What is a histogram? How do we draw it?
Histograms
It consists of a number of rectangles, those are vertically adjacent. Class intervals are taken on X-axis and frequencies on Y-axis. Rectangles are formed of the height proportionate to their frequencies.
Image Source: mspoodry180.files.wordpress.com/2012/10/histogram.jpg
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All the class intervals should be equal. In case it is not there, we make it so, as we will see in the coming examples.
Moreover series must be exclusive for Histogram, Ogive and Frequency polygon. If it is in any other form e.g. inclusive, open end, or cumulative, it must first be converted into exclusive series.
These can be of two types:
- Histograms with equal class intervals
- Histograms with Unequal class intervals
The technique of constructing histogram is as follows:
- For distribution having equal class-intervals.
- For distribution having unequal class intervals.
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When class-intervals are equal, take frequency on Y axis, variable on X-axis and construct adjacent rectangles.
In such cases the height of the rectangles will be proportional to the frequency; When class-intervals are unequal, a correction of unequal class-intervals must be made. The correction consists of finding for each class the frequency density or the relative frequency density. The frequency density is the frequency for that class divided by the width of that class. A histogram is constructed when these density values would have the same general appearance as the corresponding graphical display developed from equal class intervals.
For making adjustment we take the class which has the lowest class-interval and adjust the frequency of other classes in the following manner. If one class-interval is twice as wide as the one having lowest class interval, we divide the height of its rectangle by two, if it is three times more we divide the height of its rectangle by three and so on.