Python  

How to Find Simple Aggregation Index Number using Python

Table of Contents

  • Introduction

  • What Is a Simple Aggregation Index Number?

  • Why Index Numbers Matter in Real Life

  • Real-World Scenario: Tracking Urban Cost of Living Changes

  • Step-by-Step Calculation Method

  • Complete Implementation with Test Cases

  • Best Practices and Common Mistakes

  • Conclusion

Introduction

Index numbers are silent workhorses of economics, policy-making, and business strategy—yet few developers understand how to compute them correctly. Among the simplest and most intuitive is the Simple Aggregation Index Number, a powerful tool for measuring overall change across multiple items without complex weighting.

In this article, you’ll learn how to calculate it from scratch in Python, applied to a timely real-world problem: tracking how the cost of urban living changes month over month. No external libraries, no fluff—just clear logic, tested code, and practical insight.

What Is a Simple Aggregation Index Number?

The Simple Aggregation Index Number compares the total price of a basket of goods or services in a current period to that in a base period. It’s calculated as:

c

  • An index of 100 means no change.

  • Above 100 indicates overall price increase (inflation).

  • Below 100 signals deflation or cost reduction.

Unlike weighted indices (e.g., CPI), this method treats all items equally—ideal for quick assessments or when weight data is unavailable.

Why Index Numbers Matter in Real Life

Governments use index numbers to adjust wages and pensions. Businesses use them to benchmark pricing. And now, smart city platforms use them to monitor affordability in real time. Misinterpreting or miscalculating them can lead to poor decisions—like underestimating rent spikes or overestimating grocery savings.

Real-World Scenario: Tracking Urban Cost of Living Changes

Imagine you’re building a dashboard for city planners in Austin, Texas. Every month, your system collects prices for 5 essential urban living items:

  • 1-bedroom apartment rent

  • Monthly public transit pass

  • Grocery basket (milk, bread, eggs, rice, veggies)

  • Internet plan (100 Mbps)

  • Gym membership

You want to know: “Has the overall cost of basic urban living increased this month compared to January (base month)?”

This is a perfect use case for the Simple Aggregation Index Number—fast, transparent, and easy to explain to non-technical stakeholders.

Step-by-Step Calculation Method

  1. Collect base period prices (e.g., January values).

  2. Collect current period prices (e.g., June values).

  3. Sum all base prices → total_base

  4. Sum all current prices → total_current

  5. Compute index: (total_current / total_base) * 100

That’s it—no weights, no logarithms, no regressions.

Complete Implementation with Test Cases

from typing import List
import unittest

def simple_aggregation_index(base_prices: List[float], current_prices: List[float]) -> float:
    """
    Calculate the Simple Aggregation Index Number.
    
    Args:
        base_prices: List of prices in the base period
        current_prices: List of prices in the current period
        
    Returns:
        Index number (e.g., 105.2 means 5.2% increase)
        
    Raises:
        ValueError: If lists are empty, unequal length, or base sum is zero
    """
    if not base_prices or not current_prices:
        raise ValueError("Price lists cannot be empty")
    
    if len(base_prices) != len(current_prices):
        raise ValueError("Base and current price lists must have the same length")
    
    total_base = sum(base_prices)
    total_current = sum(current_prices)
    
    if total_base == 0:
        raise ValueError("Sum of base prices cannot be zero")
    
    index = (total_current / total_base) * 100
    return round(index, 2)

class TestSimpleAggregationIndex(unittest.TestCase):
    
    def test_basic_increase(self):
        # Base Sum: 1200 + 50 + 200 + 60 + 40 = 1550
        base = [1200, 50, 200, 60, 40]       # Jan prices
        # Current Sum: 1250 + 52 + 210 + 62 + 42 = 1616
        current = [1250, 52, 210, 62, 42]    # Jun prices
        # Calculation: (1616 / 1550) * 100 ≈ 104.258... -> 104.26
        index = simple_aggregation_index(base, current)
        self.assertAlmostEqual(index, 104.26, places=2) # Corrected from 103.77

    def test_no_change(self):
        prices = [100, 200, 300]
        index = simple_aggregation_index(prices, prices)
        self.assertEqual(index, 100.0)

    def test_decrease(self):
        base = [500, 100]
        current = [450, 90]
        index = simple_aggregation_index(base, current)
        self.assertEqual(index, 90.0)  # 10% decrease

    def test_error_cases(self):
        with self.assertRaises(ValueError):
            simple_aggregation_index([], [1, 2])
        with self.assertRaises(ValueError):
            simple_aggregation_index([1, 2], [3])
        with self.assertRaises(ValueError):
            simple_aggregation_index([0, 0], [1, 2])

if __name__ == "__main__":
    # Realistic Austin cost-of-living data (USD)
    january_prices = [1450, 55, 220, 65, 35]   # Base: Jan
    june_prices = [1520, 58, 235, 68, 38]       # Current: Jun
    
    index = simple_aggregation_index(january_prices, june_prices)
    
    print("=== Urban Cost of Living Index (Austin) ===")
    print(f"Base Period: January")
    print(f"Current Period: June")
    print(f"Simple Aggregation Index: {index}")
    
    if index > 100:
        print(f"→ Overall cost of living increased by {index - 100:.2f}%")
    elif index < 100:
        print(f"→ Overall cost of living decreased by {100 - index:.2f}%")
    else:
        print("→ No change in overall cost")
    
    # Run tests
    unittest.main(argv=[''], exit=False, verbosity=2)
qa

Best Practices and Common Mistakes

  • Use consistent units: All prices must be in the same currency and time unit (e.g., monthly USD).

  • Match items exactly: Don’t compare “basic internet” in base vs “premium internet” in current.

  • Don’t use this for policy-critical decisions without weighting—simple aggregation ignores item importance (e.g., rent matters more than gym).

  • Always validate inputs: Zero or negative prices can distort results.

  • Pair with visualization: Show the index trend over time for maximum impact.

Conclusion

The Simple Aggregation Index Number is a lightweight, interpretable metric perfect for rapid assessments of price trends—whether you’re monitoring urban affordability, SaaS subscription costs, or supply chain expenses. By implementing it correctly and understanding its limitations, you empower teams to spot inflationary pressures early and act with confidence. In a world drowning in data, sometimes the simplest index tells the clearest story.

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