First, it is important to understand the terms used in the problem.
The Arithmetic Mean: (this is the mean we are used to seeing)
[tex]m= \frac{a+b+c}{n} [/tex]
(n= number of variables, in this case n=3)
To Find the Geometric Mean of n #'s:
[tex]m_{geometric} = \sqrt[n]{a*b} [/tex]
(n= number of variables, in this case n=2)
So, using this information we can find the geometric mean of 6,7 by plugging them into the equation as "a" and "b". n=2 (when n=2 a square root can be used)[tex]m_{geometric} = \sqrt[n]{a*b}[/tex]
[tex]m_{geometric} = \sqrt{a*b} [/tex]
[tex]m_{geometric} = \sqrt{6*7} [/tex]
[tex]m_{geometric} = \sqrt{42} [/tex]
So the answer in this case is A.[tex] \sqrt{42} [/tex]
