statistical-analysis-central-tendency

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%)?