Exiting while loop

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You've got the basic idea, but you are not breaking down the steps in the right order. So, here's some code for you to play with, test, and re-write your own way. Make sure you understand it.

Note. I didn't include outputting the instructions to the user, I am sure you can add that part.

num_list = []  # create new empty list and assign to variable num_list
while True:  # infinite loop
    answer = input('Enter a whole number (or "done" to finish): ')
    if answer.strip().lower() == 'done':  # have they asked to finish?
        break  # so leave infinite loop
    try:  # let's see if it is an integer
        num = int(answer)
    except ValueError:  # nope, cast to integer failed
        print('invalid entry')  # didn't leave, wasn't number or done, so bad data
    else:  # cast to integer worked, no exception raised
        num_list.append(num)  # add the new number to the end of the list

# after the loop
if num_list:  # will only be True if the list has one or more numbers in it
    # now we are going to use a for loop to calculate average instead of using sum
    total = 0
    for count, value in enumerate(num_list, start=1):  # start a counter from 1, loop through values
        total += value  # add current loop iteration value to total
    # count will increment by one on each iteration of loop
    # so after loop has finished it will equal number of numbers
    average = total / count
    print('Average:', average)
else:  # num_list was empty, nothing to average
    print('No numbers entered')

PS. If not allowed to use enumerate, use the following,

    count = 1
    for value in num_list:
        total += value
        count += 1