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| Histogram |
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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. |
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| To draw a histogram, follow the steps stated below |
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| (1) Mark class intervals on X-axis and frequencies on Y-axis. |
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| (2) The scales for both the axes need not be the same. |
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| (3) Class intervals must be exclusive. If the intervals are in inclusive form, convert them to the exclusive form. |
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| (4) Draw rectangles with class intervals as bases and the corresponding frequencies as heights. |
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| 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. |
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| If the intervals are equal, then the height of each rectangle is proportional to the corresponding class frequency. |
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| If the intervals are unequal, then the area of each rectangle is proportional to the corresponding class frequency. |
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| Draw a histogram for the following data: |
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| In the above example, the intervals are exclusive. Now, let us consider an example with inclusive intervals. |
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| The daily wages of 50 workers, in rupees, are given below: |
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| In table (a), the class intervals are inclusive. So we convert them to the exclusive form as shown in table (b). |
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| Table (a) |
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| Table (b) |
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| (i) The class intervals are made continuous and then the histogram is constructed. |
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| (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. |
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| (iii) The horizontal scale and vertical scale need not be the same. |
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| Distribution of shops according to the number of wage - earners employed at a shopping complex is given below: |
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| Illustrate the above table by a histogram, showing clearly how you deal with the unequal class intervals. |
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| When the intervals are unequal, we construct each rectangle with the class intervals as base and frequency density as height. |
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Frequency density  |
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