Elementary Statistics (1+1)

5.2.2 Technique of Constructing Graphs

For constructing graphs, we make use of graph paper. Two simple lines are first drawn which intersect each other at right angles. The lines are known as coordinate axes. The point of intersection is known as the point of origin or the ‘zero’ point. The horizontal line is called the axis of X or ‘abscissa’ and the vertical line the axis of Y or ‘ordinate’. The alternative appellations are X-axis and Y-axis respectively.

O is the point of origin, XOX’ is the axis of X or the ‘abscissa’ and YOY’ the axis of Y or the ‘ordinate’. Both positive as well as negative values can be shown on the graphs. Distances measured towards the right or upward from the origin are positive and those measured towards the left or downwards are negative.

The whole plotting area is divided into four quadrants as shown above. In quadrant I, both the values of X and Y are positive. In quadrant II, Y is positive, X is negative; in quadrant III, both X as well as Y are negative and in quadrant IV, X is positive whereas Y is negative. Since most business data are positive quadrant I is most frequently used.

It is conventional to take the independent variable on the horizontal scale and the dependent on the vertical scale. In case of time series, time is represented on the horizontal sale and the variable on the vertical scale. For each axis a convenient scale is chosen which represents the unit of a variable. The choice is made in such a manner that the entire data is accommodated in the space available. The scale on X-axis and Y-axis need not be identical.

On the arithmetic line graph, the Y scale must begin at zero as origin. Thus the X-axis always runs through this zero origin. The zero line is the base line and the curve is interpreted in terms of distance from this base line. In one special case, when we present graphically a series of changes from a norm of 100% then the 100% line is considered the base line.

Once the scale is chosen equal space would represent equal amounts in case of natural scale. However, in case of ratio scale, it is not so. No hard and fast rule can be laid down about the ratio of the scale on the abscissa and on the ordinate because much would depend upon the given data and the size of the paper. However, conventionally X-axis is taken 1 ½ times as long as Y-axis. But there is no rigidity about it.

After the choice of the scale is made the last step in constructing a graph is to plot the given data by taking the corresponding values of X and Y. The various points so obtained are then joined by line segments.