Graphical representation of Cumulative Frequency Distribution

As we all know, pictures speak better than words. A graphical representation helps us in understanding given data at a glance. In Class IX, we have represented the data through bar graphs, histograms and frequency polygons. Let us now represent a cumulative frequency distribution graphically.

For example, let us consider the cumulative frequency distribution given in example.

For drawing ogives, it should be ensured that the class intervals are continuous, because cumulative frequencies are linked with boundaries, but not with limits.

Recall that the values 10, 20, 30, ..., 100 are the upper boundaries of the respective class intervals. To represent the data graphically, we mark the upper boundaries of the class intervals on the horizontal axis (X-axis) and their corresponding cumulative frequencies on the vertical axis (Y-axis), choosing a convenient scale.

Now plot the points corresponding to the ordered pairs given by (upper boundary, corresponding cumulative frequency), i.e., (10, 5), (20, 8), (30, 12), (40, 15), (50, 18), (60, 22), (70, 29), (80, 38), (90, 45), (100, 53) on a graph paper and join them by a free-hand smooth curve. The curve we get is called a cumulative frequency curve, or an ogive (of the less than type).

The term 'ogive is pronounced as 'ojeev' and is derived from the word ogee. An ogee is a shape consisting of a concave arc flowing into a convex arc, so forming an S-shaped curve with vertical ends. In architecture, the ogee shape is one of the characteristics of the 14th and 15th century Gothic styles.

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The annual profits earned by 30 shops in Sangareddy locality give rise to the following distribution:

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