Page 116 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes = 1.455 – 0.503 5 = 0.952 5 = 0.976 × 5 = 4.88
×
×
σ 4.88
C.V. = × 100 = × 100 = 23.24%.
X 21
Manufacturer B

Calculation of Mean and Standard Deviation

⎛ – 17.45 ⎞ m
Bursting pressure m f ⎜ ⎟ fd fd 2
⎝ 5 ⎠
(lb.) d

4.95–9.95 7.45 9 – 2 –18 36
9.95–14.95 12.45 11 – 1 – 11 11
14.95–19.95 17.45 18 0 0 0
19.95–24.95 22.45 54 + 1 + 54 54
24.95-29.95 27.45 27 + 2 + 54 108
29.95–34.95 32.45 13 + 3 + 39 117
2
N = 110 Σfd = 96 Σfd = 304
Σfd 96
X = A+ N × i = 17.45 + 110 × 5 = 17.45 + 4.36 = 21.18

Σ fd 2 ⎛ Σ fd ⎞ 2 304 ⎛ 96 ⎞ 2
σ = – ⎜ ⎟ i × = – ⎜ ⎟ × 5
N ⎝ N ⎠ 110 ⎝ 110 ⎠

×
= 2.764 – 0.762 5 = 1.4149 × 5 = 7.075
σ 7.075
C.V. = × 100 = × 100 = 32.44%
X 21.81
Since the average bursting pressure is higher for manufacturer B, the bags of
manufacturer B have a higher bursting pressure. The bags of manufacturer A have
more uniform pressure since the coefficient of variation is less for manufacturer A. If
princes are the same, the bags of manufacturer A should be preferred by the buyer
because they have more uniform pressure.
Variance
The term variance was used to describe the square of the standard deviation by R.A.
Fisher in 1918. The concept of variance is highly important in advanced work where
it is possible to split the total into several parts, each attributable to one of the factors
causing variation in the original series. Variance is defined as follows:

Σ ( ) X – X 2
Variance = .
N
Thus, variance is nothing but the square of the standard deviation, i.e.,
Variance = σ 2

or σ = Variance.

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