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FREQUENCY DISTRIBUTION

The frequency distribution is a tabulation of data which are obtained from measurement or observation or experiment, arranged in ascending or descending order.

Let us consider the resistance of 50 units of certain electrical product :

 

The following table shows the simple frequency distribution of these data with all data and their frequencies of occurrences.

When there is a large amount of highly variable data, the above frequency distribution can become large. The data may be grouped into classes to provide a better presentation. But there is no rule about the number of classes to be taken for the given data. In the above, the lowest data is 2.7 and the highest data is 4.4. Let us consider six classes of equal width and the following table is called grouped frequency distribution.

In the above table, the left side value of each class, i.e., 2.7, 3.0, ...... , 4.2 is called lower class limit and the right side of each class, i.e., 2.9, 3.2, ........ , 4.4 is called upper class limit. The width of each class is 0.2.

In this example the classes are not continuous. To make it continuous we add 0.05 to the upper limits and subtract 0.05 from the lower limits where 0.05 + 0.05 = 0.1 is the difference  between the previous upper limit and the next lower limit between any two consecutive classes. In this case, the class limits are called class boundaries. The middle value of any class is called class mark. So we obtain the following table :