statistical-analysis

Statistical Analysis Skill

Descriptive statistics, trend analysis, outlier detection, hypothesis testing, and guidance on when to be cautious about statistical claims.

Descriptive Statistics Methodology

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%)?