As the problem indicates, degrees of freedom are the number of values that can be independently selected before it is necessary to choose specific values to arrive at the desired result.
The average, on the other hand, results from the sum of a list of values divided by the amount of values in the summed list.
Assume that the mean sought is 
and consider that the list is composed of a single element 
, in that case no random number can be selected, since the mean must correspond to that number.
If the list were composed of two elements and 
, one of the two values could be chosen randomly, and according to the chosen value the second should be the one whose sum with the previous one results in 
, this given that the formula of the average 
.
With three values , and 
, it is possible to select two freely, since the thirteen must be the one that balances the sum of 
, that is 
.
Thus, in general, with n values, it is possible to select 
values freely whose sum must be balanced by the last value so that the whole sum is 
.
Answer
In a list of 
values you can assign 
values freely, that is, you have <em>degrees of freedom.</em>
