If G is the GM of the product of r sets of observations with geometric means G1,G2,…,Gr respectively, then G is equal to

Taking X as the product of varieties X1,X2,…,Xr corresponding tor sets of observations i. e. X=X1X2…Xr we havelog⁡X=log⁡X1+log⁡X2+…log⁡Xr⇒ ∑log⁡X=∑log⁡X1+∑log⁡X2+…+∑log⁡Xr⇒ 1n∑log⁡X=1n∑log⁡X1+1n∑log⁡X2+…+1n∑log⁡Xr⇒ log⁡G=log⁡G1+log⁡G2+…+log⁡Gr⇒ G=G1G2…Gr.