The Coefficient of Dispersion is a relative measure of dispersion used to compare variability across different datasets, especially when their units or means differ. It is derived from absolute measures like Range, Quartile Deviation, Mean Deviation, or Standard Deviation by dividing them with a central tendency value such as Mean or Median.
Definition
The Coefficient of Dispersion provides a unit-free, standardized value of variability. It is especially useful when comparing datasets with different units or scales.
General Formula
Coefficient of Dispersion = Absolute Measure of Dispersion / Central Tendency
Types and Formulas
1. Coefficient of Range
Coefficient of Range = (L − S) / (L + S)
Where L = Largest value, S = Smallest value
2. Coefficient of Quartile Deviation
Coefficient of Q.D. = (Q3 − Q1) / (Q3 + Q1)
3. Coefficient of Mean Deviation
Based on Mean: Coefficient = M.D. / Mean
Based on Median: Coefficient = M.D. / Median
4. Coefficient of Standard Deviation
Coefficient = Standard Deviation / Mean
Example
Data: 10, 12, 14, 16, 18
- Mean = (10 + 12 + 14 + 16 + 18) / 5 = 14
- Deviations: -4, -2, 0, 2, 4
- Squares: 16, 4, 0, 4, 16
- Σ(X − X̄)² = 40, N = 5
- Standard Deviation = √(40 / 5) = √8 ≈ 2.83
- Coefficient = 2.83 / 14 ≈ 0.202
Merits of Coefficient of Dispersion
- Removes unit dependency; results are in pure numbers or ratios
- Facilitates comparison across different datasets
- Useful in relative analysis (e.g., comparing variation in incomes or prices)
Demerits of Coefficient of Dispersion
- Depends on the reliability of the absolute measure used
- Inconsistent results if central tendency (like mean) is unstable
- Less informative when used in isolation without context
Use Cases in Business Statistics
- Comparing price volatility of two different stocks
- Evaluating consistency of employee performance across departments
- Analyzing spread of income across different regions
Comparison Table
| Type | Formula | Based On | Suitable When |
|---|---|---|---|
| Coefficient of Range | (L − S) / (L + S) | Extreme values | Quick comparison |
| Coefficient of Q.D. | (Q3 − Q1) / (Q3 + Q1) | Middle 50% | Less affected by outliers |
| Coefficient of M.D. | M.D. / Mean or Median | Absolute deviations | More balanced dispersion |
| Coefficient of S.D. | S.D. / Mean | Squared deviations | Statistical analysis and consistency |
Conclusion
The Coefficient of Dispersion plays a vital role in understanding relative variability and making statistical comparisons between different datasets. For UGC NET Commerce aspirants, mastering this concept enhances their ability to interpret statistical data meaningfully and make informed conclusions. It bridges the gap between raw dispersion and analytical utility by offering a standardized metric for comparison.