Coefficient of Variation (C.V.) – Interpretation & Applications 📊📉

The Coefficient of Variation (C.V.) is a relative measure of dispersion. It compares the degree of variation between two or more datasets, even when their means and units differ.

It is widely used in business, finance, economics, and quality control to judge consistency.

1. Definition

The Coefficient of Variation expresses Standard Deviation as a percentage of the Mean.

It shows how much variation exists relative to the average value.

Formula

C.V. = (Standard Deviation / Mean) × 100

• Lower C.V. → Higher consistency / Lower variability
• Higher C.V. → Lower consistency / Higher variability

2. Solved Examples

Example 1 — Compare Consistency of Two Workers

Compute C.V.

C.V.(A) = (6 / 40) × 100 = 15%
C.V.(B) = (4 / 30) × 100 = 13.33%

Interpretation

• Worker B has a lower C.V., so B is more consistent.

Example 2 — Compare Two Companies' Daily Sales

Compute C.V.

C.V.(X) = (8000 / 50000) × 100 = 16%
C.V.(Y) = (5000 / 40000) × 100 = 12.5%

Conclusion

• Company Y has more stable sales because its C.V. is lower.

Example 3 — Population Study

Heights (Mean = 160 cm, S.D. = 8 cm)

C.V. = (8 / 160) × 100 = 5%

A very low C.V. indicates high uniformity in height.

3. Merits of C.V. ✔️

• Removes effect of units
• Useful for comparison of consistency
• Works even when means differ widely
• Simple and easy to compute
• Essential in finance for risk comparison

4. Limitations ❌

• Cannot be used when mean = 0 (undefined)
• Misleading if mean is very small
• Highly sensitive to extreme values (because S.D. used)

5. Applications in Business & Economics

• Risk analysis of investments
• Compare productivity of workers
• Compare stability of demand, sales, costs
• Quality control
• Portfolio management in finance

6. Summary ✨

• C.V. = (S.D. / Mean) × 100
• Relative measure of dispersion
• Lower C.V. = greater consistency
• Ideal for comparisons across units and scales

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