Moments About Origin In Term Of Moments About Any Point

Moments about Origin in Term of Moments about any Point:

Method I: Convert the moments about a in terms of moments about mean and then obtain moments about origin.

Method II: Obtain by the formula.

Example:1 The arithmetic mean of a series is 22 and first four central moments are 0,81,-144 and 14817. Find the first four moments (i) about assumed 25 and (ii) about origin.

Solution:
(i) Moments about assumed mean a = 25:

(ii) Moments about origin:

Example:2 The first four moments of a frequency distribution about the value 4 are -1.5.1.7,-30 and 108. Calculate the moments about origin.

Solutions: Let v′r = rth moment about 4. then