Measures of asymmetry and pointing

is denoted by:

g2

They are those that analyze whether a frequency distribution is more or less sharper when comparing it as a normal distribution, i.e. with the same size and variance.

Defined for:

Variable X

Y= X-B

Parameters

g2 (X) the distribution is leptokurtic

g2 (X) = 0

Its distribution is mesocurtic, i.e., the same as the normal distribution.

g2 (X) < 0

The distribution is platicurtic, more flattened than normal.

measures

ungrouped data

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Frequency tables

data grouped in intervals

types

leptocurtica

mesocurtica

platicurtica

It is such a measure of the shape of a distribution that allows us to describe the data in which it tends to identify characteristics of the data distribution.

to measure the skewness of a distribution, different coefficients are used, in which the so-called skewness coefficient can be obtained.

is denoted by g1

is defined as a central moment of order 3 and standard deviation raised to the cube

the values of the variables are more frequent, i.e. the highest and if the distribution has a tail to the left, this skewness is negative.

when the most common values of the distribution are smaller, this asymmetry is positive