# Statistical Analysis Central Tendency

> Sub-skill of statistical-analysis: Central Tendency (+3).

- Skill: `vamseeachanta/statistical-analysis-central-tendency` (Agent Skill)
- Install (CLI): `npx skillmds@latest add vamseeachanta/statistical-analysis-central-tendency`
- Raw SKILL.md: https://api.skillmd.com/api/skills/vamseeachanta/statistical-analysis-central-tendency/raw
- Safety review: PASS (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Data & Analytics
- Author: vamseeachanta (https://skillmd.com/u/vamseeachanta)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/vamseeachanta/statistical-analysis-central-tendency

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# 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%)?