What is Dispersion?
Before diving into the Coefficient of Variation, recall that dispersion is the statistical term used to describe the extent to which data points in a distribution differ from the average (mean, median, or mode). In simpler terms, it tells us how spread out the data is.
What is Coefficient of Variation?
The Coefficient of Variation (CV) is a statistical tool that allows us to compare the degree of variation from one dataset to another, even if the means are drastically different. It expresses the standard deviation as a percentage of the mean.
Definition: The Coefficient of Variation is the ratio of the standard deviation to the mean, expressed as a percentage.
Formula
Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100
Symbolically, CV = (σ / μ) × 100
Where:
- σ = Standard Deviation
- μ = Mean
Why Use Coefficient of Variation?
When comparing two or more datasets that have different units or significantly different means, the absolute standard deviation alone may be misleading. That’s where CV becomes useful — it provides a unitless, percentage-based measure of variability that enables fair comparison.
Example:
Suppose we have the following marks (out of 100) of two classes:
Class A: 45, 50, 55, 60, 65
Class B: 30, 35, 40, 45, 50
- Mean of A = (45+50+55+60+65)/5 = 275/5 = 55
- Standard Deviation (A) = √[(Σ(X - X̄)²)/N] = √(250/5) = √50 ≈ 7.07
- CV (A) = (7.07 / 55) × 100 ≈ 12.86%
- Mean of B = 200/5 = 40
- Standard Deviation (B) = √(250/5) = √50 ≈ 7.07
- CV (B) = (7.07 / 40) × 100 ≈ 17.68%
Interpretation: Even though both classes have the same standard deviation, Class B has more relative variation in scores. Class A is more consistent.
Applications of Coefficient of Variation
- To compare risk in investment portfolios
- To measure consistency in performance (sales, manufacturing, marketing, etc.)
- Used in quality control to measure product consistency
- In research and experiments, to determine the reliability of data
Merits of Coefficient of Variation
- Unit-free: CV is independent of the units of measurement
- Ideal for comparing datasets with different means
- Helps in choosing between consistent and inconsistent data sets
- Widely accepted in business, economics, and finance
Demerits of Coefficient of Variation
- Not reliable if the mean is close to zero (since it will inflate CV)
- Assumes data is normally distributed — may mislead in skewed datasets
- Can be sensitive to outliers
Coefficient of Variation vs Standard Deviation
| Aspect | Standard Deviation | Coefficient of Variation |
|---|---|---|
| Units | Same as data | No units (percentage) |
| Absolute or Relative? | Absolute Measure | Relative Measure |
| Comparability | Limited comparability across datasets | Highly useful for comparison |
| Formula | σ = √[Σ(X − X̄)² / N] | (σ / μ) × 100 |
Tips for UGC NET Preparation
- Always mention whether the CV is high or low — it affects interpretation.
- Memorize the formula with clarity — don’t confuse it with standard deviation.
- Use CV when comparing across different units, like comparing rainfall data with income data.
- Understand the logic behind using percentage — it normalizes the values.
In summary, the Coefficient of Variation is an essential statistical tool for business analysis. It empowers analysts, researchers, and students to compare variability across different datasets, even when those datasets use different scales or units. As you prepare for the UGC NET Commerce exam, ensure you not only understand how to calculate CV but also when and why to use it. With a clear understanding, this topic becomes one of your strongest assets in both academic and professional spheres.