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AP Statistics

AP · College BoardStatistics44 notes in 5 folders, 263 KB

Notes for AP Statistics (College Board), in folders for the five units of the course framework in its order: one-variable data and data collection, probability and distributions, inference for proportions, inference for means and regression. Each note covers one topic with definitions, conditions for each method, worked examples and how to read a result in context. Delete any folder or note you don't need once the notes are yours.

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What is inside

  • Exploring one-variable data and collecting data
    • Statistical studies, investigative questions and variables6 KB
    • Categorical data: tables and graphs5 KB
    • Quantitative data: dotplots, stem-and-leaf plots and histograms5 KB
    • Describing a distribution6 KB
    • Center, position and spread6 KB
    • Outliers, resistance and boxplots6 KB
    • Comparing distributions and z-scores5 KB
    • Observational studies, surveys and experiments7 KB
    • Random sampling methods7 KB
    • Bias in sampling6 KB
    • Experimental design7 KB
    • Blocking, matched pairs and conclusions from experiments7 KB
  • Probability, random variables and probability distributions
    • Two-way tables and association6 KB
    • Probability and simulation6 KB
    • Mutually exclusive events, unions and the addition rule4 KB
    • Conditional probability, the multiplication rule and independence5 KB
    • Discrete random variables and probability distributions5 KB
    • Mean and standard deviation of a discrete random variable5 KB
    • The binomial distribution6 KB
    • The normal distribution and the empirical rule6 KB
    • Normal calculations: areas, z-scores and boundaries5 KB
    • Sampling distributions, simulation and the central limit theorem6 KB
  • Inference for categorical data: proportions
    • Estimators and the sampling distribution of a sample proportion6 KB
    • Confidence intervals for a population proportion6 KB
    • Interpreting and using a confidence interval6 KB
    • Setting up a test for a population proportion6 KB
    • p-values, significance and conclusions7 KB
    • Carrying out a one-proportion z-test6 KB
    • Type I and Type II errors and power6 KB
    • Confidence intervals for the difference between two proportions7 KB
    • Tests for the difference between two proportions7 KB
    • Chi-square tests: homogeneity and independence, setting up7 KB
    • Chi-square tests: homogeneity and independence, carrying out7 KB
  • Inference for quantitative data: means
    • The sampling distribution of a sample mean5 KB
    • t-distributions and confidence intervals for a mean7 KB
    • Tests for a population mean and a mean difference7 KB
    • The sampling distribution of a difference in sample means5 KB
    • Confidence intervals for the difference between two means6 KB
    • Two-sample t-tests7 KB
    • Choosing an inference procedure7 KB
  • Regression analysis
    • Scatterplots and correlation7 KB
    • Linear regression models and prediction5 KB
    • Residuals and residual plots5 KB
    • Least-squares regression: slope, intercept and $r^2$6 KB

The first note

Exploring one-variable data and collecting data / Statistical studies, investigative questions and variables

## What a statistical study does A **statistical study** collects data from a sample in order to answer an **investigative question** about a larger population. A study is needed when the population is too large, or too hard to reach, for every member to be measured. A school cannot ask every adult in a city how they travel to work, so it asks some of them and uses what it finds to say something about all of them. A single piece of information about one item or individual is a **datum**, and a collection of them is a **data set**. The **population** is all the items or individuals of interest, and its size is written $N$. A **sample** is the subset of the population from which data are actually obtained, and its size is written $n$. The word "in context" means that every component of a study and every calculation is tied back to the real situation it came from: a mean is not just 14.2, it is the mean number of minutes late for the buses in this depot. ### Parts of an investigative question An investigative question has a defined purpose, and it is fixed before the data are analysed. Changing the question after seeing which result looks interesting would make the analysis meaningless, because an effect found only by searching for one is easy to find by chance. The question must also be posed so that the data it needs can actually be collected and analysed. A well-formed question has three parts. 1. A part that guides data collection, phrased in terms of the population and…

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