Page 103 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 7: Mean Deviation and Standard Deviation

Notes
∑ f M 16,700
X = ∑ f = 50 = 334

∑ fd
δ X = N X

∑ fd X = 6,592, N = 50

6,592
δ X = 50 = 131.84

Merits and Limitations of Mean Deviation

Merits
(i) The outstanding advantage of the average deviation is its relative simplicity. It is simple to
understand and easy to compute. Anyone familiar with the concept of the average can readily
appreciate the meaning of the average deviation. If a situation requires a measure of dispersion
that will be presented to the general public or any group not thoroughly grounded in statistics,
the average deviation is very useful.
(ii) It is based on each and every item of the data. Consequently change in the value of any item
would change the value of mean deviation.
(iii) Mean deviation is less affected by the values of extreme items than the standard deviation.
(iv) Since deviations are taken from a central value, comparison about, formation of different
distributions can easily be made.
Limitations

(i) The greatest drawback of this method is that algebraic signs are ignored while taking the
deviations of the items. For example if from twenty, fifty is deducted we write 30 and not – 30.
This is mathematically wrong and makes the method non-algebraic. If the signs of the deviations
are not ignored the net sum of the deviations will be zero if the reference point is the mean or
approximately zero if the reference point is median.
(ii) This method may not give us very accurate results. The reason is that mean deviation gives us
best results when deviations are taken from median. But median is not a satisfactory measure
when the degree of variability in a series is very high. And if we compute mean deviation from
mean that is also not desirable because the sum of the deviations from mean (ignoring signs) is
greater than the sum of the deviations from median (ignoring signs). If mean deviation is
computed from mode that is also not scientific because the value of mode cannot always be
determined.
(iii) It is not capable of further algebraic treatment.
(iv) It is rarely used in sociological studies.
Because of these limitations its use is limited and it is overshadowed as a measure of variation
by the superior standard deviation.
Usefulness of the Mean Deviation: The serious drawbacks of the average deviation should not
blind us to its practical utility. Because of its simplicity in meaning and computation, it is especially
effective in reports presented to the general public or to groups not familiar with statistical methods.
This measure is useful for small samples with no elaborate analysis required. Incidentally it may be
mentioned that the National Bureau of Economic Research has found in its work on forecasting
business cycles, that the average deviation is the most practical measure of dispersion to use for this
purpose.

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