Page 135 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Methodology of Research and Statistical Techniques

Notes in a table which gives the frequency in each group. Such a frequency table gives a better
overall view of the distribution of data and enables a person to rapidly comprehend important
characteristics of the data.
For example, a test of 50 marks is administered on a class of 40 students and the marks
obtained by these students are as listed below in Table 9.1.

Table 9.1

35, 40, 22, 32, 41, 18, 20, 40, 36, 29, 24, 28, 28, 31, 39, 37, 27, 29, 40, 35, 38, 30,
45, 26, 20, 25, 32, 31, 42, 28, 33, 32, 29, 26, 48, 32, 16, 46, 18, 44.

By going through the marks of 40 students listed in Table 9.1, you may be able to see that the
marks vary from 16 to 48, but if you try to comprehend the overall performance it is a difficult
proposition.
Now consider the same set of marks, arranged in a tabular form, as shown in Table 9.2.

Table 9.2
Marks No. of Students
45–49 3
40–44 6

35–39 6
30–34 8
25–29 10
20–24 4

15–19 3
Total 40
From Table 9.2 one can easily comprehend the distribution of marks e.g., 10 students have
scores from 25 to 29, while only 7 students have a score lower than 50% etc. Various terms
related to the tabulation of data are being discussed below:
Table 9.2 shows the marks arranged in descending order of magnitude and their corresponding
frequencies. Such a table is known as frequency distribution. A grouped frequency distribution
has a minimum of two columns—the first has the classes arranged in some meaningful order,
and a second has the corresponding frequencies. The classes are also referred to as class
intervals. The range of scores or values in each class interval is the same. In the given example
the first class interval is from 45 to 49 having a range of 5 marks i.e., 45, 46, 47, 48 and 49. Here
45 is the lower class limit and 49 is the upper class limit. As discussed earlier the score of 45
may be anywhere from 44.5 to 45.5, so the exact lower class limit is 44.5 instead of 45. Similarly,
the exact upper class limit is 49.5 instead of 49. The range of the class interval is 49.5 – 44.5
= 5 i.e., the difference between the upper limit of class interval and the lower limit of class
interval.
For the presentation of data in the form of a frequency distribution for grouped data, a
number of steps are required. These steps are :
1. Selection of non-overlapping classes.
2. Enumeration of data values that fall in each class.
3 . Construction of the table.

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