Question

The total of a set of observations is equal to the product of their number of observations
and the
(a) A.M
(b) G.M
(c) H.M
(d) none
please explain it with an example​

Answer 1

Answer:

G.M. = (x1. x2 … xn) 1⁄n

Taking log on both sides, we have

log G.M. = 1⁄n (log ((x1. x2 … xn))

or, log G.M. = 1⁄n (log x1 + log x2 + … + log xn)

or, log G.M. = (1⁄n) ∑ i= 1n log xi

or, G.M. = Antilog(1⁄n (∑ i= 1n log xi)).

Geometric Mean of Frequency Distribution

For a grouped frequency distribution, the geometric mean G.M. is

G.M. = (x1 f1. x2 f2 … xn fn) 1⁄N , where N = ∑ i= 1n fi

Taking logarithms on both sides, we get