Page 148 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Unit 7: Measures of Dispersion

Self Assessment Notes

Multiple Choice Questions:
25. An important requirement of a measure of dispersion is that it should be based on
......................... the observations.

(a) Some of (b) Few of
(c) All (d) None of
26. ................................... is a measure of dispersion based on all the observations.

(a) Mean (b) Mean deviation
(c) Quartiles (d) Standard deviation
27. Mean deviation is defined as the ............................. of the absolute deviations of observations
from a central value like mean, median or mode.
(a) Mean (b) Arithmetic mean
(c) Geometric mean (d) Harmonic mean
28. Mean deviation will be .......................... for an observation greater than the central value.
(a) Zero (b) Positive

(c) Negative (d) undetermined

7.8 Standard Deviation

From the mathematical point of view, the practice of ignoring minus sign of the deviations,
while computing mean deviation, is very inconvenient and this makes the formula, for mean
deviation, unsuitable for further mathematical treatment. Further, if the signs are taken into
account, the sum of deviations taken from their arithmetic mean is zero. This would mean that
there is no dispersion in the observations. However, the fact remains that various observations
are different from each other. In order to escape this problem, the squares of the deviations from
arithmetic mean are taken and the positive square root 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. Square of standard deviation is known as
variance. The concept of standard deviation was introduced by Karl Pearson in 1893.
The standard deviation is denoted by Greek letter ‘ ’ which is called ‘small sigma’ or simply
sigma.
In terms of symbols

1 n 2
X i X , for n individual observations, X , X ...... X , and
n i 1 1 2 n

1 n 2
f X i X , for a grouped or ungrouped frequency distribution, where an
i
N i 1
n
observation X occurs with frequency f for i = 1,2, ...... n and f i N.
i i
i 1
It should be noted here that the units of are same as the units of X.

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