AP®︎ Statistics | 1 Big School (By Blue Brain)

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
Two-way tables
Two-way frequency tables and Venn diagrams
Two-way relative frequency tables
Interpreting two-way tables
Distributions in two-way tables
Marginal and conditional distributions

Displaying and describing quantitative data

Frequency tables and dot plots
Frequency tables & dot plots
Histograms and stem-and-leaf plots
Creating a histogram
Interpreting a histogram
Stem-and-leaf 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 n-1 for the unbiased sample variance
Why we divide by n – 1 in variance
Simulation showing bias in sample variance
Simulation providing evidence that (n-1) 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
Z-scores
Z-score introduction
Comparing with z-scores

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 z-score 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
Least-squares regression equations
Introduction to residuals and least-squares regression
Calculating residual example
Calculating the equation of a regression line
Interpreting slope of regression line
Interpreting y-intercept in regression model
Using least squares regression output

Exploring bivariate numerical data

Assessing the fit in least-squares regression
Residual plots
R-squared 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
Free-throw probability
Three-pointer vs free-throw 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)
TI-84 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
P-values and significance tests
Comparing P-values to different significance levels
Estimating a P-value 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 P-value 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 P-value from t statistic
Using a table to estimate P-value from t statistic
Comparing P-value 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 two-sample t test
Example of hypotheses for paired and two-sample t tests
Two-sample t test for difference of means
Conclusion for a two-sample t test using a P-value
Conclusion for a two-sample t test using a confidence interval
Chi-square goodness-of-fit tests
Chi-square statistic for hypothesis testing
Chi-square goodness-of-fit example

Significance tests (hypothesis testing)

Chi-square tests for relationships
Introduction to the chi-square test for homogeneity
Chi-square 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 P-value 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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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

Two-way tables

Two-way frequency tables and Venn diagrams

Two-way relative frequency tables

Interpreting two-way tables

Distributions in two-way tables

Marginal and conditional distributions

Displaying and describing quantitative data

Frequency tables and dot plots

Frequency tables & dot plots

Histograms and stem-and-leaf plots

Creating a histogram

Interpreting a histogram

Stem-and-leaf 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 n-1 for the unbiased sample variance

Why we divide by n – 1 in variance

Simulation showing bias in sample variance

Simulation providing evidence that (n-1) 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

Z-scores

Z-score introduction

Comparing with z-scores

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 z-score for a percentile

Making and describing scatterplots

Constructing a scatter plot

Example of direction in scatterplots

Bivariate relationship linearity, strength and direction