AP®︎ Statistics
Categories: Mathematics, Statistics
Course Content
Analyzing categorical data

Welcome to AP Statistics

Meet Jeff, a creator of AP Statistics on Khan Academy

Analyzing one categorical variable

Identifying individuals, variables and categorical variables in a data set

Creating a bar graph

Reading bar charts: comparing two sets of data

Twoway tables

Twoway frequency tables and Venn diagrams

Twoway relative frequency tables

Interpreting twoway tables

Distributions in twoway tables

Marginal and conditional distributions
Displaying and describing quantitative data

Frequency tables and dot plots

Frequency tables & dot plots

Histograms and stemandleaf plots

Creating a histogram

Interpreting a histogram

Stemandleaf plots

Reading stem and leaf plots

Describing and comparing distributions

Classifying shapes of distributions

Example: Describing a distribution

Example: Comparing distributions

Measuring center in quantitative data

Statistics intro: Mean, median, & mode

Mean, median, & mode example

Median in a histogram
Summarizing quantitative data

More on mean and median

Missing value given the mean

Impact on median & mean: increasing an outlier

Impact on median & mean: removing an outlier

Estimating mean and median in data displays

Measuring spread in quantitative data

Interquartile range (IQR)

Sample variance

Sample standard deviation and bias

Visually assessing standard deviation

Mean and standard deviation versus median and IQR

More on standard deviation (optional)

Review and intuition why we divide by n1 for the unbiased sample variance

Why we divide by n – 1 in variance

Simulation showing bias in sample variance

Simulation providing evidence that (n1) gives us unbiased estimate

Box and whisker plots

Worked example: Creating a box plot (odd number of data points)

Worked example: Creating a box plot (even number of data points)

Reading box plots

Interpreting box plots

Judging outliers in a dataset

Percentiles (cumulative relative frequency)

Calculating percentile

Analyzing a cumulative relative frequency graph

Zscores

Zscore introduction

Comparing with zscores
Modeling data distributions

Effects of linear transformations

How parameters change as data is shifted and scaled

Density curves

Density Curves

Median, mean and skew from density curves

Density curve worked example

Worked example finding area under density curves

Normal distributions and the empirical rule

Qualitative sense of normal distributions (from ck12.org)

Normal distribution problems: Empirical rule (from ck12.org)

Threshold for low percentile

Normal distribution calculations

Standard normal table for proportion below

Standard normal table for proportion above

Standard normal table for proportion between values

Finding zscore for a percentile

Making and describing scatterplots

Constructing a scatter plot

Example of direction in scatterplots

Bivariate relationship linearity, strength and direction

Correlation coefficients

Calculating correlation coefficient r

Example: Correlation coefficient intuition

Leastsquares regression equations

Introduction to residuals and leastsquares regression

Calculating residual example

Calculating the equation of a regression line

Interpreting slope of regression line

Interpreting yintercept in regression model

Using least squares regression output
Exploring bivariate numerical data

Assessing the fit in leastsquares regression

Residual plots

Rsquared or coefficient of determination

Standard deviation of residuals or root mean square deviation (RMSD)

Interpreting computer regression data

Impact of removing outliers on regression lines

Sampling and observational studies

Identifying a sample and population

Generalizabilty of survey results example

Examples of bias in surveys

Example of undercoverage introducing bias

Sampling methods

Techniques for generating a simple random sample

Techniques for random sampling and avoiding bias

Types of studies (experimental vs. observational)

Types of statistical studies

Worked example identifying experiment

Worked example identifying observational study

Experiments

Introduction to experiment design

Matched pairs experiment design

Invalid conclusions from studies example

Can causality be established from this study?
Study design

Addition rule

Probability with Venn diagrams

Addition rule for probability

Multiplication rule

Compound probability of independent events

Independent events example: test taking

Freethrow probability

Threepointer vs freethrow probability

Dependent probability introduction

Coin flipping probability

Conditional probability

Conditional probability and independence

Conditional probability with Bayes’ Theorem

Conditional probability tree diagram example

Randomness, probability, and simulation

Intro to theoretical probability

Experimental versus theoretical probability simulation

Random number list to run experiment

Random numbers for experimental probability

Statistical significance of experiment

Discrete random variables

Constructing a probability distribution for random variable

Valid discrete probability distribution examples

Probability with discrete random variable example

Mean (expected value) of a discrete random variable

Variance and standard deviation of a discrete random variable
Probability

Continuous random variables

Probabilities from density curves

Transforming random variables

Impact of transforming (scaling and shifting) random variables

Example: Transforming a discrete random variable (Opens a modal)

Combining random variables

Mean of sum and difference of random variables

Variance of sum and difference of random variables

Intuition for why independence matters for variance of sum

Deriving the variance of the difference of random variables

Example: Analyzing distribution of sum of two normally distributed random variables

Example: Analyzing the difference in distributions

Binomial random variables

Binomial variables

Recognizing binomial variables

10% Rule of assuming “independence” between trials

Binomial probability example

Generalizing k scores in n attempts

Free throw binomial probability distribution

Graphing basketball binomial distribution

Binompdf and binomcdf functions

Binomial mean and standard deviation formulas

Expected value of a binomial variable

Variance of a binomial variable

Finding the mean and standard deviation of a binomial random variable
Random variables

Geometric random variables

Geometric random variables introduction

Probability for a geometric random variable

Cumulative geometric probability (greater than a value)

Cumulative geometric probability (less than a value)

TI84 geometpdf and geometcdf functions

Proof of expected value of geometric random variable

What is a sampling distribution?

Introduction to sampling distributions

Sample statistic bias worked example

Sampling distribution of a sample proportion

Sampling distribution of sample proportion part 1

Sampling distribution of sample proportion part 2

Normal conditions for sampling distributions of sample proportions

Probability of sample proportions example

Sampling distribution of a sample mean

Central limit theorem

Sampling distribution of the sample mean

Sampling distribution of the sample mean 2

Standard error of the mean

Example: Probability of sample mean exceeding a value

Introduction to confidence intervals

Confidence intervals and margin of error

Confidence interval simulation

Interpreting confidence level example

Conditions for confidence intervals worked examples

Critical value (z*) for a given confidence level

Example constructing and interpreting a confidence interval for p

Determining sample size based on confidence and margin of error

Confidence intervals for proportions

Conditions for valid confidence intervals

Introduction to t statistics

Simulation showing value of t statistic

Conditions for valid t intervals

Example finding critical t value

Example constructing a t interval for a mean

Confidence interval for a mean with paired data

Sample size for a given margin of error for a mean

Confidence intervals for means

The idea of significance tests

Idea behind hypothesis testing

Examples of null and alternative hypotheses

Pvalues and significance tests

Comparing Pvalues to different significance levels

Estimating a Pvalue from a simulation
Sampling distributions

Error probabilities and power

Introduction to Type I and Type II errors

Examples identifying Type I and Type II errors

Introduction to power in significance tests

Examples thinking about power in significance tests

Testing hypotheses about a proportion

Constructing hypotheses for a significance test about a proportion

Conditions for a z test about a proportion

Calculating a z statistic in a test about a proportion

Calculating a Pvalue given a z statistic

Making conclusions in a test about a proportion

Significance test for a proportion free response example

Significance test for a proportion free response (part 2 with correction)

Testing hypotheses about a mean

Writing hypotheses for a significance test about a mean

Conditions for a t test about a mean

When to use z or t statistics in significance tests

Example calculating t statistic for a test about a mean

Using TI calculator for Pvalue from t statistic

Using a table to estimate Pvalue from t statistic

Comparing Pvalue from t statistic to significance level

Free response example: Significance test for a mean

Confidence intervals for the difference between two proportions

Confidence intervals for the difference between two proportions

Examples identifying conditions for inference on two proportions

Calculating a confidence interval for the difference of proportions
Confidence intervals

Testing the difference between two proportions

Hypothesis test for difference in proportions

Constructing hypotheses for two proportions

Hypothesis test for difference in proportions example

Comparing P value to significance level for test involving difference of proportions

Confidence interval for hypothesis test for difference in proportions

Confidence intervals for the difference between two means

Conditions for inference for difference of means

Constructing t interval for difference of means

Calculating confidence interval for difference of means

Testing the difference between two means

Hypotheses for a twosample t test

Example of hypotheses for paired and twosample t tests

Twosample t test for difference of means

Conclusion for a twosample t test using a Pvalue

Conclusion for a twosample t test using a confidence interval

Chisquare goodnessoffit tests

Chisquare statistic for hypothesis testing

Chisquare goodnessoffit example
Significance tests (hypothesis testing)

Chisquare tests for relationships

Introduction to the chisquare test for homogeneity

Chisquare test for association (independence)

Inference about slope

Introduction to inference about slope in linear regression

Conditions for inference on slope

Confidence interval for the slope of a regression line

Calculating t statistic for slope of regression line

Using a Pvalue to make conclusions in a test about slope

Using a confidence interval to test slope

Transformations to achieve linearity

Transforming nonlinear data

Worked example of linear regression using transformed data
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