Introduction and Textual Presentation of Data

Introduction

After data has been collected and organised, the next step is to present it in a clear, compact, and presentable form. Since collected data is generally voluminous, effective presentation is crucial to make it readily usable and easily comprehensible. 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 within the text of a paragraph. This method is most suitable when the quantity of data is not too large. It allows the presenter to emphasize certain points and provide context.

Drawback of Textual Presentation

A serious drawback of this method is that a reader has to go through the complete text to comprehend the data. This can be time-consuming and may make it difficult to grasp the key information at a glance. For large datasets, this method is highly impractical.

Tabular Presentation of Data

In a tabular presentation, data is presented systematically in rows (read horizontally) and columns (read vertically). The intersection of a row and a column is called a "cell". The most important advantage of tabulation is that it organises data for further statistical analysis and decision-making.

Types of Classification in Tabulation

The classification used in tabulation can be of four kinds:

1. Qualitative Classification: When classification is done according to non-numerical attributes like social status, gender, nationality, etc. The classification by sex (Male/Female) and location (Rural/Urban) in the table below is qualitative.
2. Quantitative Classification: When data is classified based on characteristics that can be measured quantitatively, like age, height, income, etc.
3. Temporal Classification: When the classifying variable is time (e.g., years, months, days).
4. Spatial Classification: When classification is done on the basis of a geographical place (e.g., country, state, district).

Parts of a Table

A good statistical table should have several essential parts to ensure clarity and completeness.

1. Table Number: Assigned for identification purposes, given at the top. (e.g., Table 4.1)
2. Title: Narrates the contents of the table. It should be clear, brief, and carefully worded. (e.g., "Population of India according to workers and non-workers...")
3. Captions (or Column Headings): Designations at the top of each column that explain the figures below.
4. Stubs (or Row Headings): Designations for each row, found in the complete left column (the stub column).
5. Body of the Table: The main part containing the actual numerical data. Each figure is located at the intersection of a specific row and column.
6. Unit of Measurement: States the unit in which the figures are expressed (e.g., "in crores", "per cent"). It is usually stated with the title.
7. Source: A brief statement indicating the source of the data, usually written at the bottom of the table.
8. Note: Explains any specific feature of the data that is not self-explanatory (e.g., "Figures are rounded to nearest crore").

Diagrammatic Presentation of Data: Geometric Diagrams

Diagrammatic presentation provides the quickest understanding of data, translating abstract numbers into a more concrete and easily comprehensible visual form. While diagrams may be less precise than tables, they are often much more effective in conveying information. Common types of diagrams include geometric diagrams, frequency diagrams, and arithmetic line graphs.

Geometric Diagrams

Bar diagrams and pie diagrams are the two main types of geometric diagrams.

1. Bar Diagram

A bar diagram consists of a group of equispaced and equiwidth rectangular bars for each class or category. The height or length of the bar represents the magnitude of the data. Bars can be visually compared by their relative heights.

• Simple Bar Diagram: Used to represent a single set of data. The height of each bar corresponds to the value of the characteristic being measured.
• Multiple Bar Diagram: Used for comparing two or more sets of data. For example, comparing male and female literacy rates across different states for two different years.
• Component Bar Diagram (or Sub-diagram): Used for comparing the sizes of different component parts of a whole. Each bar is divided into segments representing the components. For example, a bar representing total enrolment can be divided into components for 'enrolled' and 'out of school' children.

2. Pie Diagram (or Pie Chart)

A pie diagram is also a component diagram, but it is a circle whose area is proportionally divided among the components it represents.

• The values of each category are first expressed as a percentage of the total.
• The entire circle (360°) is treated as 100%.
• To find the angle for each component, its percentage figure is multiplied by 3.6° (since $360^\circ / 100 = 3.6^\circ$).

Diagrammatic Presentation of Data: Frequency Diagrams

Data in the form of grouped frequency distributions is generally represented by frequency diagrams like histograms, frequency polygons, frequency curves, and ogives.

1. Histogram

A histogram is a two-dimensional diagram consisting of a set of adjacent rectangles.

• The base of each rectangle is the class interval (along the X-axis).
• The area of each rectangle is proportional to the class frequency.
• If the class intervals are equal, the height of the rectangles is proportional to the frequencies.
• If the class intervals are unequal, the heights of the rectangles are adjusted by using frequency density (Class Frequency / Width of the Class Interval).
• There is no space between consecutive rectangles as it represents a continuous variable.
• A histogram can be used to graphically determine the mode of the distribution.

2. Frequency Polygon

A frequency polygon is a plane bounded by straight lines. It can be drawn either by joining the midpoints of the tops of the rectangles in a histogram or independently by plotting the frequencies against the midpoints of the classes. The two endpoints of the polygon are joined to the base line at the midpoints of the two classes with zero frequency just before the first class and after the last class. This is done to ensure that the area under the polygon is equal to the area of the histogram.

3. Frequency Curve

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

4. Ogive (or Cumulative Frequency Curve)

An ogive is a graph of a cumulative frequency distribution. There are two types:

• '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.

The intersection point of the 'less than' and 'more than' ogives gives the median of the frequency distribution.

Diagrammatic Presentation of Data: Arithmetic Line Graph

Arithmetic Line Graph (or Time Series Graph)

An arithmetic line graph is used to represent time series data. In this graph:

• Time (hour, day, week, month, year, etc.) is plotted along the X-axis.
• The value of the variable is plotted along the Y-axis.

The plotted points are then joined by a line to form the graph. This type of graph is very useful for understanding the trend, periodicity, and fluctuations in data over a long period.

Conclusion

Data can be presented in three main forms: textual, tabular, and diagrammatic. While textual presentation is suitable for small datasets, tabular presentation helps in systematically organizing large volumes of data. Diagrammatic presentation, including bar diagrams, pie charts, histograms, and line graphs, makes the data visually appealing and enables quicker comprehension of the facts. The choice of the form of presentation and the type of diagram depends on the nature of the data and the purpose of the presentation, with the ultimate goal of making the data meaningful, comprehensive, and purposeful.

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