I think it is C) II Only.
We are computing average of 5 numbers and if you double the sum and divide by 10 (equivalent to moving decimal point) then we have the answer.
The other options don't work..
I) Fifth root does not give a solution...
II) This is the correct solution
III) This is median not the average.
Which of the following procedures is always equivalent to adding 5 given numbers and then dividing the sum by 5?
I) Multiplying the 5 numbers and then finding the 5th root of the product.
II) Adding the 5 numbers, doubling the sum, and then moving the decimal point one place to the left
III) Ordering the 5 numbers numerically and then selecting the middle number
B) I only
C) II only
D) III only
E) I and III