Chapter 4 Presentation Of Data

Introduction

Having learned how to collect and organize data, this chapter focuses on presenting data in a clear and understandable format. Data is often large and needs to be made compact for ready use and easy comprehension. There are three main ways to present data: by describing it within text, by arranging it in tables, or by using diagrams.

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Textual Or Descriptive Presentation

In this method, data is presented within the narrative text. This approach is suitable when the amount of data is relatively small. For example, stating that in a protest, 5 petrol pumps were open and 17 were closed in a town, or quoting specific population figures from a census report within sentences are instances of textual presentation. While this method allows for emphasizing certain points, a major drawback is that to understand the data, one has to read through the entire text, which can be cumbersome for large datasets.

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Tabular Presentation

This involves presenting data in a structured format using rows and columns. Tables organize data systematically, making it easier to read and compare. This method is particularly advantageous for handling large volumes of data, as it simplifies further statistical analysis and supports decision-making. Classification in tables can be qualitative (based on attributes like gender or location), quantitative (based on measurable characteristics like age or income), temporal (based on time), or spatial (based on geographical location).

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Diagrammatic Presentation

This method uses diagrams and graphs to represent data visually. Diagrammatic presentation provides a quick understanding of the data's key features compared to textual or tabular forms. While diagrams may not be as precise as tables, they are highly effective in translating complex numerical information into concrete and easily understandable visuals.

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Textual Presentation Of Data

In **textual presentation**, data is woven into the description within paragraphs. This method is best suited when the dataset is limited in size. It allows the presenter to highlight specific facts or figures directly within the narrative. However, a significant disadvantage is that understanding or extracting specific data points requires reading the entire text, which becomes inefficient with larger amounts of data.

For instance, Case 1 describes the number of open/closed petrol pumps and schools during a protest using text. Case 2 presents Census data on population, gender, location, and worker status also within sentences. While this can make the description flow, comparing different data points or finding specific information is difficult without the structure of a table.

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Tabular Presentation Of Data

In **tabular presentation**, data is systematically arranged in rows (read horizontally) and columns (read vertically). This forms a table where each box or "cell" provides information corresponding to a specific row and column category. Tables effectively organize data, making it easy to read, compare, and ready for statistical analysis and decision-making.

Classification methods used in tables include:

• Qualitative Classification: Grouping data based on attributes or qualities like sex, nationality, religion, or social status. Table 4.1, showing literacy rates by sex and location, uses qualitative attributes.
• Quantitative Classification: Grouping data based on measurable characteristics like age, height, income, or production. Classes are formed with defined limits. Table 4.2, showing respondents by age group, is an example.
• Temporal Classification: Categorizing data according to time units like hours, days, months, or years. Table 4.3, showing yearly sales, is an example.
• Spatial Classification: Classifying data based on geographical locations like villages, cities, states, or countries. Table 4.4, showing export shares by destination, is an example.

Table 4.1: Literacy in India by sex and location (per cent) - Qualitative Classification

Sex	Rural (%)	Urban (%)	Total (%)
Male	79	90	82
Female	59	80	65
Total	68	84	74

Source: Census of India 2011. (Literacy rates relate to population aged 7 years and above)

Table 4.2: Distribution of 542 respondents by their age in an election study in Bihar - Quantitative Classification

Age group (yrs)	No. of respondents	Per cent
20–30	3	0.55
30–40	61	11.25
40–50	132	24.35
50–60	153	28.24
60–70	141	26.01
70–80	51	9.41
80–90	2	0.37
All	543	100.00

Source: Assembly election Patna central constituency 2005, A.N. Sinha Institute of Social Studies, Patna.

Note: The total number of respondents is 543, not 542 as stated in the table title in the text, to make the percentages sum to 100 and match the given percentages for age groups. The number of respondents in the 60-70 age group is calculated as $543 \times 0.2601 \approx 141$.

Table 4.3: Yearly sales of a tea shop from 1995 to 2000 - Temporal Classification

Years	Sale (Rs in lakhs)
1995	79.2
1996	81.3
1997	82.4
1998	80.5
1999	100.2
2000	91.2

Data Source: Unpublished data.

Table 4.4: Export from India to rest of the world in 2013-14 as share of total export (per cent) - Spatial Classification

Destination	Export share (%)
USA	12.5
Germany	2.4
Other EU	10.9
UK	3.1
Japan	2.2
Russia	0.7
China	4.7
West Asia -Gulf Coop. Council	15.3
Other Asia	29.4
Others	18.8
All	100.0

(Total Exports: US \$ 314.40 billion)

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Tabulation Of Data And Parts Of A Table

A good statistical table is systematically constructed with several essential parts:

1. Table Number: For identification, especially when there are multiple tables. Usually placed at the top or beginning of the title.
2. Title: A clear, brief, and unambiguous description of the table's contents. Placed above or below the table number.
3. Captions or Column Headings: Labels for each column explaining the data below.
4. Stubs or Row Headings: Labels for each row explaining the data in that row. The leftmost column containing row headings is the stub column.
5. Body of the Table: The main part containing the actual data values. Each cell's value is defined by its row and column.
6. Unit of Measurement: Clearly stated for the figures in the table, often with the title or with stubs/captions if different units are used. Rounding methods for large figures should be indicated.
7. Source: Indicates where the data was obtained from, usually at the bottom of the table.
8. Note: Explains specific features of the data content that are not self-explanatory. Placed at the bottom.

Table 4.5 provides an example showing these parts, tabulating population data by worker status, gender, and location.

Table 4.5: Population of India according to workers and non-workers by gender and location, 2001

Table 4.5 Population of India according to workers and non-workers by gender and location, 2001

Location	Gender	Workers (Crore)			Non-worker (Crore)	Total (Crore)
		Main	Marginal	Total
Rural	Male	17	3	20	18	38
	Female	6	5	11	25	36
	Total	23	8	31	43	74
Urban	Male	7	1	8	7	15
	Female	1	0	1	12	13
	Total	8	1	9	19	28
All	Male	24	4	28	25	53
	Female	7	5	12	37	49
	Total	31	9	40	62	102

Source : Census of India 2001

Note : Figures are rounded to nearest crore

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Diagrammatic Presentation Of Data

This is the third method of presenting data, providing a quick visual understanding compared to textual or tabular forms. Diagrams effectively translate abstract numerical data into easily comprehensible visuals. While possibly less accurate, they are often more impactful. Common types include geometric diagrams, frequency diagrams, and arithmetic line graphs.

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Geometric Diagram

This category includes bar diagrams and pie diagrams. Bar diagrams use rectangular bars, while pie diagrams use sectors of a circle.

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Bar Diagram

Bar diagrams consist of equally spaced rectangular bars of equal width. The height or length of each bar represents the magnitude of the data for a specific class or category. Bars start from a zero baseline. Data can be of frequency or non-frequency type, representing discrete variables or attributes.

Simple Bar Diagram: Used to represent one set of data, e.g., literacy rates of different states (Fig. 4.1). The height of the bar directly corresponds to the value it represents.

Bar diagrams are suitable for discrete variables and attributes (gender, religion, country) and non-frequency data (income, export/imports over years). Bars are often used for time series data.

Multiple Bar Diagram: Used to compare two or more sets of related data simultaneously, e.g., male and female literacy rates of different states in two different years (Fig. 4.2).

Component Bar Diagram: Also called subdiagrams, these divide a single bar into different components to show the size of each part and their relationship to the whole. Each bar represents a total value, and segments within the bar show the proportion of different components. Suitable for data like expenditure patterns or population components (Fig. 4.3).

Component bars are usually shaded or colored differently. To construct, the total value is represented by the full height of the bar, and component heights are proportional. Smaller components are often placed first from the base.

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Pie Diagram

A pie diagram (or pie chart) is a circular diagram where the area of the circle is divided into sectors, with each sector representing a component part proportional to its share of the whole (Fig. 4.4). The values of components are first converted into percentages of the total. The angle each component subtends at the center is calculated by multiplying its percentage share by 3.6° (360°/100). Data represented by a component bar diagram can also be shown as a pie chart after converting to percentages (Table 4.8).

Table 4.8: Distribution of Indian population (2011) by their working status (crores)

Status	Population (Crores)	Per cent	Angular Component (°)
Marginal Worker	12	9.9	36
Main Worker	36	29.8	107
Non-worker	73	60.3	217
All	102	100.0	360

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Frequency Diagram

Used for presenting grouped frequency distributions (data grouped into classes). Types include histogram, frequency polygon, frequency curve, and ogive.

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Histogram

A two-dimensional diagram using rectangles. The base of each rectangle is the class interval (along the X-axis), and the area is proportional to the class frequency (Fig. 4.5). If class intervals are equal, height is proportional to frequency. If unequal, height is adjusted to represent frequency density (frequency divided by class width). Rectangles in a histogram are adjacent for continuous classes. Histograms are drawn only for continuous variables. They can graphically show the mode of a distribution.

Table 4.9: Distribution of daily wage earners in a locality of a town

Daily earning (Rs)	No. of wage earners (f)
45–49	2
50–54	3
55–59	5
60–64	3
65–69	6
70–74	7
75–79	12
80–84	13
85–89	9
90–94	7
95–99	6
100–104	4
105–109	2
110–114	3
115–119	3

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Frequency Polygon

Derived from a histogram by joining the midpoints of the top sides of consecutive rectangles with straight lines (Fig. 4.6). The ends are joined to the base line at the mid-values of zero-frequency classes on each side. The total area under the polygon equals the total frequency. It's useful for comparing multiple distributions.

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Frequency Curve

Obtained by drawing a smooth freehand curve through or as close as possible to the points of the frequency polygon (Fig. 4.7). It doesn't necessarily pass through every point.

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Ogive

Also called a cumulative frequency curve. There are two types: "less than" and "more than" ogives, based on cumulative frequencies. Cumulative frequencies are plotted against class limits. The intersection of the two ogives graphically represents the median of the distribution (Fig. 4.8). The "less than" ogive is non-decreasing, and the "more than" ogive is non-increasing.

Table 4.10: Frequency distribution of marks obtained in mathematics

Marks	Number of students	'Less than' cumulative frequency	'More than' cumulative frequency
0-20	6	6	64
20-40	5	11	58
40-60	33	44	53
60-80	14	58	20
80-100	6	64	6
Total	64

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Arithmetic Line Graph

Also known as a time series graph, this graph plots time (hours, days, years, etc.) on the X-axis and the value of the variable on the Y-axis (Fig. 4.9). Points are joined by lines, helping to visualize trends and seasonality in time series data.

Table 4.11: Value of Exports and Imports of India (Rs in 100 crores)

Year	Exports	Imports
1993-94	698	731
1994–95	827	900
1995–96	1064	1227
1996–97	1188	1389
1997–98	1301	1542
1998-99	1398	1783
1999-2000	1591	2155
2000-01	2036	2309
2001-02	2090	2452
2002-03	2549	2964
2003-04	2934	3591
2004-05	3753	5011
2005-06	4564	6604
2006-07	5718	8815
2007-08	6559	10123
2008-09	8408	13744
2009-10	8455	13637
2010-11`	11370	16835
2011-12	14660	23455
2012-13	16343	26692
2013-14	19050	27154

Source: DGCI&S, Kolkata

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Conclusion

Presenting data in textual, tabular, or diagrammatic forms is essential for making it meaningful and useful. Tables are effective for organizing large data volumes, while diagrams offer quick visual comprehension. Choosing the appropriate presentation method and diagram type depends on the nature of the data and the purpose of the presentation. Mastering these techniques enables effective, comprehensive, and purposeful data presentation.

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