bus-stat-book1

# 5 285 standard deviation 5 45 no of workers 476 524 1

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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.

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