statistical-analysislisted

# 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% / pow