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The geometric mean of the observation x(...

The geometric mean of the observation `x_(1),x_(2),x_(3),……..,_(n)` is `G_(1)`, The geometric mean of the observation `y_(1),y_(2),y_(3),…..y_(n)` is `G_(2)`. The geometric mean of observations
`(x_(1))/(y_(1)),(x_(2))/(y_(2)),(x_(3))/(y_(3)),……(x_(n))/(y_(n))` us

A

`G_(1)G_(2)`

B

`ln(G_(1)G_(2))`

C

`(G_(1))/(G_(2))`

D

`ln((G_(1))/(G_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
C
`G_(1)=[x_(1)xxx_(2)xxx_(3)xx...........xxx_(n)]^(1//n)`
`G_(2)=[y_(1)xxy_(2)xxy_(3)xx........xxy_(n)]^(1//2)`
`rArr (G_(1))/(G_(2))=[(x_(1))/(y_(1))xx(x_(2))/(y_(2))xx(x_(3))/(y_(3))xx........xx(x_(n))/(y_(n))]^(1//n)`
`therefore (G_(1))/(G_(2))" is the G.M of"(x_(1))/(y_(1)),(x_(2))/(y_(2)),(x_(3))/(y_(3)),.......,(x_(n))/(y_(n))`
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