Distinguish between a frequency array and a frequency distribution.

Frequency Array : We obtain a frequency array if the variable x is discrete and we have frequencies corresponding to each value (there are no class intervals). Let us illustrate with the following example.

Example : A survey of 100 households was carried out to obtain information on their size, i.e., the number of members of households. The results of the survey are classified as a frequency array in table below :

Frequency Array of Size of Households

The column (1) of the table gives the values which the variable x (size of the households) takes; and column (2) gives the corresponding frequencies (number of households). Thus, there are 5 households whose size is 1, there are 15 households of size 2, and so on.

Frequency Distribution : The largest value of X is B and smallest value is A. Then X = B – A is the total range of X. A large range indicates that the values of X are spread over a large interval or the variation of value of X is large. A small range indicates smaller variation in the values of X. Thus, the range is measure of variation (or dispersion) of X.

For example : Suppose we have data on monthly income of 10,000 individuals, the maximum of which is Rs.50,000 and minimum is Rs. 1,000. Thus, the range is Rs.49,000. We observe that majority of individuals say, 70% have small incomes close to Rs. 5,000 and minority, say 2% have income close to Rs.30,000.

In order to get a better idea about the distribution of values within the range, we should subdivide the total range into a number of class intervals and find out the number of values in different classes.