AP Statistics Resources

Essential resources to support your AP Statistics review

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AP Statistics Formula Sheet

This comprehensive formula sheet includes all the key formulas you'll need for the AP Statistics exam.

DESCRIPTIVE STATISTICS
Measures of Center:
Mean: x̄ = (Σx)/n
Median: Middle value of ordered data (or average of two middle values)
Mode: Most frequent value(s)
Measures of Spread:
Range: Maximum - Minimum
Interquartile Range (IQR): Q3 - Q1
Sample Variance: s² = Σ(x - x̄)²/(n-1)
Sample Standard Deviation: s = √[Σ(x - x̄)²/(n-1)]
Population Variance: σ² = Σ(x - μ)²/N
Population Standard Deviation: σ = √[Σ(x - μ)²/N]
Linear Transformations:
If Y = a + bX, then:
μY = a + bμX
σY = |b|σX
PROBABILITY
Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
Multiplication Rule: P(A and B) = P(A) × P(B|A)
Conditional Probability: P(B|A) = P(A and B)/P(A)
Independence: P(A and B) = P(A) × P(B)
Complement Rule: P(A') = 1 - P(A)
RANDOM VARIABLES
Expected Value (Discrete): μX = Σ[x × P(x)]
Variance (Discrete): σ²X = Σ[(x - μX)² × P(x)] = Σ[x² × P(x)] - μ²X
Standard Deviation: σX = √σ²X
Binomial Distribution: X ~ B(n, p)
P(X = k) = (n choose k) × p^k × (1-p)^(n-k)
μX = np
σX = √[np(1-p)]
Geometric Distribution: X ~ Geo(p)
P(X = k) = (1-p)^(k-1) × p
μX = 1/p
σX = √[(1-p)/p²]
SAMPLING DISTRIBUTIONS
Standard Error of the Mean: σx̄ = σ/√n
Central Limit Theorem: For large n, x̄ ~ N(μ, σ/√n)
Standard Error of the Proportion: σp̂ = √[p(1-p)/n]
Sampling Distribution of p̂: For large n, p̂ ~ N(p, √[p(1-p)/n])
CONFIDENCE INTERVALS
For a Mean (σ known): x̄ ± z* × (σ/√n)
For a Mean (σ unknown): x̄ ± t* × (s/√n)
For a Proportion: p̂ ± z* × √[p̂(1-p̂)/n]
For a Difference of Means (independent): (x̄₁ - x̄₂) ± t* × √(s₁²/n₁ + s₂²/n₂)
For a Difference of Proportions: (p̂₁ - p̂₂) ± z* × √[p̂₁(1-p̂₁)/n₁ + p̂₂(1-p̂₂)/n₂]
HYPOTHESIS TESTING
For a Mean (σ known): z = (x̄ - μ₀)/(σ/√n)
For a Mean (σ unknown): t = (x̄ - μ₀)/(s/√n)
For a Proportion: z = (p̂ - p₀)/√[p₀(1-p₀)/n]
For a Difference of Means (independent): t = (x̄₁ - x̄₂ - d₀)/√(s₁²/n₁ + s₂²/n₂)
For a Difference of Proportions: z = (p̂₁ - p̂₂ - d₀)/√[p̂₁(1-p̂₁)/n₁ + p̂₂(1-p̂₂)/n₂]
CHI-SQUARE TESTS
Chi-Square Statistic: χ² = Σ[(O - E)²/E]
Degrees of Freedom:
Goodness of Fit: df = k - 1 (k = number of categories)
Independence/Homogeneity: df = (r - 1)(c - 1) (r = rows, c = columns)
REGRESSION
Least Squares Regression Line: ŷ = a + bx
Slope: b = r × (sy/sx)
y-intercept: a = ȳ - b × x̄
Coefficient of Determination: r²
Standard Error of the Slope: SE_b = √[Σ(y - ŷ)²/((n-2)Σ(x - x̄)²)]
t-statistic for Slope: t = (b - 0)/SE_b

Study Guides

Concise study guides for each topic covered in the AP Statistics curriculum.

Key Concepts:

  • Types of data (categorical vs. quantitative, discrete vs. continuous)
  • Measures of center (mean, median, mode)
  • Measures of spread (range, IQR, standard deviation)
  • Graphical displays (dotplots, histograms, boxplots, stemplots)
  • Describing distributions (shape, center, spread, outliers)
  • Effects of transformations on data

View Full Study Guide

Key Concepts:

  • Basic probability rules (addition, multiplication, complement)
  • Conditional probability and independence
  • Random variables (discrete vs. continuous)
  • Expected value and variance
  • Binomial and geometric distributions

View Full Study Guide

Online Resources

Curated online resources to supplement your AP Statistics review.

College Board Resources
Video Resources
  • Khan Academy AP Statistics: Comprehensive video lessons covering all topics
  • AP Statistics YouTube Channel: Video explanations of key concepts and problem-solving strategies
  • Crash Course Statistics: Fast-paced overview videos of statistical concepts
Interactive Tools
  • StatCrunch: Online statistical software for data analysis
  • Desmos: Online graphing calculator with statistical capabilities
  • Rossman/Chance Applet Collection: Interactive demonstrations of statistical concepts
Practice Exam Resources
  • Albert.io: AP Statistics practice questions and explanations
  • Varsity Tutors: Free AP Statistics diagnostic tests
  • AP Statistics Released Exams: Official past exams from College Board

Common Misconceptions and Clarifications

Understanding and avoiding common statistical misconceptions is crucial for success on the AP exam.

Probability vs. Statistics

Misconception: Probability and statistics are the same thing.

Clarification:

  • Probability: Using known parameters to predict data
  • Statistics: Using data to estimate unknown parameters
Correlation vs. Causation

Misconception: If two variables are correlated, one must cause the other.

Clarification:

  • Correlation measures the strength and direction of a linear relationship
  • Correlation does not imply causation
  • Lurking variables may explain observed correlations
p-value Interpretation

Misconception: A p-value is the probability that the null hypothesis is true.

Clarification:

  • A p-value is NOT the probability that the null hypothesis is true
  • A p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true
  • Small p-values indicate evidence against the null hypothesis
Confidence Interval Interpretation

Misconception: A 95% confidence interval means there is a 95% chance the parameter is in the interval.

Clarification:

  • A 95% confidence interval does NOT mean there is a 95% chance the parameter is in the interval
  • It means if we took many samples and constructed many intervals, about 95% of them would contain the true parameter
Type I vs. Type II Errors

Misconception: Type I and Type II errors are equally problematic in all contexts.

Clarification:

  • Type I error: Rejecting a true null hypothesis (false positive)
  • Type II error: Failing to reject a false null hypothesis (false negative)
  • The relative seriousness of these errors depends on the context
  • Decreasing α reduces Type I errors but increases Type II errors