Page 33 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes In the example, given above, L = 1.98 and S = 1.03 and n = 8.
Approximate size of a class interval
1.98 1.03
0.1188 or 0.12 (approx.)
8
Before taking a final decision on the width of various class intervals, it is worthwhile to
consider the following points:
(a) Normally a class interval should be a multiple of 5, because it is easy to grasp
numbers like 5, 10, 15, ...., etc.

(b) It should be convenient to find the mid-value of a class interval.
(c) Most of the observations in a class should be uniformly distributed or concentrated
around its mid-value.

(d) As far as possible, all the classes should be of equal width. A frequency distribution
of equal class width is convenient to be represented diagrammatically and easy to
analyse.
On the basis of above considerations, it will be more appropriate to have classes, each,
with interval of 0.10 rather than 0.12. Further, the number of classes should also be revised
in the light of this decision.
L- S 1.98- 1.03 0.95
n = = = =9.5 or 10
Class Interval 0.10 0.10
(rounded to the next whole number)
3. Designation of Class Limits: The class limits are the smallest and the largest observation
in a class. These are respectively known as the lower limit and the upper limit of a class.
For a frequency distribution, it is necessary to designate these class limits very
unambiguously, because the mid-value of a class is obtained by using these limits. As will
be obvious later, this mid-value will be used in all the computations about a frequency
distribution and the accuracy of these computations will depend upon the proper
specification of class limits. The class limits should be designated keeping the following
points in mind:
(a) It is not necessary to have lower limit of the first class exactly equal to the smallest
observation of the data. In fact it can be less than or equal to the smallest observation.
Similarly, the upper limit of the last class can be equal to or greater than the largest
observation of the data.
(b) It is convenient to have lower limit of a class either equal to zero or some multiple
of 5.
(c) The chosen class limits should be such that the observations in a class tend to
concentrate around its mid-value. This will be true if the observations are uniformly
distributed in a class.
The designation of class limits for various class intervals can be done in two ways: (1) Exclusive
Method and (2) Inclusive Method.

1. Exclusive Method: In this method the upper limit of a class is taken to be equal to the lower
limit of the following class. To keep various class intervals as mutually exclusive, the
observations with magnitude greater than or equal to lower limit but less than the upper
limit of a class are included in it. For example, if the lower limit of a class is 10 and its

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