The arrangement of data according to magnitude or size is called a frequency distribution. It is the method of putting data into different groups which are called class intervals or simply classes. From the frequency distribution comes the concept of grouped data (data presented in frequency distribution) and ungrouped data (data in original form). The concept of frequency distribution and other related terms can be explained with the help of following table.
Class Intervals (C.I)
There are five groups in the above table namely 201 – 210, 211 – 220, 221 – 230, less than 200.5 and 230.5 or more. These groups are called class intervals.
Size or Width of Class Interval
Size or width of class interval is the total number of observations on which a class interval is formed. There are two types of class intervals i.e. equal size class intervals (size of each class interval is same) and unequal size class interval (size of each class interval is different). In the above table size of each class interval is same i.e. 10 (211- 201 = 10 Or 220 – 210 = 10).
Class limits are the opening and closing limits of a class interval. There are two class limits of each interval i.e. Lower Class Limit and Upper Class Limit.
a. Lower class limit
Lower class limit is that limit at which class interval starts for example 201, 211 and 221.
b. Upper class limit
Upper class limit is that limit at which class interval ends e.g. 210, 220 and 230.
c. Open class limit
Open class limit has either no lower class limit or no upper class limit e.g. less than 200.5 and 230.5 or more.
Class Boundaries (C.B)
Class boundaries briefly indicate the exact numbers, for example in above table if the weights are recorded to the nearest pound the class interval 201 – 210 includes all measurements from 200.500 to 210.500. These numbers are called class boundaries.
In case of frequency distribution when data is arranged in different intervals, the actual observations are lost. This loss of information occurs due to significant difference between the results obtained from frequency distribution and results obtained from a raw data. The difference between the two results is called a grouping error. Grouping error can be reduced with the help of following assumptions.
a. The values in each interval concentrate around the centre of the interval
b. The values in each interval spread through out the interval.