The Coefficient of Dispersion (COD) is a statistical measure used to evaluate the spread or variability of data points relative to the median. It is commonly used in economics, real estate assessments, and statistical research to determine uniformity in datasets.
Formula
The Coefficient of Dispersion is calculated as:
COD = (Σ |xi – M|) / (n × M)
Where:
- xi = Each individual value in the dataset
- M = Median of the dataset
- n = Total number of values
How to Use
- Enter the number of values in the dataset.
- Input the values separated by commas.
- Click the Calculate button to get the Coefficient of Dispersion (COD).
Example
Consider the dataset: 10, 15, 20, 25, 30
- Arrange in ascending order: 10, 15, 20, 25, 30
- Find the median (M): 20
- Calculate absolute deviations:
- |10 – 20| = 10
- |15 – 20| = 5
- |20 – 20| = 0
- |25 – 20| = 5
- |30 – 20| = 10
- Sum of absolute deviations: 10 + 5 + 0 + 5 + 10 = 30
- COD = 30 / (5 × 20) = 0.3
FAQs
1. What does the Coefficient of Dispersion indicate?
It shows how dispersed values are around the median in a dataset.
2. Why use the median instead of the mean in COD?
The median is less sensitive to outliers, making COD a robust measure of dispersion.
3. What is a high Coefficient of Dispersion?
A high COD indicates greater variability, while a low COD means more uniformity.
4. How does COD differ from standard deviation?
COD uses absolute differences from the median, while standard deviation uses squared differences from the mean.
5. Can COD be negative?
No, since it is based on absolute deviations, COD is always non-negative.
6. Is COD useful in real estate analysis?
Yes, it helps assess property value uniformity in a given market area.
7. How is COD applied in economics?
It measures income or price dispersion within an economy.
8. What is a good COD value?
It depends on the context; in real estate, a lower COD suggests a stable market.
9. Can COD be used for small datasets?
Yes, but the reliability increases with larger datasets.
10. How is COD different from the Coefficient of Variation (CV)?
COD uses the median, while CV uses the mean and is expressed as a percentage.
11. What happens if the dataset has extreme values?
Since COD uses the median, it remains stable even with outliers.
12. Is COD applicable in financial risk analysis?
Yes, it helps evaluate investment consistency over time.
13. How do I calculate COD in Excel?
Use formulas to find the median, compute absolute deviations, and divide their sum by n × median.
14. What industries commonly use COD?
Real estate, economics, sociology, and risk management.
15. Does COD apply to categorical data?
No, it is only used for numerical data.
16. Can COD be greater than 1?
Yes, if absolute deviations are significantly larger than the median.
17. How is COD used in social sciences?
It helps study income inequality and economic disparity.
18. What role does COD play in survey analysis?
It measures response variability across different groups.
19. Is a lower COD always better?
Not necessarily; it depends on the desired level of consistency in the data.
20. How can COD be reduced?
By improving data consistency or using more uniform sample selection methods.
Conclusion
The Coefficient of Dispersion Calculator is an essential tool for analyzing data spread around the median. It provides valuable insights into data consistency across various fields, from real estate to economics.