Basic statistics
AP Statistics the Genghis Khan way 1
AP Statistics the Genghis Khan way 2
Descriptive statistics and inferential statistics
Numerical versus categorical variable
Uniform distribution definition, with examples
Using graphs to describe data
What should you hate about AP Statistics? The TI-83+ and TI-84 graphing calculators are terrible
How to prevent cheating with TI-83+ and TI-84
Minitab is overpriced. Use Excel instead
What is a Pareto chart and how is it different from a histogram?
The stem-and-leaf plot is an archaism - it's time to leave it behind
Histogram versus time series plot, with video
Comparing histogram, Pareto chart and times series plot
Using statistical tables for normal distribution
Probability
Little tricks for AP Statistics
What is probability. Includes sample space; elementary, impossible, sure events; completeness axiom, de Morgan’s laws, link between logic and geometry
Independence of events. Includes conditional probability, multiplication rule and visual illustration of independence
Law of total probability - you could have invented this
Significance level and power of test
Reevaluating probabilities based on piece of evidence
Using numerical measures to describe data
What is a median, with an exercise
Using financial examples to explain properties of sample means
What is a mean value. All means in one place: population mean, sample mean, grouped data formula, mean of a continuous random variable
Unbiasedness definition, with intuition
Marginal probabilities and densities
All properties of variance in one place
Variance of a vector: motivation and visualization
Different faces of vector variance: again visualization helps
Inductive introduction to Chebyshev inequality
Properties of standard deviation
Correlation coefficient: the last block of statistical foundation
Statistical measures and their geometric roots
Population mean versus sample mean: summary comparison
Mean plus deviation-from-mean decomposition
What is a z score: the scientific explanation
What is a binomial random variable - analogy with market demand
Active learning - away from boredom of lectures, with Excel file and video. How to simulate several random variables at the same time.
From independence of events to independence of random variables. Includes multiplicativity of means and additivity of variance
Normal distributions. Includes standard normal distribution, (general) normal variable, linear transformation and their properties, video and Mathematica file
Definitions of chi-square, t statistic and F statistic
Student's t distribution: one-line explanation of its origin
Confidence interval and margin of error derivation using z-score. Includes confidence and significance levels, critical value
Confidence interval using t statistic: attach probability or not attach?
Distribution function
Distribution function properties
Examples of distribution functions
Distribution and density functions of a linear transformation
Binary choice models: theoretical obstacles
Maximum likelihood
Maximum likelihood: idea and life of a bulb
Maximum likelihood: application to linear model
Conditioning
Properties of conditional expectation
Conditional expectation generalized to continuous random variables
Conditional variance properties
Simulation of random variables
Importance of simulation in Excel for elementary stats courses
Generating the Bernoulli random variable (coin), with Excel file
Simulating the binomial variable in Excel and deriving its distribution, with Excel file
Creating frequency table and histogram and using Excel macros, with Excel file
Modeling a sample from a normal distribution, with Excel file
Modeling a pair of random variables and scatterplot definition, with video
Sampling distributions
Demystifying sampling distributions: too much talking about nothing
Law of large numbers and central limit theorem
Law of large numbers explained
Law of large numbers illustrated
Law of large numbers: the mega delusion of AP Statistics, with Excel file
All about the law of large numbers. Includes convergence in probability, preservation of arithmetic operations and application to simple regression
Central Limit Theorem versus Law of Large Numbers. Includes convergence in distribution and Excel file