Multiple Bar Diagram
Component Bar Diagram

Include definitions, uses, and examples.

3. Distinguish between Histogram and Bar Diagram.

Histogram	Bar Diagram
Continuous data	Discrete/Qualitative data
No gaps	Gaps present
Area important	Height important
Rectangles touch	Bars separated

4. Explain Frequency Polygon, Frequency Curve, and Ogive.

Answer:

Frequency Polygon: Joining class midpoint frequencies.
Frequency Curve: Smooth form of frequency polygon.
Ogive: Cumulative frequency curve used to locate median.

Numerical Questions

1. Find the angle in a pie chart for a category representing 25%.

Answer:

Angle = 25 × 3.6

= 90°

2. Find the angle for 40% of the total.

Answer:

Angle = 40 × 3.6

= 144°

3. Find the angle for 15% of the total.

Answer:

Angle = 15 × 3.6

= 54°