Concept of Histogram with Examples

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A two dimensional frequency density diagram is called a histogram. A histogram is a diagram which represents the class interval and frequency in the form of a rectangle. There will be as many adjoining rectangles as there are class intervals.

To draw a histogram, follow the steps stated below

(1) Mark class intervals on X-axis and frequencies on Y-axis.

(2) The scales for both the axes need not be the same.

(3) Class intervals must be exclusive. If the intervals are in inclusive form, convert them to the exclusive form.

(4) Draw rectangles with class intervals as bases and the corresponding frequencies as heights.

The class limits are marked on the horizontal axis and the frequency is marked on the vertical axis. Thus a rectangle is constructed on each class interval.

If the intervals are equal, then the height of each rectangle is proportional to the corresponding class frequency.

If the intervals are unequal, then the area of each rectangle is proportional to the corresponding class frequency.

Draw a histogram for the following data:

In the above example, the intervals are exclusive. Now, let us consider an example with inclusive intervals.

The daily wages of 50 workers, in rupees, are given below:

In table (a), the class intervals are inclusive. So we convert them to the exclusive form as shown in table (b).

Table (a)

Table (b)

(i) The class intervals are made continuous and then the histogram is constructed.

(ii) A kink or a zig - zag curve is shown near the origin. It indicates that the scale along the horizontal axis does not start at the origin.

(iii) The horizontal scale and vertical scale need not be the same.

Distribution of shops according to the number of wage - earners employed at a shopping complex is given below:

Illustrate the above table by a histogram, showing clearly how you deal with the unequal class intervals.

When the intervals are unequal, we construct each rectangle with the class intervals as base and frequency density as height.

Frequency density

Comparison of Histogram and Bar Graph