Lecture Notes: Absolute Change vs. Relative Change

Introduction

Understanding the difference between absolute change and relative change.

Definition: The absolute change is the absolute value of the ending quantity minus the starting quantity.
- Formula: ( | \text{Ending Quantity} - \text{Starting Quantity} | )
Example 1: COVID-19 Cases
- July 21, 2020: 65,277 new cases (Starting Quantity)
- January 8, 2021: 300,594 new cases (Ending Quantity)
- Calculation:
  - Absolute Change = |300,594 - 65,277| = 235,317
  - Interpretation: 235,317 additional cases
Example 2: Politician's Approval Rating
- Approval dropped from 52% to 47%
- Calculation:
  - Absolute Change = |47 - 52| = 5%
  - Interpretation: A decrease of 5%

Definition: Relative change takes into account the initial amount, showing how the change relates to what was started with.
- Formula: ( \frac{\text{Absolute Change}}{\text{Starting Quantity}} )
Example 1: COVID-19 Cases
- Absolute Change = 235,317 (as calculated earlier)
- Starting Quantity = 65,277
- Calculation:
  - Relative Change = ( \frac{235,317}{65,277} \approx 3.6048 )
  - Expressed as a percentage: 360.5%
  - Interpretation: Approximately a 360.5% increase
Example 2: Politician's Approval Rating
- Absolute Change = 5% (as calculated earlier)
- Starting Quantity = 52%
- Calculation:
  - Relative Change = ( \frac{5}{52} \approx 0.096 )
  - Expressed as a percentage: 9.6%
  - Interpretation: A 9.6% decrease

Understanding the difference between absolute and relative change is essential in interpreting data correctly.
Reminder: Relative change often provides a better understanding of the context in terms of initial quantities.