Presentation of Data — Study Notes

1. Introduction

After data have been organised into frequency distributions, the next task is to present them in a clear and attractive manner so that their salient features can be grasped quickly. A well-presented table or diagram communicates in seconds what pages of numbers cannot. Presentation of data makes the data easy to understand, facilitates comparison, and prepares the ground for analysis. Poorly presented data, by contrast, confuse the reader and hide the truth.

Data can be presented in three broad ways: textual presentation, tabular presentation, and diagrammatic or graphical presentation. Textual presentation describes data in words and is suited to small data sets. Tabular presentation arranges data in rows and columns, which is the most common and rigorous method. Diagrammatic and graphical presentation uses bars, pies, lines, histograms, polygons and ogives to make the data visually striking and easy to compare.

This chapter explains the essentials of a good table, the components of a table, the general rules of tabulation, the different kinds of diagrams such as bar diagrams and pie charts, and the graphical methods such as histograms, frequency polygons and ogives, along with their construction and uses.

2. Textual Presentation

Textual presentation is the presentation of data in the form of descriptive statements in words. For example: "The production of rice in India was 100 million tonnes in 2020, 105 million tonnes in 2021 and 110 million tonnes in 2022." This method is suitable when the volume of data is small and only a few figures are to be communicated.

The advantages of textual presentation are that it is simple, easy to write and requires no special skill. However, its disadvantages are serious: it is dull, it cannot handle large data sets, it makes comparison difficult, and it consumes much time and space. Hence textual presentation is rarely used alone; it is usually combined with tables and diagrams.

3. Tabular Presentation

Tabular presentation is the arrangement of data in rows and columns, which is the most common and precise method of presenting statistical data. A statistical table is a systematic organisation of data in which related facts are arranged in rows (horizontal) and columns (vertical) so that they can be easily compared and analysed.

A good table is one that is simple, self-explanatory, complete and designed to bring out the desired comparison clearly. The following are the essentials of a good table:

1. The table should be compact, clear and self-explanatory.
2. It should serve the specific purpose of the enquiry.
3. It should be well-labelled with a clear title.
4. It should be easy to read and compare.
5. It should be accurate and complete.
6. Units of measurement should be clearly stated.

4. Components of a Statistical Table

The main components of a table are:

1. Table number: Every table is given a number (e.g. Table 3.1) for easy reference.
2. Title: The title describes the content of the table - what the data are about, where they relate to, and the time period. A good title should be brief, clear and complete.
3. Caption and stub head: The caption is the heading of the columns at the top of the table, and the stub head is the heading of the rows at the left of the table.
4. Head note: A brief explanatory statement given just below the title, often stating the units of measurement.
5. Stub: The left-hand part of the table listing the row headings or items.
6. Body: The main part of the table containing the actual numerical data.
7. Source note: It mentions the source from which the data were taken.
8. Footnote: A note at the bottom of the table giving explanation of any item or figure in the table that requires clarification.

5. General Rules of Tabulation

The general rules for constructing a good table are:

1. The table should be prepared keeping in mind the objective of the enquiry.
2. The title should be brief, clear and complete, indicating what, where and when.
3. The units of measurement should be stated clearly.
4. The rows and columns should be arranged in a logical order, such as alphabetical, chronological or by magnitude.
5. The number of rows and columns should be kept as small as possible.
6. The table should be accurate, complete and free from irrelevant details.
7. The source should be mentioned, and abbreviations and symbols should be explained through a footnote.

6. Diagrammatic Presentation

Diagrams are visual representations of statistical data that make the data attractive and easy to understand. The main types of diagrams are:

1. One-dimensional or bar diagrams: In these diagrams only the length (height) of the bar varies with the magnitude of the data, the width remaining constant. Bars may be vertical (column) or horizontal. Types of bar diagrams include: - Simple bar diagram: Used for a single variable over time, e.g. production in different years. - Multiple or grouped bar diagram: Used to compare two or more related variables side by side, e.g. imports and exports of different years. - Sub-divided or component bar diagram: A single bar is divided into parts showing the components of a total, e.g. production divided into wheat, rice and pulses. - Percentage bar diagram: Bars of equal height representing 100 percent are divided into parts showing the percentage of each component.
2. Two-dimensional or area diagrams: The area of the figure represents the magnitude. The most important is the pie chart or pie diagram, in which a circle is divided into sectors or slices, the angle of each sector being proportional to the magnitude of the component. The angle of each component = (Component value / Total value) x 360 degrees.

7. Graphical Presentation

Graphs differ from diagrams in that they are plotted with the help of a coordinate system, with values on the X-axis and Y-axis. The important graphs are:

1. Histogram: A histogram is a set of adjacent rectangles drawn for a continuous frequency distribution. The class intervals are taken on the X-axis and the frequencies on the Y-axis. For equal class intervals, the area of each rectangle is proportional to the frequency of the class. The histogram represents the frequency distribution graphically.

2. Frequency polygon: A frequency polygon is obtained by joining the mid-points of the tops of the rectangles of the histogram with straight lines. It can also be drawn without a histogram by plotting the mid-values against the frequencies and joining the points. The polygon is closed by joining it to the base at the mid-value points of the imaginary classes at the two ends.

3. Ogive (cumulative frequency curve): An ogive is the graph of a cumulative frequency distribution. Two types are drawn: - Less than ogive: Cumulative frequencies 'less than' the upper limits of the classes are plotted against the upper limits. - More than ogive: Cumulative frequencies 'more than' the lower limits are plotted against the lower limits. The point where the two ogives intersect gives the median of the distribution.

8. Relative Merits and Demerits of Diagrams and Graphs

Diagrams and graphs are attractive, easy to understand, facilitate comparison and make data memorable. They are particularly useful in presentations and for highlighting trends and patterns. However, they have limitations: they cannot present large or very precise data, they give only an approximate picture, they may be misleading if drawn with false base lines or unsuitable scales, and they are not suitable for further statistical calculations. Hence tables, which present precise figures, must always accompany diagrams and graphs.

Quick Revision Tables

Mind Map

Important Diagrams (SVG)

Diagram 1: Types of Bar Diagrams and Pie Chart

Diagram 2: Histogram, Frequency Polygon and Ogive

Common Mistakes

1. Forgetting that in a histogram the rectangles are adjacent (no gaps), and the area of each rectangle is proportional to its frequency.
2. Confusing the frequency polygon with the histogram; the polygon joins mid-values of the tops of rectangles with straight lines.
3. Using a pie chart for comparing magnitudes over time; pie charts are meant to show parts of a whole, while bars compare magnitudes.
4. Making errors in computing the pie angle; angle = (component value / total value) x 360 degrees.
5. Omitting essential components of a table such as title, head note, source and footnote.
6. Drawing a graph without a proper scale or with a false base line, which misrepresents the data.
7. Confusing the less than ogive with the more than ogive; the former cumulates from the lowest class, the latter from the highest.

Exam Tips

1. State the three ways of presenting data: textual, tabular and diagrammatic/graphical.
2. List and explain the components of a statistical table: number, title, caption, stub, head note, body, source, footnote.
3. Distinguish between one-dimensional (bar) and two-dimensional (pie) diagrams.
4. Explain the four types of bar diagrams - simple, multiple, sub-divided and percentage.
5. Give the formula for the pie angle: (component / total) x 360.
6. Explain how to construct a histogram, frequency polygon and ogive, and state the use of the ogive in finding the median.
7. Compare the relative merits and demerits of diagrams and graphs.

Conclusion

This chapter dealt with the presentation of data, the link between organised data and statistical analysis. We saw that data may be presented textually, in tables, or in diagrams and graphs. The statistical table, with its components of title, caption, stub, head note, body, source and footnote, presents data precisely and is the backbone of statistical reporting. Diagrams such as simple, multiple, sub-divided and percentage bars, and the pie chart, make data attractive and easy to compare. Graphs such as the histogram, the frequency polygon and the less than and more than ogives provide a graphical picture of the frequency distribution, and the intersection of the two ogives gives the median. With data thus organised and presented, we are now ready to compute the statistical measures of central tendency, dispersion and correlation in the chapters that follow.