Added average absolute deviation (TheAlgorithms#5951)

* Added average absolute deviation

* Formats program with black

* reruns updated pre commit

* Update average_absolute_deviation.py

Co-authored-by: Christian Clauss <cclauss@me.com>

Author: lukasdotcom

DIRECTORY.md

@@ -454,6 +454,7 @@
   * [Area](https://github.com/TheAlgorithms/Python/blob/master/maths/area.py)
   * [Area Under Curve](https://github.com/TheAlgorithms/Python/blob/master/maths/area_under_curve.py)
   * [Armstrong Numbers](https://github.com/TheAlgorithms/Python/blob/master/maths/armstrong_numbers.py)
+  * [Average Absolute Deviation](https://github.com/TheAlgorithms/Python/blob/master/maths/average_absolute_deviation.py)
   * [Average Mean](https://github.com/TheAlgorithms/Python/blob/master/maths/average_mean.py)
   * [Average Median](https://github.com/TheAlgorithms/Python/blob/master/maths/average_median.py)
   * [Average Mode](https://github.com/TheAlgorithms/Python/blob/master/maths/average_mode.py)

maths/average_absolute_deviation.py

@@ -0,0 +1,29 @@
+def average_absolute_deviation(nums: list[int]) -> float:
+    """
+    Return the average absolute deviation of a list of numbers.
+    Wiki: https://en.wikipedia.org/wiki/Average_absolute_deviation
+
+    >>> average_absolute_deviation([0])
+    0.0
+    >>> average_absolute_deviation([4, 1, 3, 2])
+    1.0
+    >>> average_absolute_deviation([2, 70, 6, 50, 20, 8, 4, 0])
+    20.0
+    >>> average_absolute_deviation([-20, 0, 30, 15])
+    16.25
+    >>> average_absolute_deviation([])
+    Traceback (most recent call last):
+        ...
+    ValueError: List is empty
+    """
+    if not nums:  # Makes sure that the list is not empty
+        raise ValueError("List is empty")
+
+    average = sum(nums) / len(nums)  # Calculate the average
+    return sum(abs(x - average) for x in nums) / len(nums)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()