Elementary Statistics (1+1)

4.2.2.4 ‘Exclusive’ Method

When the class intervals are so fixed that the upper limit of one class is the lower limit of the next class it is known as the exclusive method of classification. The following data are classified on this basis :

Income (Rs.)	No. of Persons
1000 – 1100 1100 – 1200 1200 – 1300 1300 – 1400 1400 – 1500 1500 – 1600	50 100 200 150 40 10
TOTAL	550

It is clear that the ‘exclusive’ method ensures continuity of data in as much as the upper limit of one class is the lower limit of the next class. Thus, in the above example, there are 50 persons whose income is between Rs.1000 and Rs.1099.99. A person whose income is Rs.1100 would be included in the class 1100-1200. This method is widely followed in practice. However, it is confusing to a layman who has no knowledge of statistics. For example, if a questionnaire includes an item asking the respondent the number of times he visits the Super Bazar in a month and he is required to tick one of the categories : 5-10, 10-15 and 15-20, a person who visits the Super Bazar 10 times may 5-10 or 10-15. In the absence of any specific instructions, some people may tick the class 5-10 while others 10-15. Hence whenever this method is used it is necessary to give clear instructions in the questionnaire. However, the reader should note that if class intervals are given like 0-10, 10-15, etc. it is always presumed that upper limit is exclusive, i.e. the item of that value is not included in that class.

A better way of expressing the classes when exclusive method is followed is :

Income (Rs.)	No. of Persons
1000 but under 1100 1100 but under 1200 1200 but under 1300 1300 but under 1400 1400 but under 1500 1500 but under 1600	50 100 200 150 40 10
TOTAL	550

It avoids confusion of the type when classes are expressed 1000-1100, 1100-1200, 1200-1300, etc. It is suggested that in practice this approach should be preferred over the previous one.