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For n observations xl' x2, .......... ,X and an arbitrary constant A, the r th moment about A is defined as,

For simple frequency distribution, the r the moment about A is defined as

For grouped frequency distribution, X; will be taken as class mark.

These moments, 1-l,.', are also known as ' raw moments'.

When A = x, then these moments are called 'central moments' and we denote as follows :

The third and fourth central moments i.e., ~3 and ~4 are used to measure skewness and kurtosis

which have been given in the following sections.

The important relations between the central and raw moments are as follows :

Note. If the above moments are called as sample moments, then we have to use the notation m', instead of ll'r- See the method of moments in Chapter 10A.