Page 166 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 7: Measures of Dispersion

Q Q Notes
Quartile Deviation or Semi-Interquartile Range QD = 3 1
2
Q Q
3 1
Coefficient of QD =
Q 3 Q 1
1
Mean Deviation from X f X i X
i
N
1
Mean Deviation from M d f X i M d
i
N
1
Mean Deviation from M o f X i M o
i
N
M D. M D. M D.
.
.
.
Coefficient of MD or or .
X M d M o
Standard Deviation Mean of squares Square of the Mean
fX 2 fX 2

N N

fd 2 fd 2
, where d X A.
N N

fu 2 fu 2 X A
h , where u .
N N h

Coefficient of s.d. =
X

Coefficient of Variation = 100
X
Standard Deviation of the combined series

n 1 1 2 d 1 2 n 2 2 2 d 2 2  n k 2 k d k 2
,
n n  n
1 2 k
where d X i X for i = 1,2, ... k
i
7.10 Keywords

Averages of second order : The measures which express the spread of observations in terms of the
average of deviations of observations from some central value are termed as the averages of
second order, e.g., mean deviation, standard deviation, etc.

Coefficient of standard deviation: A relative measure of dispersion, based on standard deviation
is known as coefficient of standard deviation.
Dispersion: Dispersion is the measure of extent to which individual items vary.

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