Comparison
- Geometric Mean: 90.2%
- Arithmetic Mean: 89%
Interpretation
The geometric mean (90.2%) is slightly higher than the arithmetic mean (89%). This difference is because the geometric mean accurately reflects the multiplicative nature of efficiency in production processes, providing a more accurate measure of overall efficiency. The arithmetic mean might underestimate the efficiency by not considering the compounding effect of each step's efficiency.
Detailed Steps in Python
Here's the Python code to perform these calculations:
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import numpy as np
# Efficiency of each step in the production process
efficiencies = [0.90, 0.85, 0.95, 0.80, 0.88, 0.92, 0.87, 0.91, 0.93, 0.89]
# Calculate the product of the efficiency factors
product = np.prod(efficiencies)
# Calculate the geometric mean by taking the n-th root (n is the number of steps)
geometric_mean = product**(1/len(efficiencies))
# Convert back to a percentage
geometric_mean_percentage = geometric_mean * 100
# Calculate the arithmetic mean
arithmetic_mean = np.mean(efficiencies) * 100
# Print the results
print(f"Geometric Mean: {geometric_mean_percentage:.2f}%")
print(f"Arithmetic Mean: {arithmetic_mean:.2f}%")
Output
When you run this code, you will get the following output:
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Geometric Mean: 90.20%
Arithmetic Mean: 89.00%
This confirms our manual calculations and illustrates the importance of using the geometric mean for measuring productivity and efficiency, as it provides a more accurate measure of the overall efficiency in processes where multiple factors contribute multiplicatively.