Page 121 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 7: Mean Deviation and Standard Deviation

• The standard deviation is the best measure of variation because of its mathematical Notes
characteristics. It is based on every item of the distribution. Also it is amenable to algebraic
treatment and is less affected by fluctuations of samlping than most other measures of dispersion.
• Mistakes in calculations are always possible. Sometimes it so happens that while calculating
mean and standard deviation we unconsciously copy out wrong items. For example, an item 21
may be copied as 12. Similarly one item 127 may be taken as only 27. In such cases if the entire
calculations are done again, it would become too tedious a task. By adopting a very simple
procedure we can correct the incorrect values of mean and standard deviation. For obtaining
correct mean we find out correct ΣX by deducting from the original ΣX the wrong items and
adding to it the correct items.
7.4 Key-Words

1. Mean Deviation : The mean deviation or the average deviation is defined as the mean of
the absolute deviations of observations from some suitable average which
may be the arithmetic mean, the median or the mode. The difference ( )
is called deviation and when we ignore the negative sign, this deviation
is written as and is read as mod deviations.
2. Standard Deviation : In statistics and probability theory, standard deviation (represented by
the symbol sigma, ?) shows how much variation or "dispersion" exists
from the average (mean, or expected value). A low standard deviation
indicates that the data points tend to be very close to the mean; high
standard deviation indicates that the data points are spread out over a
large range of values
7.5 Review Questions

1. Discuss ‘mean deviation’ method of measuring dispersion giving its merits and demerits.
2. Explain the concept of Standard deviation. What are its merits and demerits ?
3. Discuss the mathematical Properties of Standard deviation.
4. Distinguish between mean deviation and Standard deviation.
Answers: Self-Assessment

1. (i)T (ii)T (iii)T (iv)F (v)T
7.6 Further Readings

1. Elementary Statistical Methods; SP. Gupta, Sultan Chand & Sons,
New Delhi - 110002.
2. Statistical Methods — An Introductory Text; Jyoti Prasad Medhi, New Age
International Publishers, New Delhi - 110002.
3. Statistics; E. Narayanan Nadar, PHI Learning Private Limied, New Delhi - 110012.
4. Quantitative Methods—Theory and Applications; J.K. Sharma, Macmillan
Publishers India Ltd., New Delhi - 110002.

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