Calculation of clocking in, minute-by-minute, vs rounding.

work-time.py

import random
import numpy as np
import matplotlib.pyplot as plt

# Initialize variables for multiple tests
num_tests = 10000
differences = []

# Loop for each test
for test in range(num_tests):
    num_days = 365  # 2 years
    total_minutes_exact = 0
    total_minutes_rounded = 0

    # Loop through each day
    for day in range(num_days):
        # Generate a random start time for the day
        start_time = random.randint(0, 540)  # Anytime from 00:00 to 08:00

        # Generate a random end time for the day
        end_time = start_time + random.randint(1, 480)  # Max of 8 hours (480 minutes)

        # Calculate the actual minutes worked for the day
        minutes_worked_exact = end_time - start_time

        # Round to nearest half-hour
        # if minutes_worked_exact % 30 >= 15:
        #     minutes_worked_rounded = (minutes_worked_exact // 30 + 1) * 30
        # else:
        #     minutes_worked_rounded = (minutes_worked_exact // 30) * 30

        # round to the nearest hour
        if minutes_worked_exact % 60 >= 30:
            minutes_worked_rounded = (minutes_worked_exact // 60 + 1) * 60
        else:
            minutes_worked_rounded = (minutes_worked_exact // 60) * 60

        # Add to the tallies
        total_minutes_exact += minutes_worked_exact
        total_minutes_rounded += minutes_worked_rounded

    # Convert total minutes to hours for easy comparison
    total_hours_exact = total_minutes_exact / 60
    total_hours_rounded = total_minutes_rounded / 60

    # Calculate the difference
    difference = total_hours_rounded - total_hours_exact

    # Append to list for later analysis
    differences.append(difference)

# Calculate statistics
median_difference = np.median(differences)
average_difference = np.mean(differences)
std_deviation = np.std(differences)

# Print statistics
print(f"Median Difference: {median_difference}")
print(f"Average Difference: {average_difference}")
print(f"Standard Deviation: {std_deviation}")

# Plotting
plt.hist(differences, bins=50, alpha=0.75, label='Difference Distribution')
plt.axvline(median_difference, color='r', linestyle='dashed', linewidth=1, label=f"Median: {median_difference}")
plt.axvline(average_difference, color='g', linestyle='dashed', linewidth=1, label=f"Mean: {average_difference}")
plt.axvline(average_difference + std_deviation, color='y', linestyle='dashed', linewidth=1, label=f"Mean+StdDev: {average_difference + std_deviation}")
plt.axvline(average_difference - std_deviation, color='y', linestyle='dashed', linewidth=1, label=f"Mean-StdDev: {average_difference - std_deviation}")

plt.legend(loc='upper right')
plt.xlabel('Hours')
plt.ylabel('Frequency')
plt.title('Difference in Hours (Rounded - Exact)')
plt.show()