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Unit 3: Classification and Tabulation of Data: Frequency and Cumulative Frequency Distribution

(6) Special Purpose Tables: They are formulated to present some specific information relating to Notes
some specific subject under study. Such tables are also called text or summary tables.
Machine Tabulation

Tables are nor prepared with the help of machines which may be either hand-operated or are operated
with electricity. Use of ‘needle sorting’ is one such machine for tabulation. Similarly ‘Punch Cards’
are also used. The work by these machines is more fast, easy and accurate.
Advantages of machine tabulation are:
(1) Greater accuracy.
(2) Less time required.
(3) Large-scale data can also be handled easily.
(4) Complex procedures like fitting trend lines etc becomes very easy with the help of computer.
(5) No work monotony can be avoided.
(6) Lowers cost by avoiding manual labour.
(7) The results are obtained without much waiting.
3.3 Frequency Distribution

The most important method of organising and summarising statistical data is by constructing a
frequency distribution table. In this method, classification is done according to quantitative magnitude.
The items are classified into groups or classes according to their increasing order in terms of magnitude
and the number of items falling into each group is determined and indicated.
We shall discuss later questions such as how the classes are to be formed and how many classes are
to be taken. We consider now how a frequency distribution table is to be constructed in the case of a
discrete variable by taking a particular example.
Example 1 (a): Suppose that the marks secured by 60 students of a class are as follows:
46, 67, 23, 5, 12, 53, 38, 58, 26, 43,
36, 63, 26, 48, 76, 45, 66, 74, 16, 86,
56, 31, 58, 90, 32, 43, 36, 66, 46, 58,
36, 59, 54, 48, 21, 36, 64, 58, 45, 76,
58, 84, 68, 65, 59, 74, 48, 64, 58, 50,
46, 53, 64, 57, 65, 58, 95, 56, 66, 44.
Statistical Methods
Construct a frequency distribution table.
Marks obtained are divided into 10 groups or intervals as follows:
Marks below 10, between 11 and 20, between 21 and 30, and so on, between 91 and 100. Represent
each mark by a tally (/), for example, corresponding to the mark 46 we put a tally (/ ) in the group 41
to 50; similarly we continue putting tallies for each mark. We continue upto four tallies and the fifth
tally is put crosswise ( \) so that it becomes clear at once that the lot contains five tallies, i.e. there are
five marks. A gap is left after a lot of five tallies, before starting again to mark the tallies after each lot.
The number of tallies in a class or group indicates the number of marks falling under that group. This
number is known as the frequency of that group or corresponding to that class interval. Proceeding
in this way, we get the following frequency table.

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