Types of Series and Frequency Distribution

Broadly speaking, the statistical series are of two types viz.

(i)            Time series and

(ii)          Frequency series.

 Time Series

A series of data that is arranged chronologically, or in relation to time is called a Time Series. The following is an example of a Time Series.

Example:

Years	No. of Students
20002001 2002 2003 2004	48 64 128 256 300

Frequency Series

A series of data that is formed along with the frequencies of their occurrences is called a frequency series. A frequency series is again, of three types viz.

1. Individual series     2. Discrete series, and    3. Continuous series.

Individual Series

An individual series is one in which each value of the variable occurs for only once. In other words, the frequency of occurrence of all the values in such a series is only one. As such, essentially such series are displayed without the frequency column. The following are the examples of individual series.

Example1                  Example2     Example 3

Marks     No.1  Students      Mark               Roll No.           Marks

 50              1                                      90                           1                    80

60                1                                      80                          2                   90

70                1                                      70                          3                   70

80                 1                                     60                          4                   50

90                 1                                     50                          5                   60

An individual series may be arranged either in ascending, or in descending, or in any other orders as it would suit the desired analysis. In the examples 1 above, the series has been arranged in ascending order, while in the example 3 above, the series has been arranged in order of the roll numbers of the students.

Array

When an individual series is arranged in some order i.e., ascending, or descending order, it is called an array.

Discrete Series

A discrete series is one in which the different values of a variable are shown in a discontinuous manner along with their respective frequencies and at least one of the values has a frequency of more than one. Such a series can also be arranged either in ascending, or in descending order.

The following are the examples of discrete series.

                              Example                                                                                                Example                                                    

                       In sending order                                                                            In descending order

    Weekly wages Rs.       No. of Workers                                                 Marks           No. of students

                70                                  15                                                                                  90                           15

                84                                  24                                                                                  80                           17

                105                                50                                                                                 70                           22

                140                                12                                                                                 60                           13

                175                                 4                                                                                  50                           3

Continuous Series 

A continuous series is one which the different values of the variables are stated in a continuous manner along with their respective frequencies. Such series can be arranyed either in ascending, or in descending order. Further, such series can be stated either in the form exclusive, or in the from of inclusive class intervals along with their respective class frequencies. Furthermore, such series can also be presented either in non-cumulative, or in cumulative from (Less than, or more than) along with their respective frequencies.