Statistical Calculator GUI Implementation

The following complete code includes all necessary functions and variables, along with comments and docstrings to facilitate understanding and usage by others.

```python

# Import required libraries for numerical operations

import numpy as np

import pandas as pd

# Define a function to calculate mean using NumPy's optimized implementation

def calculate_mean(arr):

"""

Calculate the arithmetic mean of an array

Parameters:

arr (array): Input array for mean calculation

Returns:

float: Mean value of the array

Algorithm: Utilizes NumPy's vectorized mean computation for efficiency

"""

return np.mean(arr)

# Define median calculation function with proper array handling

def calculate_median(arr):

"""

Calculate the median value of an array

Parameters:

arr (array): Input array for median calculation

Returns:

float: Median value of the array

Implementation: Uses NumPy's median function which automatically handles

both even and odd-length arrays

"""

return np.median(arr)

# Standard deviation function with population standard deviation calculation

def calculate_std(arr):

"""

Calculate the standard deviation of an array

Parameters:

arr (array): Input array for standard deviation calculation

Returns:

float: Standard deviation of the array

Note: By default, NumPy's std() calculates population standard deviation (ddof=0)

"""

return np.std(arr)

# Variance calculation function using mathematical variance formula

def calculate_variance(arr):

"""

Calculate the variance of an array

Parameters:

arr (array): Input array for variance calculation

Returns:

float: Variance of the array

Mathematical Basis: Variance measures the spread of data points

around the mean value

"""

return np.var(arr)

# Test code with sample array to verify all statistical functions

if __name__ == '__main__':

arr = np.array([1, 2, 3, 4, 5])

print("Array:", arr)

print("Mean:", calculate_mean(arr))

print("Median:", calculate_median(arr))

print("Standard Deviation:", calculate_std(arr))

print("Variance:", calculate_variance(arr))

```

This code provides a solid foundation for statistical calculations and can be easily integrated into GUI applications. The functions demonstrate proper use of NumPy's mathematical operations for efficient numerical computations.