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Unit 2: Classification of Data

1. Number of Class Intervals: Though there is no hard and fast rule regarding the number of Notes
classes to be formed, yet their number should be neither very large nor very small. If there
are too many classes, the frequency distribution appears to be too fragmented to reveal
the pattern of behaviour of characteristics. Fewer classes imply that the width of the class
intervals will be broad and accordingly it would include a large number of observations.
As will be obvious later that in any statistical analysis, the value of a class is represented
by its mid-value and hence, a class interval with broader width will be representative of
a large number of observations. Thus, the magnitude of loss of information due to grouping
will be large when there are small number of classes. On the other hand, if the number of
observations is small or the distribution of observations is irregular, i.e., not uniform,
having more number of classes might result in zero or very small frequencies of some
classes, thus, revealing no pattern of behaviour. Therefore, the number of classes depends
upon the nature and the number of observations. If the number of observations is large or
the distribution of observations is regular, one may have more number of classes. In
practice, the minimum number of classes should not be less than 5 or 6 and in any case
there should not be more than 20 classes.
The approximate number of classes can also be determined by Struge’s formula: n = 1 +
3.322 × log10N, where n (rounded to the next whole number) denotes the number of
classes and N denotes the total number of observations.

Based on this formula, we have
n = 1 + 3.322 × 2.000 = 7.644 or 8, when N = 100
n = 1 + 3.322 × 2.699 = 9.966 or 10, when N = 500
n = 1 + 3.322 × 4.000 = 14.288 or 15, when N = 10,000

n = 1 + 3.322 × 4.699 = 16.610 or 17, when N = 50,000
From the above calculations we may note that even the formation of 20 class intervals is
very rarely needed.

For the given data on the measurement of diameter, there are 90 observations. The number
of classes by the Sturge’s formula are
n = 1 + 3.322 × log1090 = 7.492 or 8

2. Width of a Class Interval: After determining the number of class intervals, one has to
determine their width. The problem of determining the width of a class interval is closely
related to the number of class intervals.
As far as possible, all the class intervals should be of equal width. However, there can be
situations where it may not be possible to have equal width of all the classes. Suppose that
there is a frequency distribution, having all classes of equal width, in which the pattern of
behaviour of the observations is not regular, i.e., there are nil or very few observations in
some classes while there is concentration of observations in other classes. In such a situation,
one may be compelled to have unequal class intervals in order that the frequency
distribution becomes regular.
The approximate size of a class interval can be decided by the use of the following formula:

Largest observation – Smallest observation
Class Interval =

Number of class intervals

L – S
or using notations, Class Interval =
n
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