Mean vs Median
MEAN = pulled by outliers. MEDIAN = middle = safe from outliers. Skewed data → use median.
Box Plot 5-Number
Min · Q1 · Median · Q3 · Max. IQR = Q3 − Q1. Outlier if > Q3+1.5·IQR or < Q1−1.5·IQR.
σ vs s
σ (sigma) = population SD. s = sample SD. Sample divides by n−1 (Bessel's correction).
Normal 68-95-99.7
68% within ±1σ · 95% within ±2σ · 99.7% within ±3σ. Memorize this rule cold!
z-score formula
z = (x − μ) / σ. Tells you how many SDs from the mean. Negative z = below mean.
Skew Direction
Right skew (positive) → tail points RIGHT → mean > median. Left skew → mean < median.
Sample Size n
Population N (whole group). Sample n (subset). Parameter = population. Statistic = sample.
Standard Normal
μ = 0, σ = 1. Use z-table to find area (= probability). Area LEFT of z.