# Basic statistics

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 cheat 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

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

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