Percentage Aggregation Strategy Matrix
Core Models
- Arithmetic Mean: Σp ÷ n (equal significance)
- Weighted Mean: Σ(p·w) ÷ Σw (differing impact)
- Geometric Mean (growth rates): (Π(1+p))^(1/n) − 1
Selection Guide
- Uniform assessments → Arithmetic
- Grade components / portfolio sectors → Weighted
- Compounding returns / efficiency gains → Geometric
Quality Diagnostics
- Outlier shift check: Recompute mean excluding extreme → Δ > 5% signals skew
- Weight normalization: Σw must = 1 (or scale consistently)
- Mixed bases? Convert to common denominator before averaging
Error Avoidance
- Don’t average already averaged unequal groups—unpack original weights
- Preserve precision until final rounding
- Document weight rationale (audit transparency)
Fast Heuristics
- Two values only → midpoint = (hi+lo)/2 if equal weight
- Dominant component ≥60% weight → mean will track that value closely
- Approx weighted: (Major% × MajorWeight%) + (Residual average × Residual weight)
FAQ
- Why geometric for returns? Captures compounding; arithmetic overstates sustained yield.
- Can weights be decimals? Yes—any proportional scale works if consistent.
- Negative percentages? Include as signed values (losses / declines) before averaging.
Action Tip: Log intermediate Σ(p·w) & Σw—enables rapid scenario tweaking without recomputing base entries.