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Python: Find x that minimizes mean squared deviation from a given list of numbers

Python Programming Puzzles: Exercise-27 with Solution

Squared deviations from the mean (SDM) are involved in various calculations. In probability theory and statistics, the definition of variance is either the expected value of the SDM (when considering a theoretical distribution) or its average value (for actual experimental data). Computations for analysis of variance involve the partitioning of a sum of SDM.
Write a Python program to find x that minimizes mean squared deviation from a given a list of numbers.
The problem requires minimizing the sum of squared deviations, which turns out to be the mean mu. Moreover, if mu is the mean of the numbers then a simple calculation.

Input:
[4, -5, 17, -9, 14, 108, -9]
Output:
17.142857142857142
Input:
[12, -2, 14, 3, -15, 10, -45, 3, 30]
Output:
1.1111111111111112

Sample Solution:

Python Code:

#License: https://bit.ly/3oLErEI

def test(nums):
    return sum(nums) / len(nums) 
nums = [4, -5, 17, -9, 14, 108, -9]
print("Original list:")
print(nums)
print("Minimizes mean squared deviation from the said list of numbers:")
print(test(nums))
nums = [12, -2, 14, 3, -15, 10, -45, 3, 30]
print("Original list:")
print(nums)
print("Minimizes mean squared deviation from the said list of numbers:")
print(test(nums))

Sample Output:

Original list:
[4, -5, 17, -9, 14, 108, -9]
Minimizes mean squared deviation from the said list of numbers:
17.142857142857142
Original list:
[12, -2, 14, 3, -15, 10, -45, 3, 30]
Minimizes mean squared deviation from the said list of numbers:
1.1111111111111112

Flowchart:

Flowchart: Python - Find x that minimizes mean squared deviation from a given list of numbers.

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Python: Tips of the Day

Find current directory and file's directory:

To get the full path to the directory a Python file is contained in, write this in that file:

import os 
dir_path = os.path.dirname(os.path.realpath(__file__))

(Note that the incantation above won't work if you've already used os.chdir() to change your current working directory, since the value of the __file__ constant is relative to the current working directory and is not changed by an os.chdir() call.)

To get the current working directory use

import os
cwd = os.getcwd()

Documentation references for the modules, constants and functions used above:

  • The os and os.path modules.
  • The __file__ constant
  • os.path.realpath(path) (returns "the canonical path of the specified filename, eliminating any symbolic links encountered in the path")
  • os.path.dirname(path) (returns "the directory name of pathname path")
  • os.getcwd() (returns "a string representing the current working directory")
  • os.chdir(path) ("change the current working directory to path")

Ref: https://bit.ly/3fy0R6m