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Methodology of Social Research

notes knowledge in cases when there is large difference between elements of a series and its mean. if we
see it from a behavioural perspective, we can find plenty of instances wherein arithmetic mean gives
uncertain knowledge about the elements of series. for example, consider the earnings of members
of a family to be ` 20, ` 60, ` 200, ` 50 and ` 70 respectively, then the average earning per members is
` 80. if we do not have knowledge about individual earnings of each member, then we would assume
that each member would have earning close to ` 80. However, the actual situation is quite different
wherein members’ earnings are very dissimilar. therefore, in these situations, it is required to have a
measure that can give maximum information about individual elements of a series. in other words,
this measure gives us information about the deviation of each individual element of the series from
the mean of the series. these measures are known as measures of variations.
The meaning of variation can still be clarified using another example. Suppose two students secure
28, 60, 60, 92 marks and 56, 60, 60, 64 marks in four subjects wherein maximum marks in each subject
is 100 and minimum passing marks is 33. If we find out the arithmetic mean to assess the level of
students, then arithmetic means for both students comes out to be 60.therefore, on this basis, it looks
like both students are of same intellect level, but this is actually not true because the first student has
failed in his first subject while the second student has passed in all subjects. Therefore, it is clear that
only mean cannot help us ascertain the true nature of any series.

Did You Know? it is also important to know how much each element of a series is deviated
from the mean. this deviation is known as variation or dispersion.

Measures of Dispersion

The chief measures of variation are as follows—

1. range
2. Quartile Deviation
3. Mean Deviation
a. from Arithmetic mean
b. from Median
c. from Mode
4. standard Deviation

range

the difference between the maximum value and minimum value of elements contained in a series
or sequence is known as the range of the series. for example, if a group contains values like 17, 10,
13, 5, 8, 20 and 25, then the element with highest value is 25 and that with least value is 5. Hence, the
range of the series will be (25 – 5) = 20.
There are certain advantages of finding out the range of any series. For example, (1) it is very easy to
find out the spread of any series, one needs to find only the maximum and minimum value. (2) Based
on the range, it can also be estimated that the individual elements lie within what values. All these
features facilitate the use of range for quick and easy estimation, but the purity of result cannot be

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