Absolute vs Relative Measures of Dispersion 📊⚖️
Measures of dispersion help us understand how spread out the data is. These measures are classified into Absolute and Relative types based on how they express variability.
This chapter explains the difference, formulas, uses, and exam-ready comparisons.
1. Absolute Measures of Dispersion
Absolute measures express the variability in the same units as the data.
Examples include:
- Range
- Quartile Deviation (Q.D.)
- Mean Deviation (M.D.)
- Standard Deviation (S.D.)
Characteristics
- Expressed in units such as kg, ₹, cm, marks, etc.
- Easy to compute and understand.
- Useful when comparing datasets measured in the same unit.
Limitation
- Cannot compare datasets with different units or scales.
2. Relative Measures of Dispersion
Relative measures express dispersion as a ratio, percentage, or coefficient.
Examples include:
- Coefficient of Range
- Coefficient of Quartile Deviation
- Coefficient of Mean Deviation
- Coefficient of Variation (C.V.)
Characteristics
- Unit-free (dimensionless)
- Allow comparison between datasets with different units or scales
- Useful for comparing stability or consistency across groups
Limitation
- More abstract and less intuitive than absolute measures.
3. Difference Between Absolute & Relative Measures
A clear exam-oriented comparison:
| Basis | Absolute Measures | Relative Measures |
|---|---|---|
| Meaning | Show actual amount of dispersion | Show proportion/percentage of dispersion |
| Units | Expressed in original units | Unit-free (dimensionless) |
| Comparison | Only for same-unit datasets | Can compare across different units |
| Examples | Range, Q.D., M.D., S.D. | Coeff. of Range, C.V., Coeff. of Q.D. |
| Purpose | Measure actual spread | Measure relative spread |
| Usefulness | Good for internal analysis | Good for cross-dataset comparison |
4. Solved Examples
Example 1 — Absolute Measure (Range)
Marks: 10, 20, 25, 30, 45
Range = Highest – Lowest = 45 – 10 = 35
Dispersion = 35 marks (in original units).
Example 2 — Relative Measure (Coefficient of Variation)
Two machines produce items with the following data:
Machine A: Mean = 50, S.D. = 5 Machine B: Mean = 80, S.D. = 12
Compute C.V.
C.V. = (S.D. / Mean) × 100
C.V.(A) = (5 / 50) × 100 = 10%
C.V.(B) = (12 / 80) × 100 = 15%
Machine A has lower C.V., so it is more consistent.
5. When to Use Which Measure?
Use Absolute Measures when:
- Units are the same (e.g., marks, kg, ₹)
- You want actual spread
- Comparing variability within the same dataset
Use Relative Measures when:
- Units are different (e.g., cm vs kg)
- Means differ widely
- Comparing risk, stability, performance
Summary ✨
- Dispersion can be measured in absolute or relative terms.
- Absolute = actual spread (units preserved).
- Relative = comparative spread (unit-free).
- C.V. is the most important relative measure for comparing consistency.
Quiz Time 🎯
Test Your Knowledge
Question 1 of 5
1. Absolute measures are expressed in: