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Presentation of Data Class 11 Statistics For Economics Notes

Introduction

After data is collected and organised, it needs to be presented in a clear and compact way. Because data is often voluminous, or very large, presenting it properly makes it easier to understand and use.

There are three main forms of data presentation:

Textual or Descriptive presentation
Tabular presentation
Diagrammatic presentation

Textual Presentation of Data

In a textual presentation, data is described as part of the text. This method is most suitable when the amount of data is not very large.

Example

Case 1: "In a bandh call given on 08 September 2005 protesting the hike in prices of petrol and diesel, 5 petrol pumps were found open and 17 were closed whereas 2 schools were closed and remaining 9 schools were found open in a town of Bihar." This is a simple textual presentation.

Case 2: "Census of India 2001 reported that Indian population had risen to 102 crore of which only 49 crore were females against 53 crore males. Seventy-four crore people resided in rural India and only 28 crore lived in towns or cities." This example shows slightly more complex data presented in text form.

The biggest drawback of this method is that a person has to read the entire text to understand the data. However, it can be useful for emphasizing specific points within a report.

Tabular Presentation of Data

In a tabular presentation, data is arranged in rows (horizontal) and columns (vertical). The boxes where rows and columns intersect are called cells.

Note

The main advantage of presenting data in a table is that it organises the information for further statistical analysis and decision-making.

Classification in tables can be of four main kinds:

Qualitative classification

This is when data is classified based on attributes or qualities that are not numerical, such as social status, nationality, gender, or location. For instance, a table classifying literacy rates by sex (male/female) and location (rural/urban) uses qualitative classification.

Quantitative classification

This is when data is classified based on characteristics that can be measured numerically, like age, height, income, or production. Classes are formed by assigning limits, known as class limits.

Example

A table showing the number of people in different age groups (20-30 years, 30-40 years, etc.) is an example of quantitative classification.

Temporal classification

In this type, the classifying variable is time. Data is categorised based on hours, days, weeks, months, or years.

Example

A table showing the yearly sales of a shop from 1995 to 2000 is a temporal classification, as the data is organised by year.

Spatial classification

This is when classification is done based on place or geographical location. The place could be a village, district, state, or country.

Example

A table showing the share of India's exports to different destinations like the USA, Germany, and China is a spatial classification.

Tabulation of Data and Parts of a Table

A good statistical table is made up of several systematic parts. Tabulation can be one-way, two-way, or three-way, depending on how many characteristics are being presented. A good table should have the following components:

(i) Table Number: Each table is assigned a number for easy identification and reference, especially when there are multiple tables in a document. It is usually placed at the top. For example, Table 4.5 would mean the fifth table in the fourth chapter.
(ii) Title: The title explains the contents of the table. It should be clear, brief, and carefully worded to avoid any confusion. It appears just below the table number.
(iii) Captions or Column Headings: These are the headings at the top of each column that explain the figures below them.
(iv) Stubs or Row Headings: These are the headings for each row, located in the far-left column (the stub column). They describe the data presented in the rows.
(v) Body of the Table: This is the main part of the table containing the actual numerical data. Each value in the body is located in a specific cell, determined by its row and column.
(vi) Unit of Measurement: The unit in which the data is measured (e.g., "in crores," "per cent," "in lakhs") should be clearly stated, usually with the title. If different columns or rows use different units, they should be specified in the captions or stubs.
(vii) Source: This is a brief statement at the bottom of the table indicating where the data came from. This is important for verifying the data's authenticity.
(viii) Note: A note is the last part of the table and is used to explain any specific feature of the data that is not self-explanatory from the title, headings, or source.

Diagrammatic Presentation of Data

This is the third method of presenting data. Diagrams help in providing the quickest understanding of a situation compared to text or tables. They translate abstract numbers into a more concrete and easily understandable form.

Note

While diagrams might be less accurate in showing precise values than tables, they are often much more effective in communicating the main message of the data.

There are three main types of diagrams:

Geometric diagram
Frequency diagram
Arithmetic line graph

Geometric Diagram

This category includes bar diagrams and pie diagrams.

Bar Diagram

A bar diagram consists of a group of rectangular bars of equal width and with equal spacing between them. The height (or length) of each bar represents the magnitude of the data. Bar diagrams are useful for comparing different categories.

Simple Bar Diagram: Represents a single set of data. For example, a diagram showing the male literacy rates of different states.
Multiple Bar Diagram: Used to compare two or more sets of data side-by-side. For example, comparing the female literacy rates in 2001 and 2011 for various states.
Component Bar Diagram: Also called a sub-diagram, this is used to show the breakdown of a total into its different parts. Each bar represents a total, and it is divided into segments representing the components. For example, a bar showing the total school-age population could be divided into "enrolled" and "out of school" components.

Pie Diagram

A pie diagram (or pie chart) is also a component diagram, but it uses a circle instead of a bar. The area of the circle is divided into sectors, with each sector representing a component of the whole.

To create a pie chart, the value of each category is first converted into a percentage of the total. Since a circle has 360 degrees, the angle for each component is calculated by multiplying its percentage by 3.6° (360° / 100).

Frequency Diagram

Data from grouped frequency distributions is often shown using frequency diagrams. The main types are histograms, frequency polygons, frequency curves, and ogives.

Histogram

A histogram is a two-dimensional diagram made of a set of rectangles with no space between them.

The base of each rectangle is the class interval.
The area of each rectangle is proportional to the class frequency.
Important: Histograms are drawn only for continuous variables. If the data is not continuous, it must be converted first.
If class intervals are unequal, the height of the rectangles must be adjusted. This is done by using frequency density (class frequency divided by the width of the class interval).
A key use of a histogram is that it can help find the mode of the frequency distribution graphically.

Frequency Polygon

A frequency polygon is a line graph formed by joining the midpoints of the tops of the rectangles in a histogram. To complete the polygon, the ends are joined to the baseline at the midpoints of the classes just before the first class and just after the last class (which have zero frequency). This is a very common way to present a grouped frequency distribution and is more useful than a histogram when comparing two or more distributions on the same graph.

Frequency Curve

A frequency curve is created by drawing a smooth, freehand curve that passes as closely as possible through the points of a frequency polygon. It gives a better idea of the shape of the distribution.

Ogive

An ogive is also known as a cumulative frequency curve. Since there are two types of cumulative frequencies ("less than" and "more than"), there are two types of ogives:

"Less than" ogive: Cumulative frequencies are plotted against the upper limits of the class intervals. This curve is never decreasing.
"More than" ogive: Cumulative frequencies are plotted against the lower limits of the class intervals. This curve is never increasing.

Note

A very useful feature of ogives is that the intersection point of the "less than" and "more than" ogives gives the median of the frequency distribution.

Arithmetic Line Graph

An arithmetic line graph is also called a time series graph. It is used to show how the value of a variable changes over time.

Time (hours, days, years, etc.) is plotted on the x-axis.
The value of the variable is plotted on the y-axis.
The points are then joined by a line. This type of graph is very helpful for understanding long-term trends, cycles, or patterns in data.

Example

A graph showing India's exports and imports from 1993 to 2014 is an arithmetic line graph. It can quickly show that imports have consistently been higher than exports and that the gap between them has widened over time.

Conclusion

Presenting data effectively is crucial for making it meaningful and understandable. Whether using text for small amounts of information, tables for organising large datasets, or diagrams for quick visual comprehension, the right method can turn raw numbers into useful knowledge. By learning these different forms of presentation, you can choose the most appropriate and purposeful way to communicate data.

Presentation of DataClass 11 Statistics For Economics Notes

Introduction

Textual Presentation of Data

Tabular Presentation of Data

Qualitative classification

Quantitative classification

Temporal classification

Spatial classification

Tabulation of Data and Parts of a Table

Diagrammatic Presentation of Data

Geometric Diagram

Bar Diagram

Pie Diagram

Frequency Diagram

Histogram

Frequency Polygon

Frequency Curve

Ogive

Arithmetic Line Graph

Conclusion