Statistics and probability

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Displaying and describing data

One of the first things we do in statistics is try to understand sets of data. This involves plotting the data in different ways and summarizing what we see with measures of center (like mean and median) and measures of spread (like range and standard deviation). This topic focuses on concepts that are often referred to as "descriptive statistics".
Statistics overview
Categorical data displays
Two-way tables for categorical data
Dot plots and frequency tables
Histograms
Comparing features of distributions
Stem-and-leaf plots
Line graphs
Mean and median: The basics
More on mean and median
Range, Interquartile range (IQR), Mean absolute deviation (MAD)
Box and whisker plots
Population variance and standard deviation
Sample variance and standard deviation

Modeling distributions of data

The normal distribution is the most commonly used model in all of statistics. Learn how to measure position using z-scores and find what percent of data falls where in a normal distribution.
Describing location in a distribution
Normal distributions

Describing relationships in quantitative data

If we want to explore a relationship between two quantitative variables, we make a scatterplot of the data. The fun doesn't stop there. We describe pattern, talk about the type of correlation we see, and sometimes fit a line to the data so we can use the pattern to make predictions.
Scatterplots and correlation
Regression
Residuals, least-squares regression, and r-squared

Designing studies

Study design focuses on collecting data properly and making the most valid conclusions we can based on how the data was collected. This topic covers explore samples, surveys, and experiments.
Sampling and surveys
Experiments

Probability

Probability tells us how often some event will happen after many repeated trials. This topic covers theoretical, experimental, compound probability, permutations, combinations, and more!
Basic theoretical probability
Probability using sample spaces
Experimental probability
Basic set operations
Addition rule for probability
Multiplication rule for independent events
Multiplication rule for dependent events
Conditional probability and independence
Counting principle and factorial
Permutations
Combinations
Combinatorics and probability

Random variables

Random variables can be any outcomes from some chance process, like how many heads will occur in a series of 20 flips. We calculate probabilities of random variables and calculate expected value for different types of random variables.
Discrete and continuous random variables and probability models
Expected value
Transforming and combining random variables
Binomial random variables
Poisson distribution

Sampling distributions

A sampling distribution shows every possible result a statistic can take in every possible sample from a population and how often each result happens. This topic covers how sample proportions and sample means behave in repeated samples.
Sample proportions
Sample means

Confidence intervals (one sample)

Confidence intervals give us a range of plausible values for some unknown value based on results from a sample. This topic covers confidence intervals for means and proportions.
Estimating a population proportion
Estimating a population mean

Significance tests (one sample)

Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. We calculate p-values to see how likely a sample result is to occur by random chance, and we use p-values to make conclusions about hypotheses.
The idea of significance tests
Tests about a population proportion
Tests about a population mean

Significance tests and confidence intervals (two samples)

Learn how to apply what you know about confidence intervals and significance tests to situations that involve comparing two samples to see if there is a significant difference between the two populations.
Comparing two proportions
Comparing two means

Inference for categorical data (chi-square tests)

Chi-square tests are a family of significance tests that give us ways to test hypotheses about distributions of categorical data. This topic covers goodness-of-fit tests to see if sample data fits a hypothesized distribution, and tests for independence between two categorical variables.
Chi-square goodness-of-fit tests
Chi-square tests for homogeneity and association/independence

Advanced regression (inference and transforming)

Advanced regression will introduce you to regression methods when data has a nonlinear pattern.
Nonlinear regression

Analysis of variance (ANOVA)

Analysis of variance, also called ANOVA, is a collection of methods for comparing multiple means across different groups.
Analysis of variance (ANOVA)

Staff picks

The Monty Hall problem
Basic set notation
Probability with permutations and combinations
Concept check: Standard deviation
R-squared or coefficient of determination
The art of randomness
Watch an introduction video2 minutes 43 seconds
Pixar in a Box explores how the concepts you learn in school are used to make movie magic. In this lesson, you will learn how Pixar uses randomness to create patterns that bring it’s characters and worlds to life.
Start learning
The art of randomness
Pixar in a Box explores how the concepts you learn in school are used to make movie magic. In this lesson, you will learn how Pixar uses randomness to create patterns that bring it’s characters and worlds to life.
Start learning
Watch an introduction video2 minutes 43 seconds

Review articles

Histograms review
Two-way tables review
Mean, median, and mode review
Sampling methods review
Interquartile range review
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