Page 132 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Similarly, Kurtosis is yet another measure which tells us about the form of a distribution. Thus,
it can be said that the central tendencies and dispersion measures should be supplemented by
measures of skewness and kurtosis so that a more elaborate picture about the distribution
given can be obtained. The study becomes more important in subjects of economics, sociology
and other social sciences where normal distribution in a series usually does not occur. However,
studies hold importance in biological sciences and other physical sciences as well.
• In the words of Simpson and Kafka, “Measures of skewness tell us the direction and the extent of
skewness. In symmetrical distribution the arithmetic mean, median and mode are identicle.
The more the mean moves away from mode, the larger the asymmetry or skewness.”
• Measure of skewness indicates the difference between the manner in which items are distributed
in a particular distribution compared with symmetrical or normal distribution. In a symmetrical
distribution, frequencies go on increasing upto a point and then begin to decrease in the same
fashion. There are various possible patterns of symmetrical distribution and normal distribution
which is bell-shaped is one of these.
• A distribution in which more than half of the area under the curve is to the right side of the
mode, it is said to be a positively skewed distribution. In this type of skewness the right tail is
longer than the left tail. In this case, mean is greater than median and the median is greater than
−
the mode and Q − 3 M>M Q .
1
• A distribution in which more than half of the area under the distribution curve is to the left side
of the mode, it is said to be a negatively skewed distribution. In this case, the elongated tail is to
the left and mean is less than the median which is less than mode and Q − 3 M M Q 1 .
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−
• Kurtosis in Greek means “bulginess”. In statistics kurtosis refers to the degree of flatness or
peakedness in the region about the mode of a frequency curve. The degree of kurtosis of a
distribution is measured relative to the peakedness of normal curve. In other words, measures
of kurtosis tell us the extent to which a distribution is more peaked or flat-topped than the
normal curve. If a curve is more peaked than the normal curve, it is called ‘leptokurtic’. In such
a case the items are more closely bunched around the mode. On the other hand, if a curve is
more flat-topped than the normal curve, it is called ‘platykurtic’. The normal curve itself is known
as ‘mesokurtic’. The condition of peakedness or flat-toppedness itself is known as kurtosis or
excess. The concept of kurtosis is rarely used in elementary statistics.
• A famous British statistician Willian S. Gosset (“Student”) has very humorously pointed out
the nature of these curves in the sentence, “Platykurtic curves, like the platypus, are squat with
short tails; lepto-kurtic curves are high with long tails like the kangaroos noted for lapping.”
8.5 Key-Words

1. Skewness and Kurtosis : Skewness and kurtosis are terms that describe the shape and
symmetry of a distribution of scores. Unless you plan to do
inferential statistics on your data set skewness and kurtosis only
serve as descriptions of the distribution of your data. Be aware that
neither of these measures should be trusted unless you have a large
sample size.
Skewness refers to whether the distribution is symmetrical with
respect to its dispersion from the mean. If on one side of the mean
has extreme scores but the other does not, the distribution is said to
be skewed. If the dispersion of scores on either side of the mean are
roughly symmetrical (i.e. one is a mirror reflection of the other, the
distribution is said to be not skewed.
2. Kelly's Methods : In probability theory, the Kelly criterion, or Kelly strategy or Kelly
formula, or Kelly bet, is a formula used to determine the optimal

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