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Chapter 4 Presentation Of Data
This chapter deals with the effective communication of organised data. While tables provide precision, diagrams offer a quick, visual understanding of the information. The chapter covers the three main forms of data presentation: Textual, Tabular, and Diagrammatic. Textual presentation is suitable for small amounts of data, while Tabular Presentation is a systematic arrangement of data in rows and columns, allowing for detailed comparison and analysis. It emphasizes the importance of a properly constructed table, detailing the essential parts of a good table, including the table number, title, captions (column headings), stubs (row headings), body, unit of measurement, and source.
Diagrammatic Presentation is highlighted as a method that translates abstract numbers into a more concrete and easily comprehensible visual form. The chapter describes two main categories of diagrams. First, Geometric Diagrams, which include Bar Diagrams (simple, multiple, and component) and Pie Charts, are excellent for comparing categories. Second, Frequency Diagrams, such as the Histogram, Frequency Polygon, and Ogive (cumulative frequency curve), are used to represent frequency distributions. It also introduces the Arithmetic Line Graph (or time-series graph) for showing how a variable changes over time.
Introduction to Presentation of Data
Once data has been collected and organised, the next step is to present it in a clear, compact, and comprehensible form. Effective presentation makes voluminous data usable and easy to understand. There are three general forms of data presentation:
- Textual or Descriptive Presentation
- Tabular Presentation
- Diagrammatic Presentation
Textual Presentation of Data
In textual presentation, data is described within a paragraph of text. This method is most suitable when the quantity of data is not too large. It allows the presenter to draw attention to and emphasise certain key points within the narrative.
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.
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. While there were 62 crore non-worker population against 40 crore workers in the entire country.
A serious drawback of this method is that a reader has to go through the complete text to understand the data, which can be inefficient for larger datasets. However, it is useful for highlighting specific findings.
Tabular Presentation of Data
In a tabular presentation, data is systematically arranged in rows (read horizontally) and columns (read vertically). The intersection of a row and a column is called a "cell". The primary advantage of tabulation is that it organises data for further statistical analysis and decision-making.
Types of Classification in Tabulation
The classification of data used in tables can be of four kinds:
- Qualitative Classification: Data is classified according to non-numerical attributes like gender, nationality, or social status. For example, Table 4.1 classifies literacy data by the qualitative attributes of sex and location.
- Quantitative Classification: Data is classified based on characteristics that are measurable, such as age, height, income, or production. Classes are formed by assigning limits (e.g., age group 20-30).
- Temporal Classification: Data is categorised according to time. The time period can be in years, months, weeks, or days.
- Spatial Classification: Data is classified on the basis of geographical location, such as country, state, district, or town.
Parts of a Table
A good statistical table is constructed systematically and should contain the following essential parts:
- Table Number: Assigned for identification, usually given at the top (e.g., Table 4.5).
- Title: A clear and brief description of the table's contents, placed just below the table number.
- Captions (or Column Headings): Headings at the top of each column that explain the figures below them.
- Stubs (or Row Headings): Headings for each row, located in the leftmost column.
- Body of the Table: The main part of the table containing the actual numerical data in cells.
- Unit of Measurement: Stated with the title to clarify the units of the data (e.g., 'in crores', 'in tonnes').
- Source: A brief statement at the bottom of the table indicating where the data was obtained from.
- Note: An optional part at the end that explains any specific feature of the data that is not self-explanatory.
Example Table with Parts Labelled. Table 4.5 Population of India according to workers and non-workers by gender and location, 2001
Diagrammatic Presentation: Geometric Diagrams
Diagrammatic presentation is a powerful method that translates abstract numerical data into a more concrete and easily comprehensible visual form. While diagrams may be less precise than tables, they are often more effective in conveying information quickly. Geometric diagrams, such as bar diagrams and pie diagrams, are commonly used.
1. Bar Diagram
A bar diagram consists of a group of rectangular bars of equal width and spacing. The height or length of each bar represents the magnitude of the data for a specific category. Bar diagrams are suitable for both frequency and non-frequency data and can be used for discrete variables and attributes.
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Simple Bar Diagram: Used to represent data for a single characteristic over different categories or time periods.
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Multiple Bar Diagram: Used to compare two or more sets of data simultaneously. For example, comparing male and female literacy rates across states.
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Component Bar Diagram (or Sub-divided Bar Diagram): Used to compare the sizes of different component parts of a whole. Each bar represents a total, and it is sub-divided into segments representing its components. For example, a bar could show the total number of children, with components showing the proportion enrolled and out of school.
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 represents the total (100%), which corresponds to 360°. To find the angle for each component, its percentage is multiplied by 3.6°.
$ \text{Angle of Component} = \text{Percentage of Component} \times 3.6^\circ $
Table 4.8. Distribution of Indian population (2011) by working status (crores)
| Status | Population | Per cent | Angular Component |
|---|---|---|---|
| Marginal Worker | 12 | 9.9 | 36° |
| Main Worker | 36 | 29.8 | 107° |
| Non-worker | 73 | 60.3 | 217° |
| All | 121 (approx) | 100.0 | 360° |
Diagrammatic Presentation: Frequency Diagrams
Data in the form of grouped frequency distributions are generally represented by frequency diagrams. The most important of these are the histogram, frequency polygon, frequency curve, and ogive.
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, and its area is proportional to the class frequency. If the class intervals are of equal width, the height of the rectangles represents the frequency.
A key difference from a bar diagram is that in a histogram, there is no space left between consecutive rectangles, representing the continuous nature of the data. Histograms are drawn only for continuous variables. They can also be used to graphically determine the mode of the frequency distribution.
2. Frequency Polygon
A frequency polygon is a plane bounded by straight lines. It is constructed by joining the midpoints of the tops of the consecutive rectangles of a histogram. To close the polygon, the two end-points are joined to the base line at the mid-points of the two classes with zero frequency, one at the beginning and one at the end of the distribution. It is particularly useful when comparing two or more frequency distributions on the same graph.
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 represents the general shape and pattern of the distribution.
4. Ogive (or Cumulative Frequency Curve)
An ogive is a curve that represents the cumulative frequency distribution. There are two types:
- 'Less Than' Ogive: The cumulative frequencies are plotted against the upper class limits of the respective class intervals. This curve is never decreasing.
- 'More Than' Ogive: The cumulative frequencies are plotted against the lower class limits of the respective 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.
Arithmetic Line Graph (or Time Series Graph)
An arithmetic line graph, also known as a time series graph, is used to represent data that changes over a period of time. In this graph, time (e.g., years, months, days) is plotted along the X-axis, and the value of the variable is plotted along the Y-axis. The plotted points are then joined by a line.
This type of graph is extremely useful for understanding trends, periodicity, and fluctuations in data over a long period. For example, it can be used to show the changes in a country's exports and imports over several years.
Table 4.11. Value of Exports and Imports of India (₹ in 100 crores)
| Year | Exports | Imports |
|---|---|---|
| 1993-94 | 698 | 731 |
| ... | ... | ... |
| 2013-14 | 19050 | 27154 |
Interpretation: The graph clearly shows that for the entire period, India's imports were higher than its exports. Both exports and imports began to rise rapidly after 2001-02, and the gap between them also widened significantly during this time.
NCERT Questions Solution
Question 1. Bar diagram is a
(i) one-dimensional diagram
(ii) two-dimensional diagram
(iii) diagram with no dimension
(iv) none of the above
Answer:
Question 2. Data represented through a histogram can help in finding graphically the
(i) mean
(ii) mode
(iii) median
(iv) all the above
Answer:
Question 3. Ogives can be helpful in locating graphically the
(i) mode
(ii) mean
(iii) median
(iv) none of the above
Answer:
Question 4. Data represented through arithmetic line graph help in understanding
(i) long term trend
(ii) cyclicity in data
(iii) seasonality in data
(iv) all the above
Answer:
Question 5. Width of bars in a bar diagram need not be equal (True/False).
Answer:
Question 6. Width of rectangles in a histogram should essentially be equal (True/False).
Answer:
Question 7. Histogram can only be formed with continuous classification of data (True/False).
Answer:
Question 8. Histogram and column diagram are the same method of presentation of data. (True/False)
Answer:
Question 9. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)
Answer:
Question 10. Median of a frequency distribution cannot be known from the ogives. (True/False)
Answer:
Question 11. What kind of diagrams are more effective in representing the following?
(i) Monthly rainfall in a year
(ii) Composition of the population of Delhi by religion
(iii) Components of cost in a factory
Answer:
Question 12. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?
Answer:
Question 13. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?
Answer:
Question 14. The Indian Sugar Mills Association reported that, ‘Sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off-take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’
(i) Present the data in tabular form.
(ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why?
(iii) Present these data diagrammatically.
Answer:
Question 15. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.
| Year | Agriculture and allied sectors | Industry | Services |
|---|---|---|---|
| 1994–95 | 5.0 | 9.2 | 7.0 |
| 1995–96 | –0.9 | 11.8 | 10.3 |
| 1996–97 | 9.6 | 6.0 | 7.1 |
| 1997–98 | –1.9 | 5.9 | 9.0 |
| 1998–99 | 7.2 | 4.0 | 8.3 |
| 1999–2000 | 0.8 | 6.9 | 8.2 |
Represent the data as multiple time series graphs.
Answer: