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).

This exercise is part of the course

Practicing Coding Interview Questions in Python

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Exercise instructions

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

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Calculate an average value of the sequence of numbers
def average(nums):
  
    # Base case
    if len(nums) == ____:  
        return ____[____]
    
    # Recursive call
    n = len(nums)
    return (____ + ____ * ____) / ____

# Testing the function
print(average([1, 2, 3, 4, 5]))

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