Numerical data or raw data can be classified in any of the two ways:
(1) Ordered Array or Individual Series
(II) Frequency Distribution:
(a) Discrete Frequency Distribution or Discrete Series
(b) Continuous Frequency Distribution or Continuous Series
(1) Ordered Array or Individual Series
An ordered array or individual series is an orderly arrangement of data according to the ascending or descending order of magnitude. So, in order to prepare an array, the only thing to be done is to arrange the data or various values of variable in ascending or descending order of magnitude. An array may be useful if the data are small, but if the variable takes a large number of values, an array becomes unwieldy.
In individual series of distribution the frequency of every variable is "1".
Example 1. Following data relate to the pocket expenses (rupees) of 10 students of B.Com. II class. Array them in ascending and descending order: 50, 20, 30, 15, 45, 40, 35, 25, 20, 43
(II) Frequency Distribution
The frequency distribution is a statistical table which shows the values the variable arranged in order of magnitude, either individually or in groups, and also the corresponding frequencies side by side. There are two types of frequency distributions:
(a) Discrete frequency distribution
(b) Grouped frequency distribution.
(a) Discrete Frequency Distribution:
It is a statistical table which shows the values of variable individually and also the corresponding frequencies side by side. The construction of discrete frequency distribution is very simple. In its construction, we count the frequencies of the various items. To find the frequency of a particular item, we make use of tally bars. Each tally bar indicates the presence of one value of the item. Tally bars are used in the form of 'Four and Cross Method' If the value of the item is repeated five times, a cross is put on four lines
(b) Grouped Frequency Distribution:
It is a statistical table which shows the values of variable individually and also the corresponding frequencies side by side.
Example:-
Daily wages (१). No. Of workers
40-50. 7
50-60. 12
60-70. 8
70-80. 6
80-90. 2
Total 35
Useful terms associated with Grouped Frequency Distribution
For a detailed study of grouped frequency distribution, it is necessary to define and understand the following terms:
(a) Class interval, or Class: It is a group of numbers in which items are placed such as 10-20, 20-30, etc.
(b) Class frequency: The number of observations falling within a class is called its class frequency. It is denoted by 'f.
(c) Class limits: Each class is located between two numbers. These two numbers constitute class limits. The lowest value of a class is its lower limit and the higher value is termed as upper limit. For example, in the class 10-20, the lower limit is 10 and the upper limit is 20.
(d) Class mark (or mid-value): It is the average value of the upper limit (l2) and the lower limit (l1).
Symbolically,
M.V.(m)= (L1 + L2)/2
(e) Width or Magnitude of the class: The width or size or magnitude of a class is the difference between its lower and upper class limits. Symbolically,
i=L2 - L1
where, i = is the size of the class interval.
