Presentation of Data
Introduction
Once data has been collected and organised, the next logical step is its presentation. Raw, unorganised data is difficult to understand, and even classified data in a frequency distribution can be dense and unappealing. The purpose of data presentation is to display the organised data in a clear, concise, and attractive manner that can be easily understood, interpreted, and analysed. An effective presentation highlights the salient features of the data, facilitates comparisons, and makes it possible to draw preliminary conclusions.
There are three primary modes of data presentation:
- Textual or Descriptive Presentation: Data is presented within the text of a paragraph.
- Tabular Presentation: Data is presented in a systematic structure of rows and columns.
- Diagrammatic Presentation: Data is presented in the form of attractive charts, diagrams, and graphs.
The choice of presentation method depends on the nature of the data and the objective of the study. This chapter will explore these different methods in detail.
Textual Presentation Of Data
In textual presentation, data is described as a part of the text of the study. It is a narrative form of presenting data. This method is generally used when the quantity of data is not very large and a researcher wants to embed the data within the flow of the discussion.
Suitability and Limitations
Suitability: This method is suitable for small datasets where only a few observations need to be highlighted. It can provide context and qualitative insights that might be lost in a table or a chart.
Limitations: For large datasets, this method is entirely unsuitable. It becomes tedious, cumbersome, and difficult for the reader to grasp the key takeaways. The reader has to go through the entire text to comprehend the data, which makes comparison and analysis challenging.
Example 1. Present the following information in a textual format.
A recent survey in a factory of 5000 workers revealed that 4000 workers were skilled and 1000 were unskilled. Among the skilled workers, 3500 were male, while among the unskilled workers, only 200 were male.
Answer:
A survey was conducted at a factory with a total of 5000 workers. The findings indicated that a vast majority, 4000 workers (or 80% of the workforce), were skilled, while the remaining 1000 workers (or 20%) were unskilled. A gender-wise breakdown revealed that among the 4000 skilled workers, 3500 were male, leaving 500 as female. In contrast, within the smaller group of 1000 unskilled workers, only 200 were male, meaning that 800 were female.
Tabular Presentation Of Data
Tabulation is the process of presenting classified data in a systematic and organised manner, arranged in rows and columns. A table is a structured format that helps to simplify complex data and facilitate comparison. It presents data more clearly than a textual presentation and provides a basis for diagrammatic representation and statistical analysis.
The classification of data in a table depends on the characteristics of the data.
Qualitative Classification
When the classification is done according to attributes or qualities that are not numerical, such as gender, nationality, or literacy, it is called qualitative classification.
Example: A table showing the number of students in a college classified by gender (Male/Female) and faculty (Arts/commerce/Science).
Quantitative Classification
When the classification is based on characteristics that are quantitative in nature, i.e., can be measured numerically like marks, income, or height, it is called quantitative classification.
Example: A table showing the distribution of households according to their monthly income brackets.
Temporal Classification
In temporal classification, the data is classified according to time. Time can be in years, months, weeks, etc.
Example: A table showing India's GDP from the year 2011 to 2020.
Spatial Classification
When the classification is done on the basis of geographical location like country, state, city, or district, it is called spatial classification.
Example: A table showing the production of rice in various states of India.
Tabulation Of Data And Parts Of A Table
A good statistical table is a work of art. It should be constructed carefully to be clear, concise, and self-explanatory. A table has several essential parts, each serving a specific purpose.
The main components of a table are:
Table Number: Each table should be numbered for easy identification and reference. For example, 'Table 4.1'.
Title: The title is a brief and clear description of the contents of the table. It should be complete and explain 'what, where, and when' the data relates to.
Captions or Column Headings: These are the headings for the vertical columns. They should be clear and concise.
Stubs or Row Headings: These are the headings for the horizontal rows. They describe the data presented in the rows.
Body of the Table: This is the main part of the table containing the numerical data. The individual data cells are the intersection of a row and a column.
Unit of Measurement: If the unit of measurement for the data is not specified in the stubs or captions, it should be mentioned at the top of the table (e.g., 'in Crores', 'in Thousands').
Source: It is important to mention the source from which the data has been collected. This adds to the credibility of the data.
Note: A footnote can be added below the table to clarify anything about the data that is not self-evident from the title, stubs, or captions.
Example of a well-structured table:
| Census Year (Stub Head) | Male (Caption) | Female (Caption) | Total (Caption) |
|---|---|---|---|
| 1951 (Stub) | 18.55 (Body) | 17.56 (Body) | 36.11 (Body) |
| 1961 (Stub) | 22.63 (Body) | 21.29 (Body) | 43.92 (Body) |
| ... | ... | ... | ... |
| 2011 (Stub) | 62.37 (Body) | 58.65 (Body) | 121.02 (Body) |
| Source: Census of India, various issues. | |||
| Note: Data for 1981 does not include Assam. | |||
Diagrammatic Presentation Of Data
Diagrammatic presentation is a highly effective method of presenting statistical data. Diagrams are visually attractive and make the data easy to understand and remember. They are particularly useful for making comparisons and for presenting data to a general audience that may not be comfortable with tables of numbers. The saying "a picture is worth a thousand words" is very true for statistical diagrams.
Geometric Diagram
These diagrams, such as bar diagrams and pie diagrams, represent data using geometric figures.
Bar Diagram
A bar diagram represents data using a set of rectangles (bars) of uniform width. The height (or length) of the bars is proportional to the magnitude of the data. The bars are drawn on a common base with equal spacing between them.
- Simple Bar Diagram: Used to represent data on a single variable. For example, the birth rate of India over different years.
- Multiple Bar Diagram: Used to compare the values of two or more variables simultaneously. For example, comparing the literacy rates of males and females across different states. The bars for each variable are drawn adjacent to each other.
- Component Bar Diagram (or Sub-divided Bar Diagram): Used to show the breakdown of a total value into its various components. A single bar represents the total, and it is divided into segments representing the components.
Example 2. Data on the production of foodgrains in India for two years is given below. Represent this using a multiple bar diagram.
| Crop | Production 2020 (Million Tonnes) | Production 2021 (Million Tonnes) |
|---|---|---|
| Rice | 122 | 127 |
| Wheat | 108 | 109 |
| Pulses | 23 | 25 |
Answer:
To create a multiple bar diagram, we would have the crops (Rice, Wheat, Pulses) on the x-axis and production (in Million Tonnes) on the y-axis. For each crop, we would draw two adjacent bars: one representing the production in 2020 and the other for 2021. A legend or key would be used to distinguish between the bars for the two years (e.g., blue bar for 2020, green bar for 2021). This would allow for easy comparison of the production of each crop across the two years.
Pie Diagram (or Pie Chart)
A pie diagram is a circle divided into sectors, where the area of each sector is proportional to the magnitude of the component it represents. It is used to show the breakdown of a total into its constituent parts (i.e., percentage shares).
Derivation of Sector Angle:
The total angle in a circle is $360^{\circ}$. This total angle is divided among the components in proportion to their values.
$ \text{Angle of a sector} = \frac{\text{Value of the Component}}{\text{Total Value}} \times 360^{\circ} $
Example: If a family's monthly income is ₹50,000 and their expenditure on food is ₹15,000, the angle of the sector representing food would be $ (\frac{15000}{50000}) \times 360^{\circ} = 0.3 \times 360^{\circ} = 108^{\circ} $.
Frequency Diagram
These diagrams are used to present frequency distributions.
Histogram
A histogram is a two-dimensional diagram used for presenting a continuous frequency distribution. It is a set of adjacent rectangles, where the class intervals are marked on the x-axis and the frequencies on the y-axis. Unlike a bar diagram, there are no gaps between the rectangles. The area of each rectangle is proportional to the class frequency.
For unequal class intervals, the heights of the rectangles must be adjusted. We plot frequency density on the y-axis instead of frequency.
$ \text{Frequency Density} = \frac{\text{Frequency of the class}}{\text{Width of the class}} $
Frequency Polygon
A frequency polygon is a line graph formed by joining the mid-points of the tops of the rectangles of a histogram. To complete the polygon, the ends are joined to the x-axis at the mid-points of the imaginary classes before the first class and after the last class.
Frequency Curve
A frequency curve is simply a smooth freehand curve drawn through the points of a frequency polygon. It provides a better approximation of the distribution of the entire population.
Ogive (Cumulative Frequency Curve)
An ogive is the graphical representation of a cumulative frequency distribution. There are two types:
- Less than Ogive: This is obtained by plotting the 'less than' cumulative frequencies against the upper class limits. It is an upward sloping curve. - More than Ogive: This is obtained by plotting the 'more than' cumulative frequencies against the lower class limits. It is a downward sloping curve.
The point where the 'less than' and 'more than' ogives intersect gives the value of the median.
Arithmetic Line Graph (or Time Series Graph)
This is a graph used to represent data that changes over a period of time (a time series). Time (e.g., years, months) is plotted on the x-axis and the value of the variable is plotted on the y-axis. The plotted points are then joined by a line to show the trend or changes over time.
Conclusion
The presentation of data is a vital link between the raw, collected information and the final analysis and interpretation. Each method of presentation—textual, tabular, and diagrammatic—has its own unique advantages and is suited for different purposes. Textual presentation is good for small datasets, while tables provide a structured and detailed view. Diagrams and graphs excel at making data visually appealing, easy to grasp, and effective for comparing trends and patterns.
A skilled researcher knows how to choose the most appropriate presentation technique to communicate their findings effectively. A well-constructed table or a clear, accurately drawn diagram can convey a complex story hidden in the data with clarity and impact, making statistics accessible to a wider audience.