[ADDED] Implementation of Geometric Mean. (#10421)

* [ADDED] Implementation of Geometric Mean.

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* Rectified type hints

* Typo

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

maths/geometric_mean.py

@@ -0,0 +1,55 @@
+"""
+The Geometric Mean of n numbers is defined as the n-th root of the product
+of those numbers. It is used to measure the central tendency of the numbers.
+https://en.wikipedia.org/wiki/Geometric_mean
+"""
+
+
+def compute_geometric_mean(*args: int) -> float:
+    """
+    Return the geometric mean of the argument numbers.
+    >>> compute_geometric_mean(2,8)
+    4.0
+    >>> compute_geometric_mean('a', 4)
+    Traceback (most recent call last):
+        ...
+    TypeError: Not a Number
+    >>> compute_geometric_mean(5, 125)
+    25.0
+    >>> compute_geometric_mean(1, 0)
+    0.0
+    >>> compute_geometric_mean(1, 5, 25, 5)
+    5.0
+    >>> compute_geometric_mean(2, -2)
+    Traceback (most recent call last):
+        ...
+    ArithmeticError: Cannot Compute Geometric Mean for these numbers.
+    >>> compute_geometric_mean(-5, 25, 1)
+    -5.0
+    """
+    product = 1
+    for number in args:
+        if not isinstance(number, int) and not isinstance(number, float):
+            raise TypeError("Not a Number")
+        product *= number
+    # Cannot calculate the even root for negative product.
+    # Frequently they are restricted to being positive.
+    if product < 0 and len(args) % 2 == 0:
+        raise ArithmeticError("Cannot Compute Geometric Mean for these numbers.")
+    mean = abs(product) ** (1 / len(args))
+    # Since python calculates complex roots for negative products with odd roots.
+    if product < 0:
+        mean = -mean
+    # Since it does floating point arithmetic, it gives 64**(1/3) as 3.99999996
+    possible_mean = float(round(mean))
+    # To check if the rounded number is actually the mean.
+    if possible_mean ** len(args) == product:
+        mean = possible_mean
+    return mean
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod(name="compute_geometric_mean")
+    print(compute_geometric_mean(-3, -27))