If G is the GM of the product of r sets of observations with geometric means `G_(1), G_(2), …,G_(r)` respectively, then G is equal to

Options

A. `log G_(1)+log G_(2) +. . . .+log G_(n)`
B. `G_(1)G_(2),…G_(r)`
C. `log G_(1),log G_(2),….log G_(n)`
D. None of the above

Answer

b

Explanation

Taking x as the product of variates ` x_(1), x_(2),…. , x_(r)`
corresponding to r set of observations i.e x = `x_(1) x_(2)….x_(r), ` we have
` log x = logx_(1) + logx_(2) +....+ logx_(r)`
` rArr Sigma log = Sigma log x_(1) +Sigma log x_(2) +... + Sigma logx_(r)`
` rArr 1/n Sigma log x = 1/n Sigma log x_(1) +1/n Sigma log x_(2) +... +1/nSigma log x_(r)`
` Sigma log x^(1//n)= Sigma log x_(1)^(1//n) + Sigma log x_(2)^(1//2) +....+Sigma log x_(r)^(1//n)`
` rArr log G = log G_(1) + log G_(2) +...+ log G_(r)`
` rArr G = G_(1) G_(2)...G_(r)`