AP Statistics Complete Study Guide

Cramming for AP Stats exam the night before

Categorical Variables

Represent qualities or characteristics. Example: hair color, grade level. They do not have numerical meaning.

Nominal

No inherent order (e.g., color).

Ordinal

Can be ordered but differences are not meaningful (e.g., class rank).

Quantitative Variables

Numerical and measurable. Example: height, number of books.

Discrete

Countable (e.g., number of pets).

Continuous

Measurable on a continuum (e.g., weight).

Bar Chart

Categorical. Shows counts/frequencies using bars.

Pie Chart

Categorical. Shows proportion of categories as slices.

Dotplot

Quantitative. Dots represent individual data points.

Stemplot

Quantitative. Shows distribution while retaining original values.

Histogram

Quantitative. Bars represent intervals (bins) of values.

Boxplot

Summarizes five-number summary; good for comparing groups.

Comparative Boxplots

Multiple boxplots on the same scale for comparison.

Shape

Symmetric (mirror image), Skewed Right (tail on right), Skewed Left (tail on left), Uniform (flat), Bimodal (two peaks).

Mean

Average value. Sensitive to outliers.

Median

Middle value. Resistant to outliers.

Range

Max - Min.

IQR (Interquartile Range)

Q3 - Q1. Resistant to outliers.

Standard Deviation

Average distance from the mean. Sensitive to outliers.

Outliers

Use 1.5 * IQR rule. Any value < Q1 - 1.5IQR or > Q3 + 1.5IQR.

Percentiles

Percent of values below a given point.

Z-scores

How many standard deviations a value is from the mean. z = (x - μ)/σ.

Simple Random Sample (SRS)

Every individual has equal chance. Use random numbers.

Stratified Random Sample

Divide population into strata, randomly sample from each.

Cluster Sample

Randomly select clusters (groups) and sample all members.

Systematic Sample

Select every nth individual after a random start.

Convenience Sample

Easy to reach; usually biased.

Voluntary Response

People choose to respond; biased toward strong opinions.

Control

Reduces lurking variables.

Randomization

Reduces bias.

Replication

Use enough subjects to generalize results.

Placebo Effect

Subjects respond to belief in treatment.

Blinding

Subjects unaware of treatment.

Double-Blind

Subjects and experimenters unaware.

Completely Randomized Design

Random assignment to groups.

Block Design

Group by similar traits, randomize within.

Matched Pairs

Pair similar units or use the same unit twice.

Undercoverage

Some groups underrepresented.

Nonresponse

Chosen individual does not participate.

Response Bias

Wording, interviewer, or dishonesty skews answers.

Sampling Variability

Different samples give different estimates.

Total probability

Total probability = 1.

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). If independent, P(A) * P(B).

Mutually Exclusive

Can't happen together. P(A and B) = 0.

Independent

One doesn't affect the other.

Conditional Probability

P(B|A) = P(A and B) / P(A). Interpret as: given A happened, what is the probability of B?

Two-way tables

Help visualize relationships between two categorical variables.

Venn diagrams

Help visualize relationships between sets.

Tree diagrams

Help visualize sequences of events and their probabilities.

Simulation

Use random digits or technology to simulate repeated trials.

Discrete

Countable outcomes (e.g., # of goals).

Continuous

Measurable (e.g., time).

Mean (Expected Value)

Mean = Σ[x * P(x)].

Standard Deviation (SD)

SD is square root of variance.

Transformations

Multiply changes spread and center. Add only changes center.

Combining Variables

If independent: Add variances to combine SDs.

Binomial

Conditions: BINS.

Binomial PDF

Use binompdf (for exact) or binomcdf (for cumulative).

Geometric

First success on the kth trial.

Proportions Mean

Mean = p, SD = √[p(1-p)/n].

Normal Approximation for Proportions

np ≥ 10, n(1-p) ≥ 10.

Means Mean

Mean = μ, SD = σ/√n.

Central Limit Theorem

Sampling distribution is approximately normal if n ≥ 30.

Confidence Intervals

Form: statistic ± (critical value)(standard error).

One-Proportion z Test

z = (p̂ - p₀)/√[p₀(1 - p₀)/n].

One-Sample t Test

Use when σ is unknown. df = n - 1.

Two-Proportion z Test

Compare two groups. z = (p̂1 - p̂2)/SE.

Two-Sample t Test

Compare means. Assume unequal variance unless told.

Paired t-Test

Use differences: x̄diff ± t*(sdiff/√n).

Chi-Square

GOF: 1 variable vs distribution; Homogeneity: Compare 2 groups; Independence: 2 variables.

Regression Inference

t = b/SEb. Conditions: Linear, Independent, Normal residuals, Equal spread.