Page 70 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 4: Research Problem

Semi-inter quartile range (Quartile deviation) semi-inter quartile range Q. Notes

Q –Q
Q is given by Q = 3 1
2

Note:
Q –Q
3 1
1. Q  Q is called the coefficient of quartile deviation.
3 1
2. Quartile deviation is not a true measure of dispersion but only a distance of scale.
Mean Deviation (MD): If A is any average then mean deviation about A is given by

 f | x – A|
MD(A) = i i
N

Note:
 f | x – x |
i
i
1. Mean deviation about mean MD   x
N
2. Of all the mean deviations taken about different averages mean derivation about the
median is the least.

MD(A)
3. is called the coefficient of mean deviation.
A
Variance and Standard Deviation

2
Variance (s ): A measure of the average squared distance between the mean and each term in the
population.

1 2
s 2 =  f x (  x)
N i i
Standard deviation (s) is the positive square root of the variance

1
s =  f (x – x) 2
i
i
N
1
2
s 2 =  f (x  x ( ) 2
N i i
Note: Combined variance of two sets of data of N and N items with means x and x and
1 2 1 2
standard deviations s and s respectively is obtained by
1 2
2
2
2
N s  N s  N d  N d 2 2
1
1
1
1
1
2
2
s 2 =
N  N
1 2
2
2
2
Where, d = (x – x ) , d  (x – x ) 2
1 1 2 2
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