Page 195 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes If we measure only the mean of these two distributions, we will miss an important difference
between A and B. To increase our understanding of the pattern of the data, we must also measure
its dispersion.
Range: It is the difference between the highest and lowest observed values.
i.e range = H – L, H = Highest, L = Lowest.
Note:
1. Range is the crudest measure of dispersion.

H L
2. is called the coefficient of range.
H L

Semi-Inter Quartile Range (Quartile deviation): Semi-Inter quartile range Q.
Q  Q
Q is given by Q = 3 1
2
Note:

Q  Q 1
3
1. is called the coefficient of quartile deviation.
Q  Q 1
3
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|
i
i
MD(A) =
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)
i
i
N
Standard deviation (s) is the positive square root of the variance:
1 2
s =  f (x  x)
i
i
N
1 2 2
s 2 =  f (x  (x)
i
i
N
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
190 LOVELY PROFESSIONAL UNIVERSITY