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---
name: statistical-analysis-central-tendency
description: 'Sub-skill of statistical-analysis: Central Tendency (+3).'
version: 1.0.0
category: data-analytics
type: reference
scripts_exempt: true
---
# Central Tendency (+3)
## Central Tendency
Choose the right measure of center based on the data:
| Situation | Use | Why |
|---|---|---|
| Symmetric distribution, no outliers | Mean | Most efficient estimator |
| Skewed distribution | Median | Robust to outliers |
| Categorical or ordinal data | Mode | Only option for non-numeric |
| Highly skewed with outliers (e.g., revenue per user) | Median + mean | Report both; the gap shows skew |
**Always report mean and median together for business metrics.** If they diverge significantly, the data is skewed and the mean alone is misleading.
## Spread and Variability
- **Standard deviation**: How far values typically fall from the mean. Use with normally distributed data.
- **Interquartile range (IQR)**: Distance from p25 to p75. Robust to outliers. Use with skewed data.
- **Coefficient of variation (CV)**: StdDev / Mean. Use to compare variability across metrics with different scales.
- **Range**: Max minus min. Sensitive to outliers but gives a quick sense of data extent.
## Percentiles for Business Context
Report key percentiles to tell a richer story than mean alone:
```
p1: Bottom 1% (floor / minimum typical value)
p5: Low end of normal range
p25: First quartile
p50: Median (typical user)
p75: Third quartile
p90: Top 10% / power users
p95: High end of normal range
p99: Top 1% / extreme users
```
**Example narrative**: "The median session duration is 4.2 minutes, but the top 10% of users spend over 22 minutes per session, pulling the mean up to 7.8 minutes."
## Describing Distributions
Characterize every numeric distribution you analyze:
- **Shape**: Normal, right-skewed, left-skewed, bimodal, uniform, heavy-tailed
- **Center**: Mean and median (and the gap between them)
- **Spread**: Standard deviation or IQR
- **Outliers**: How many and how extreme
- **Bounds**: Is there a natural floor (zero) or ceiling (100%)?
