Absolute Difference vs Relative Difference

Key Concepts

• Absolute Difference: Calculated as the compared value minus the reference value.
• Relative Difference: Calculated as the absolute difference divided by the reference value, then multiplied by 100% to get a percentage.

Formulae

• Absolute Difference: [ \text{Compared Value} - \text{Reference Value} ]
• Relative Difference: [ \left( \frac{\text{Absolute Difference}}{\text{Reference Value}} \right) \times 100% ]

Example Problem

Two individuals, Clint and Helen, had salary increases over a three-year period.

Clint's Salary Increase

• Beginning Salary: $23,000
• Ending Salary: $36,800
• Absolute Difference:
  • [ \text{Ending Salary} - \text{Beginning Salary} = 36,800 - 23,000 = 13,800 ]
  • Clint gained $13,800 over three years.
• Relative Difference:
  • [ \left( \frac{13,800}{23,000} \right) \times 100% = 60% ]
  • Clint's salary increased by 60% in relative terms compared to his original salary.

Helen's Salary Increase

• Beginning Salary: $29,000
• Ending Salary: $44,950
• Absolute Difference:
  • [ \text{Ending Salary} - \text{Beginning Salary} = 44,950 - 29,000 = 15,950 ]
  • Helen gained $15,950 over three years.
• Relative Difference:
  • [ \left( \frac{15,950}{29,000} \right) \times 100% = 55% ]
  • Helen's salary increased by 55% in relative terms compared to her original salary.

Comparison

• Absolute Terms: Helen had a higher absolute increase ($15,950) compared to Clint ($13,800).
• Relative Terms: Clint had a higher relative increase (60%) compared to Helen (55%).

Conclusion

• Absolute difference measures the total change in monetary terms.
• Relative difference measures the change in relation to the initial value, providing a percentage increase.
• Clint had a greater percentage increase, while Helen had a greater total increase in dollars.