Calculate an average value

We all know how to calculate an average value iteratively:

def average(nums):

    result = 0

    for num in nums:
        result += num

    return result/len(nums)

Could you provide a recursive solution? A formula for updating an average value given a new input might be handy:

$$ \bar{x} \leftarrow \frac{x_i + (n-1)\bar{x}}{n} $$

Here, $\bar x$ stands for an average value, $x_i$ is a new supplied value which is used to update the average, and $n$ corresponds to the recursive call number (excluding the initial call to the function).

Provide the base case for the algorithm.
Define the recursive call for updating the average value.

Exercise

Calculate an average value

Instructions