Page 142 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 7: Measures of Dispersion

Calculation of P Notes
90
90N 90 80
Since 72, P lies in the class interval 21 - 23
100 100 90
= 21, = 11, h = 2 and C = 65
P P
90 90
72 65
.
P 21 2 22 27.
Hence, 90
11
Thus, the percentile range = P – P = 22.27 – 13.0 = 9.27.
90 10
7.6.2 Quartile Deviation or Semi-Interquartile Range
Half of the interquartile range is called the quartile deviation or semi-interquartile range.
Q 3 Q 1
Symbolically, Q D. . .
2
The value of Q.D. gives the average magnitude by which the two quartiles deviate from median.
If the distribution is approximately symmetrical, then M ± Q.D. will include about 50% of the
d
observations and, thus, we can write Q = M – Q.D. and Q = M + Q.D.
1 d 3 d
Further, a low value of Q.D. indicates a high concentration of central 50% observations and vice-
versa.
Quartile deviation is an absolute measure of dispersion. The corresponding relative measure is
known as coefficient of quartile deviation defined as
Q Q
3 1
2 Q 3 Q 1
Coefficient of Q.D. = Q Q
3 1 Q 3 Q 1
2
Analogous to quartile deviation and the coefficient of quartile deviation we can also define a
P 100 i P i P P
percentile deviation and coefficient of percentile deviation as and 100 i i ,
2 P P
100 i i
respectively.

Example: Find the quartile deviation, percentile deviation and their coefficients from
the following data:
(
Age in years) : 15 16 17 18 19 20 21
No of Students : 4 6 10 15 12 9 4
.
Solution:
Table for the calculation of Q.D. and P.D.
Age ( ) No .of Students ( ) Less than c . .
f
X
f
15 4 4
16 6 10
17 10 20
18 15 35
19 12 47
20 9 56
21 4 60

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