Part I
Core Concepts & Formulas
Topic 1
Exploring Data
Center: mean, median. Spread: SD, IQR, range. Shape: symmetric, skewed. Outlier fence = Q1 − 1.5·IQR or Q3 + 1.5·IQR. Resistant stats: median & IQR. Adding constant shifts mean; multiplying scales mean AND SD.
Topic 2
Normal Distribution
68–95–99.7 rule. Z = (x − μ)/σ. Use z-table for P(Z < z). 90th percentile: z ≈ 1.28. 95th: z ≈ 1.645. 97.5th: z ≈ 1.96. To find x: x = μ + z·σ.
Topic 3
Linear Regression
ŷ = a + bx, b = r(Sy/Sx), a = ȳ − bx̄. Residual = observed − predicted. r² = % variation explained. Random scatter in residual plot = good linear fit. r describes strength & direction; r² describes fit.
Topic 4
Probability
Addition: P(A∪B) = P(A) + P(B) − P(A∩B). Independent: P(A∩B) = P(A)·P(B). Conditional: P(A|B) = P(A∩B)/P(B). Complement: P(Aᶜ) = 1 − P(A). Bayes: P(A|B) = P(B|A)·P(A) / P(B).
Topic 5
Sampling Distributions
x̄: mean μ, SE = σ/√n. p̂: mean p, SE = √(p(1−p)/n). CLT: n ≥ 30 for means. Normal approx for p̂ when np ≥ 10 and n(1−p) ≥ 10. Larger n → smaller SE → less variability.
Topic 6
Inference
CI = statistic ± z*(or t*)·SE. p-value = P(data this extreme | H₀ true). Reject H₀ if p < α. Type I (α): reject true H₀. Type II (β): keep false H₀. Power = 1 − β. df = (r−1)(c−1) for χ².
📐 Key Formulas — Memorize These
Z-score: z = (x − μ) / σ
SE of x̄: SE = σ / √n
SE of p̂: SE = √[ p(1−p) / n ]
Regression slope: b = r · (Sy / Sx)
Regression intercept:a = ȳ − b·x̄
t-statistic: t = (x̄ − μ₀) / (s / √n)
Chi-square: χ² = Σ[ (O − E)² / E ], df = (r−1)(c−1)
Expected value: E(X) = Σ[ x · P(X = x) ]
Confidence Interval:estimate ± (critical value) × SE
SE of x̄: SE = σ / √n
SE of p̂: SE = √[ p(1−p) / n ]
Regression slope: b = r · (Sy / Sx)
Regression intercept:a = ȳ − b·x̄
t-statistic: t = (x̄ − μ₀) / (s / √n)
Chi-square: χ² = Σ[ (O − E)² / E ], df = (r−1)(c−1)
Expected value: E(X) = Σ[ x · P(X = x) ]
Confidence Interval:estimate ± (critical value) × SE
🧠 Memory Anchors: SOCS (Shape, Outliers, Center, Spread) for describing distributions. LINER (Linear, Independent, Normal, Equal variance, Random) for regression conditions. STATE → PLAN → DO → CONCLUDE for inference. The p-value is NOT the probability H₀ is true — it assumes H₀ is true! We NEVER accept H₀; we only fail to reject it.
Part II
20 Practice Questions
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