IQR function is added (#8851)

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* inter quartile range (IQR) function is added

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* IQR function is added

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* Update maths/interquartile_range.py

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* Changes on interquartile_range

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maths/interquartile_range.py

@@ -0,0 +1,66 @@
+"""
+An implementation of interquartile range (IQR) which is a measure of statistical
+dispersion, which is the spread of the data.
+
+The function takes the list of numeric values as input and returns the IQR.
+
+Script inspired by this Wikipedia article:
+https://en.wikipedia.org/wiki/Interquartile_range
+"""
+from __future__ import annotations
+
+
+def find_median(nums: list[int | float]) -> float:
+    """
+    This is the implementation of the median.
+    :param nums: The list of numeric nums
+    :return: Median of the list
+    >>> find_median(nums=([1, 2, 2, 3, 4]))
+    2
+    >>> find_median(nums=([1, 2, 2, 3, 4, 4]))
+    2.5
+    >>> find_median(nums=([-1, 2, 0, 3, 4, -4]))
+    1.5
+    >>> find_median(nums=([1.1, 2.2, 2, 3.3, 4.4, 4]))
+    2.65
+    """
+    div, mod = divmod(len(nums), 2)
+    if mod:
+        return nums[div]
+    return (nums[div] + nums[(div) - 1]) / 2
+
+
+def interquartile_range(nums: list[int | float]) -> float:
+    """
+    Return the interquartile range for a list of numeric values.
+    :param nums: The list of numeric values.
+    :return: interquartile range
+
+    >>> interquartile_range(nums=[4, 1, 2, 3, 2])
+    2.0
+    >>> interquartile_range(nums = [-2, -7, -10, 9, 8, 4, -67, 45])
+    17.0
+    >>> interquartile_range(nums = [-2.1, -7.1, -10.1, 9.1, 8.1, 4.1, -67.1, 45.1])
+    17.2
+    >>> interquartile_range(nums = [0, 0, 0, 0, 0])
+    0.0
+    >>> interquartile_range(nums=[])
+    Traceback (most recent call last):
+    ...
+    ValueError: The list is empty. Provide a non-empty list.
+    """
+    if not nums:
+        raise ValueError("The list is empty. Provide a non-empty list.")
+    nums.sort()
+    length = len(nums)
+    div, mod = divmod(length, 2)
+    q1 = find_median(nums[:div])
+    half_length = sum((div, mod))
+    q3 = find_median(nums[half_length:length])
+    return q3 - q1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()