Chapter 4 — Presentation of Data

Chapter 4 deals with how to present voluminous collected data in a compact, usable, and easily comprehensible form. It covers three forms of presentation: textual or descriptive, tabular, and diagrammatic, explaining when and how to use each.

The three forms are textual or descriptive presentation (data described within text), tabular presentation (data arranged in rows and columns), and diagrammatic presentation (data represented through diagrams). Diagrammatic presentation provides the quickest understanding of the actual situation.

Textual presentation describes data within the text. It is more suitable when the quantity of data is not too large and can help emphasise certain points. However, its serious drawback is that one has to go through the complete text of the presentation for comprehension.

The four types are qualitative classification (by attributes such as social status, nationality, or sex), quantitative classification (by measurable characteristics such as age, height, or income), temporal classification (by time, such as hours, days, months, or years), and spatial classification (by place, such as village, district, state, or country).

A good statistical table must have: (i) table number for identification, (ii) title describing the table's contents, (iii) captions or column headings at the top of each column, (iv) stubs or row headings for each row, (v) body containing the actual data, (vi) unit of measurement, (vii) source written at the bottom, and (viii) a note explaining specific features not explained elsewhere.

A histogram is a two-dimensional diagram with rectangles whose bases are class boundaries and areas are proportional to class frequency. Unlike a bar diagram, there is no space between consecutive rectangles in a histogram, and a histogram is drawn only for continuous variables. In a bar diagram the width is arbitrary and spacing must be left between bars, while in a histogram the width of the rectangle is as important as its height.

A histogram can give the value of the mode of the frequency distribution graphically. The x-coordinate of the dotted vertical line drawn on the histogram at the tallest rectangle gives the mode of the frequency distribution.

An ogive is also called a cumulative frequency curve. There are two types: 'less than' ogive (cumulative frequencies plotted against upper class limits) and 'more than' ogive (plotted against lower class limits). An important feature is that the intersection point of the two ogives gives the median of the frequency distribution.

A multiple bar diagram is used for comparing two or more sets of data side by side, such as income and expenditure for different years or marks in different subjects. A component bar diagram (also called a sub-diagram) divides each bar into its component parts to show the sizes of those parts and the relationship among them, and is usually shaded or coloured suitably.

In a pie diagram, values of each category are first expressed as a percentage of the total. A circle is treated as having 100 equal parts of 3.6° each (since 360°/100 = 3.6°). To find each component's angle, its percentage figure is multiplied by 3.6°. The circle is then divided into parts by drawing straight lines from the centre to the circumference.

An arithmetic line graph, also called a time series graph, plots time (hour, day, week, month, year, etc.) along the x-axis and the value of the variable along the y-axis. Joining the plotted points gives the arithmetic line graph. It helps in understanding long-term trend and periodicity in time series data.

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