Page 94 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes The methods given above are approximations for use in small-sample statistics. In general terms, for
very large populations percentiles may often be represented by reference to a normal curve plot. The
normal curve is plotted along an axis scaled to standard deviation, or sigma, units. Mathematically,
the normal curve extends to negative infinity on the left and positive infinity on the right. Note,
however, that a very small portion of individuals in a population will fall outside the – 3 to + 3 range.
In humans, for example, a small portion of all people can be expected to fall above the + 3 sigma
height level.
Percentiles represent the area under the normal curve, increasing from left to right. Each standard
deviation represents a fixed percentile. Thus, rounding to two decimal places, – 3 is the 0.13 percentile,
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– 2 the 2.28 percentile, – 1 the 15.87 percentile, 0 the 50 percentile (both the mean and median of
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the distribution), + 1 the 84.13 percentile, + 2 the 97.72 percentile, and + 3 the 99.87 percentile.
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Note that the 0 percentile falls at negative infinity and the 100 percentile at positive infinity.
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Self-Assessment
1. Indicate whether the following statements are True or False:
(i) A good measure of dispersion is the one which is not defined rigidly.
(ii) Range is the best measure of dispersion.
(iii) Quartile Deviation is more suitable in case of openend distributions.
(iv) Absolute measure of dispersion can be used for purposes of comparison.
6.4 Summary

• The term dispersion refers to the variability of the size of items. Dispersion explains the size of
various items in a series are not uniform rather, they vary. For example, if in a series the lowest
and highest values vary only a little, the dispersion is said to be low.
• “A measure of variation or dispersion describes the degree of scatter shown by observations
and is usually measured by comparing the individual values of the variable with the average of
all the values and then calculating the average of all the individual differences.
• Therefore, in case of heterogeneous data, dispersion is measured to guage the reliability of the
average calculated. When the value of dispersion is small, it is concluded that the average
closely represents the data but when value of dispersion comes out to be large, it should be
concluded that the average obtained is not very reliable.
• The consistency of uniformity of two series can be compared with the help of dispersion. If the
value of dispersion measured comes out to be large, it may be concluded that the series lacks
uniformity or consistency. Such studies are very useful in many fields like profit of companies,
share values, performance individuals, studies related to demand, supply, prices etc.
• It can be concluded that due to inconsistencies and lack of uniformity of the data, averages can
not prove to be closely representing the data, in most of the cases. In such a situation, dispersion
presents a more better picture about the data, and gives logic to find out whether the average
calculated is reliable or not. It also helps in comparing the two series and also help in finding
out ways to control the variations. In this way dispersion is a very strong tool into the hands of
statisticians to know about the structure of data more closely and reliably.
• When the dispersion of a series is calculated in terms of the absolute or actual figures in the
data and the value of dispersion obtained can be expressed in the same units as the items of
data are expressed, such measures are called absolute measures of dispersion. For example, if
we calculate dispersion of a series indicating the income of group of persons in rupees, and the
value of dispersion is obtained in rupees, it is termed as absolute measure of dispersion.

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