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.
(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 -220.127.116.11,-30 and 108. Calculate the moments about origin.
Solutions: Let v′r = rth moment about 4. then