Page 37 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes There are two types of cumulative frequency distributions.
Less than cumulative frequency distribution: It is obtained by adding successively the frequencies
of all the previous classes including the class against which it is written. The cumulate is started
from the lowest to the highest size.
More than cumulative frequency distribution: It is obtained by finding the cumulate total of
frequencies starting from the highest to the lowest class
These frequency distributions, for the data on the measurements of diameter of a wire, are
shown in Table I and Table II respectively.

Converting a cumulative frequency distribution table into a frequency distribution

The above cumulative frequency distribution table can be presented in a frequency distribution
as follows:
Class
Intervals Frequency
1.00 - 1.10 4
1.10 - 1.20 7
1.20 - 1.30 10
1.30 - 1.40 14
1.40 - 1.50 20
1.50 - 1.60 13
1.60 - 1.70 9
1.70 - 1.80 6
1.80 - 1.90 4
1.90 - 2.00 3
Total 90

2.3.5 Frequency Density

Frequency density in a class is defined as the number of observations per unit of its width.
Frequency density gives the rate of concentration of observations in a class:
Frequency of the class
Frequency Density =
Width of the class
Table showing Frequency Density of Various Classes:

Class Frequency
Intervals Frequency Density
1.00 - 1.10 4 40
1.10 - 1.20 7 70
1.20 - 1.30 10 100
1.30 - 1.40 14 140
1.40 - 1.50 20 200
1.50 - 1.60 13 130
1.60 - 1.70 9 90
1.70 - 1.80 6 60
1.80 - 1.90 4 40
1.90 - 2.00 3 30
Total 90

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