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**Types of class intervals:**

**Types of class intervals:**

There are three methods of classifying the data according to class intervals –

a) Exclusive method

b) Inclusive method

c) Open-end classes

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**a) Exclusive method:**

**a) 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.

It is clear that the exclusive method ensures continuity of data as much as the upper limit of one class is the lower limit of the next class. In the above example, there are so families whose expenditure is between Rs.0 and Rs.4999.99. A family whose expenditure is Rs.5000 would be included in the class interval 5000-10000. This method is widely used in practice.

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**b) Inclusive method:**

**b) Inclusive method:**

In this method, the overlapping of the class intervals is avoided. Both the lower and upper limits are included in the class interval. This type of classification may be used for a grouped frequency distribution for discrete variable like members in a family, number of workers in a factory etc., where the variable may take only integral values. It cannot be used with fractional values like age, height, weight etc.

This method may be illustrated as follows:

Thus to decide whether to use the inclusive method or the exclusive method, it is important to determine whether the variable under observation in a continuous or discrete one. In case of continuous variables, the exclusive method must be used. The inclusive method should be used in case of discrete variable.

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**c) Open end classes:**

**c) Open end classes:**

A class limit is missing either at the lower end of the first class interval or at the upper end of the last class interval or both are not specified. The necessity of open end classes arises in a number of practical situations, particularly relating to economic and medical data when there are few very high values or few very low values which are far apart from the majority of observations.

**The example for the open-end classes as follows :**