Page 97 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 7: Mean Deviation and Standard Deviation
Dilfraz Singh, Lovely Professional University

Unit 7: Mean Deviation and Standard Deviation Notes

CONTENTS
Objectives
Introduction
7.1 The Mean Deviation
7.2 The Standard Deviation
7.3 Summary
7.4 Key-Words
7.5 Review Questions
7.6 Further Readings

Objectives

After reading this unit students will be able to:
• Describe the Mean Deviation.
• Explain the Standard Deviation.
Introduction

The two methods of dispersion discussed earlier in this book, namely, range and quartile deviation,
are not measures of dispersion in the strict sense of the term because they do not show the scatterness
around an average. However, to study the formation of a distribution we should take the deviations
from an average. The two other measures, namely, the average deviation and the standard deviation,
help us in achieving this goal.
The average deviation is sometimes called the mean deviation. It is the average difference between
the items in a distribution and the median or mean of that series. Theoretically, there is an advantage
in taking the deviations from median because the sum of the deviations of items from median is minimum
when signs are ignored. However, in practice the arithmetic mean is more frequently used in calculating
the value of average deviation and this is the reason why it is more commonly called mean deviation.
In any case, the average used must be clearly stated in a given problem so that any possible confusion
in meaning is avoided.
The standard deviation of a random variable, statistical population, data set, or probability distribution
is the square root of its variance. It is algebraically simpler though practically less robust than the
average absolute deviation. A useful property of standard deviation is that, unlike variance, it is
expressed in the same units as the data.

In statistics standard deviation (represented by the symbol sigma, σ ) 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.

In addition to expressing the variability of a population, standard deviation is commonly used to
measure confidence in statistical conclusions. For example, the margin of error in polling data is
determined by calculating the expected standard deviation in the results if the same poll were to be

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