The reasoning
| Measure | Definition | Strengths | Limitations | Use |
|---|---|---|---|---|
| Arithmetic mean | Σx/n | Uses all values; basis of parametric tests | Sensitive to outliers and skew | Symmetric data |
| Median | Middle value (50th percentile): position (n + 1)/2 | Robust to extremes | Ignores magnitudes; less efficient for normal data | Skewed data, ordinal data, censored data (median survival) |
| Mode | Most frequent value | Applies to nominal data | May be multiple or absent; unstable | Categorical; most common shoe/dose size |
| Geometric mean | ⁿ√(x₁·x₂·…·xₙ) = antilog of the mean of logs | Suits multiplicative, log‑normal data | Only positive values | Antibody titres, bacterial counts, population growth |
| Harmonic mean | n / Σ(1/x) | Averages rates with fixed numerators | Specialised | Average speed, some rate problems |