Relative Frequency Distribution
At many times it may be desirable to convert class frequencies into relative class frequencies to show that the percentage of the total number of observations in each class. For e.g., we may be concerned in knowing the percentage of employees earning less than $.2, 000 per month.
In order to convert a frequency distribution into a relative frequency distribution, each of the class frequencies is divided by the total number of frequencies so that the relative frequencies would always provides the total 1.
For illustration given above, the relative frequency distribution would be as follows:
|
marks
|
frequency
|
Relative frequency
|
Obtained by
|
|
0-10
|
2
|
0.04
|
2+50
|
|
10-20
|
5
|
0.10
|
5+50
|
|
20-30
|
4
|
0.08
|
4+50
|
|
30-40
|
5
|
0.10
|
Etc
|
|
40-50
|
8
|
0.16
|
|
|
50-60
|
8
|
0.16
|
|
|
60-70
|
7
|
0.14
|
|
|
70-80
|
5
|
0.10
|
|
|
80-90
|
4
|
0.08
|
|
|
90-100
|
2
|
0.04
|
|
|
|
N=50
|
|
|
Illustration: Represent the following information in a suitable tabular form with the proper rulings and headings:
The annual report of Ishapore Public Library reveals the following points, regarding the reading habits of their members:
Out of total 3713 books issued to the members in the month of July 2009, 2100 were fictions. There were 467 members of the library during that period and they were classified into five classes A, B, C, D & E. The no. of members belonging to the first four classes were respectively, 15, 176, 98 and 129; and the number of fictions issued to them were 103, 1187, 647 & 58 respectively. The number of books, other than the text-books and fictions issued to these four classes of members were respectively 4390, 217 and 341. The text books were issued only to members belonging to the classes C and D .The numbers of text-books issued to them were respectively 3317 and 160.
During the same time period, 1246 periodicals were issued to members of class B, 45 to class D and 315 to class E.
To the members of the classes B, C, D and E the number of other journals issued over the last month, though there was a corresponding decrease by 6.1% in the number of periodicals and journals issued to members.
Solution: As complete information is not given we will first obtain the missing values on the basis of given information.
(i) Total no. of members = 467
No. of members belonging to class E = 467 - (15 + 176 + 98 + 129) = 49
(ii) Total no. of books (fictions, text-books and other books) issued = 3713
Total no. of text books issued = 3 + 317 + 160 = 480
Total number of fictions issued = 2100
Total no of books issued = 3713 - (2100 + 480) = 1133
(iii) Total no. of periodicals (technical journals and other journals) issued = 1246
No. of technical journals = 396
No. of other journals = 1246 - 396 = 850
No. of journals issued to class A = 850 - (419 + 26 + 231 + 99) = 75
Figures for last month (May)
Books: since it is reported that there is an increase of 3.9% in the number of books issued in June over the last month, we have:
(a) The total no. of books issued in the last month = 3713 × 100/103.9 = 3573.63 or 3574
(b) the total no. of text books issued last month = 2100 × 100/103.9 = 2021.17 or 2021
(c) The total no. of text books issued last month = 480 × 100/103.9 = 461.98 or 462
Therefore, total no. of other books issued last month = 3574 - (2021 + 462) = 1091
Periodicals: since, a decrease of 6.1 percent is reported in the issue of periodicals in June over the last month, we have
(a) the total periodicals issued last month = 1246 × 100/93.9 = 1326.94 or 1327
(b) The no. of technical journals issued last month = 396 × 100/93.9 = 421.72 or 422
(c) No. of other journals issued last month = 1327 - 422 = 905.