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Unit–28: Measures of Dispersion: Standard Deviation

σ = 10 3.12 −− ) = 10 3.12 · 211 notes
2
( · 47
−
σ = 10 2.909
σ = 17 (Approx.)

in the table for this question, the mid–point (x) of class–interval and the variation between the mid–point
and the assumed mean are not required to be mentioned. it is only shown for better understanding
of the readers.

28.9 Importance of Variability

the computation of variation plays a very important role in bringing statistical research to a realisable
level. Mean, median and mode do not convey complete features of the values of elements and there
is always a possibility that our knowledge may be doubtful. the role of variation in removing this
doubt is worth mentioning. in reality, mean and variation are inseparable and one without another
is always incomplete. the combined computation of mean and variation can only introduce us about
the true situation. for example, when we calculate the per capita income of the citizens of a country,
then we cannot have accurate information about the richness or poorness of that country. if there is a
localization of income and property towards few rich people and these people become very wealthy,
then the per capita income which we will calculate using some computation will be more than the real
income of most of the citizens. therefore, true knowledge about the real situation cannot be ascertained
until we consider variation. Hence, mean is incomplete without variation.

28.10 summary

y Variation or dispersion is that quality which tells us the measure of deviation of a set of values
from its mean (or average of values).
y Measures of variation are of four types– (a) range (b) Quartile Deviation (c) Mean Deviation
(d) standard Deviation
y Mean deviation is the arithmetic mean of the mean and the elements of series.

28.11 Keywords

1. standard Deviation: in order to eliminate the positive and negative signs of variation, the
variation is squared to calculate the standard deviation.

28.12 review Questions

1. What is meant by variation?
2. How is mean deviation calculated from arithmetic mean?
3. Give the formula for short–cut method to compute standard deviation and what does
standard Deviation signify? Explain.

answers: self assessment
1. Arithmetic means 2. Mean deviation 3. Deviation mean

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