Page 165 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes
(Mean Deviation and Standard Deviation) are to the statistician what the axe and cross-cut
saw are to the woodsman – the basic tools for working upon his raw materials”. Since the
mean deviation is inconvenient to handle mathematically, the standard deviation is often
used as a measure of dispersion in the absence of any special reason.

Self Assessment

State whether the following statements are true or false:
29. The squares root of the deviations from arithmetic mean are taken and the positive square
of the arithmetic mean of sum of squares of these deviations is taken as a measure of
dispersion. This measure of dispersion is known as standard deviation or root-mean
square deviation.
30. The concept of standard deviation was introduced by Karl Pearson in 1897.
31. The standard deviation is an absolute measure of dispersion and is expressed in the same
units as the units of variable X.
32. A relative measure of dispersion, based on standard deviation is known as coefficient of
standard deviation.

Case Study Philips India Ltd.

hilips India Ltd., manufactures the famous Philips tube-lights of 40 watts. The
company has developed a new variety of Flouroscent 24 watt tube lights for specific
Papplications in control equipments used in defence components. Before it is
commercially launched the manager R&D desires to ensure its reliability and quality. The
test results conducted on 400 such tube lights are shown below.
Life Time (hours) No. of Tubes
14 300-400
46 400-500
58 500-600
76 600-700
68 700-800
62 800-900
48 900-1000
22 1000-1100
6 1100-1200

Compute the coefficient of skewness.

7.9 Summary

Range = L – S, L = largest observation and S = smallest observation.
L S
Coefficient of Range =
L S

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