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Unit–28: Measures of Dispersion: Standard Deviation

guaranteed. Therefore, range is classified as the crude measure of variation of a set of data. Moreover, notes
range is also susceptible to very large and extremely small values contained within a series.

28.2 Quartile Deviation

N + 1
if N values of a variable are arranged in ascending or descending order, then the value is known
4
(N + ) 1 (N + ) 1
as the first quartile (Q ), 2 4 th value is known as second quartile(Q ), 3 4 value is known
1
2
as third quartile (Q ). The half of the difference between the third quartile and first quartile is known
3
as the quartile deviation and is represented as:
Q − Q
Quartile Deviation = 3 1
2

Example 1 find out the Quartile Deviation of the below given values:
10, 17, 12, 28, 24, 22, 15, 30, 35, 38, 20.

solution: on arranging values in ascending order
10, 12, 15, 17, 20, 22, 24, 28, 30, 35, 38
since the number of values here is 11, therefore N = 11.
+
11 1
therefore, Q 3 = 4
= 3 Value
rd
Q = 15
1
3 (11 1+ )
similarly Q =
2 4
3 12
×
=
4
= 9 value
th
so, Q = 30
3
Q − Q
Quaterly Deviation = 3 1
2
−
30 15
=
2
= 7.5 marks

28.3 Coefficient of Quartile Deviation

it is not possible to compare the variation of different series using quartile deviation since it is an
absolute measure. Another term known as Coefficient of Quartile Deviation is derived using quartile
deviation, which is represented as

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