Moments

Moments

Raw moments:

Raw moments can be defined as the arithmetic mean of various powers of deviations taken from origin. The r^th Raw moment is denoted by μ_r’, r=1,2,3…. Then the first raw moments are given by

Central Moments:

Central moments can be defined as the arithmetic mean of various powers of deviation taken from the mean of the distribution. The r^th central moment is denoted by μ_r, r=1,2,3….

In general, given n observation x₁, x₂,…….x_n the r^th order raw moments (r=0,1,2,…) are defined as follows:

Relation between raw moments and central moments

Example 6.15

The first two moments of the distribution about the value 5 of the variable, are 2 and 20. Find the mean and the variance.

Solution: