Find the find the quadratic average and the geometric average. To do this I have these informations : The standart deviation, the arithmetic average and the number of values.

Nathalie Fields 2022-07-17 Answered
Find the find the quadratic average and the geometric average. To do this I have these informations :
The standart deviation, the arithmetic average and the number of values.
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Answers (2)

Lance Long
Answered 2022-07-18 Author has 8 answers
You can't get the geometric average when n = 3. Knowing the arithmetic and quadratic average of three numbers ( x , y , z ) is equivalent to knowing x + y + z and x 2 + y 2 + z 2 , while knowing the geometric average means knowing x y z. If xyz were a function of the other two, its gradient at any point would be a linear combination of the other two gradients. But
( x + y + z ) = ( 1 , 1 , 1 ) ( x 2 + y 2 + z 2 ) = 2 ( x , y , z ) ( x y z ) = ( y z , x z , x y )
At ( x , y , z ) = ( 1 , 2 , 3 ), say, the three gradients are linearly independent.
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prkosnognm
Answered 2022-07-19 Author has 5 answers
It's not possible for the geometric average, there are infinitely many solutions depending on the number of observations.
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