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Unformatted text preview: d by factory A
= 34.5 × 476
= Rs.16.422
Total wages paid by factory B
= 28.5 × 524
= Rs.14,934.
Therefore factory A pays out larger amount as weekly wages.
2. C.V. of distribution of weekly wages of factory A and B are
σ1 × 100
X1
5
=
× 100
34.5
= 14.49
σ
C.V (B) = 2 × 100
X2
4.5
=
× 100
28.5
= 15.79
Factory B has greater variability in individual wages, since
C.V. of factory B is greater than C.V of factory A
C.V.(A) = Example 16:
Prices of a particular commodity in five years in two cities are
given below:
Price in city A
Price in city B
10
20
20
22
18
19
12
23
15
16
Which city has more stable prices?
168 Solution:
Actual mean method 20
22
19
23
16 City A
Deviations
from X=20
dx
0
2
1
3
4 ∑x=100 ∑dx=0 Prices
(X) City A: X = σx=
= 2 dx Prices
(Y) 0
4
1
9
16 10
20
18
12
15 ∑dx2=30 ∑y=75
Σx
n = 100
= 20
5 Σ(x − x)2
=
n
30
=
5 ∑ dx 2
n 6 =2.45 σx ×100
x
2.45
=
× 100
20
= 12.25 %
75
Σy
City B: Y =
=
= 15
n
5
C.V(x) = σy = Σ(y − y)2
=
n ∑ dy2
n
169 City B
Deviations
from Y =15
dy
5
5
3
3
0
∑dy=0 dy2 25
25
9
9
0
∑dy2
=68 68
= 13.6 = 3.69
5
σy
C.V.(y) =
x 100
y
3.69
=
×100
15
= 24.6 %
City A had more stable prices than City B, because the
coefficient of variation is less in City A.
= 7.7
Moments:
7.7.1 Definition of moments:
Moments can be defined as the arithmetic mean of various
powers of deviations taken from the mean of a distribution. These
moments are known as central moments.
The first four moments about arithmetic mean or central
moments are defined below.
Individual series
Discrete series
First moments
Σ(x − x)
∑ f (x − x)
=0
=0
about the mean; µ1
n
N
Second moments
∑ (x − x)2
∑ f (x − x)2
= σ2
about the mean; µ2
n
N
Third moments
∑ (x − x)3
∑ f (x − x)3
about the mean ; µ3
n
N
4
Fourth
moment ∑ (x − x)
∑ f (x − x)4
about the
n
N
Mean ; µ4
µ is a Greek letter, pronounced as ‘ mu’ .
If the mean is a fractional value, then it becomes a difficult
task to work out the moments. In such cases, we can calculate
moments about a working origin and then change it into moment...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.
 Winter '08
 Moshiri
 Business

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