Can I pick a red frog out of a bag that only contains marbles? Is it smart to buy a lottery ticket? Even if we are unsure about whether something will happen, can we start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others). These tutorials will introduce us to the tools that allow us to think about random events.

Poisson process from Khan Academy Statistics

** Keywords: **Random variables and probability distributions

Now that we know what a random variable is, we can think about expected value. As we'll see, it can be viewed as a probability-weighted average of possible outcomes!

** Keywords: **Random variables and probability distributions

Binomial distribution from Khan Academy Statistics

** Keywords: **Random variables and probability distributions

The normal distribution (often referred to as the "bell curve" is at the core of most of inferential statistics. By assuming that most complex processes result in a normal distribution (we'll see why this is reasonable), we can gauge the probability of it happening by chance. To best enjoy this...

** Keywords: **Inferential statistics

In this tutorial, we experience one of the most exciting ideas in statistics--the central limit theorem. Without it, it would be a lot harder to make any inferences about population parameters given sample statistics. It tells us that, regardless of what the population distribution looks like,...

** Keywords: **Inferential statistics

We all have confidence intervals ("I'm the king of the world!!!!") and non-confidence intervals ("No one loves me"). That is not what this tutorial is about. This tutorial takes what you already know about the central limit theorem, sampling distributions, and z-scores and uses these tools to...

** Keywords: **Inferential statistics

Ever wondered what pollsters are talking about when they said that there is a 3% "margin of error" in their results. Well, this tutorial will not only explain what it means, but give you the tools and understanding to be a pollster yourself!

** Keywords: **Inferential statistics

This tutorial helps us answer one of the most important questions not only in statistics, but all of science: how confident are we that a result from a new drug or process is not due to random chance but due to an actual impact. If you are familiar with sampling distributions and confidence...

** Keywords: **Inferential statistics

You're already familiar with hypothesis testing with one sample. In this tutorial, we'll go further by testing whether the difference between the means of two samples seems to be unlikely purely due to chance.

** Keywords: **Inferential statistics

You've gotten good at hypothesis testing when you can make assumptions about the underlying distributions. In this tutorial, we'll learn about a new distribution (the chi-square one) and how it can help you (yes, you) infer what an underlying distribution even is!

** Keywords: **Inferential statistics

You already know a good bit about hypothesis testing with one or two samples. Now we take things further by making inferences based on three or more samples. We'll use the very special F-distribution to do it (F stands for "fabulous").

** Keywords: **Inferential statistics

Scatter plots from Khan Academy Statistics

** Keywords: **Regression

Even when there might be a rough linear relationship between two variables, the data in the real-world is never as clean as you want it to be. This tutorial helps you think about how you can best fit a line to the relationship between two variables.

** Keywords: **Regression

Residuals from Khan Academy Statistics

** Keywords: **Regression

Random variables and probability distributions from Khan Academy Statistics

** Keywords: **Random variables and probability distributions

This is the foundational tutorial for the rest of statistics. We start thinking about how you can represent a set of numbers with one number that somehow represents the "center". We then talk about the differences between populations, samples, parameters and statistics.

** Keywords: **Descriptive statistics

Whether you're looking at scientific data or stock price charts, box-and-whisker plots can show up in your life. This tutorial covers what they are, how to read them and how to construct them. We'd consider this tutorial very optional, but it is a good application of dealing with medians and...

** Keywords: **Descriptive statistics

We have tools (like the arithmetic mean) to measure central tendency and are now curious about representing how much the data in a set varies from that central tendency. In this tutorial we introduce the variance and standard deviation (which is just the square root of the variance) as two...

** Keywords: **Descriptive statistics

This tutorial covers central tendency and dispersion. It is redundant with the other tutorials on this topic, but it has the benefit of messy handwriting and a cheap microphone. This is Sal circa 2007 so take it all with a grain of salt (or just skip it altogether).

** Keywords: **Descriptive statistics

Statistical questions from Khan Academy Statistics

** Keywords: **Statistical studies

Types of statistical studies from Khan Academy Statistics

** Keywords: **Statistical studies

Hypothesis testing from Khan Academy Statistics

** Keywords: **Statistical studies

Categorical data from Khan Academy Statistics

** Keywords: **Statistical studies

You want to display your Chuck Norris dolls on your desk at school and there is only room for five of them. Unfortunately, you own 50. How many ways can you pick the dolls and arrange them on your desk?

** Keywords: **Probability and combinatorics

You are already familiar with calculating permutation ("How many ways could 7 different people sit in 4 different seats?"). But what if you didn't care about which seat they sat in? What if you just cared about which 4 people were in the car? Or put another way, you want to know how many...

** Keywords: **Probability and combinatorics

This tutorial will apply the permutation and combination tools you learned in the last tutorial to problems of probability. You'll finally learn that there may be better "investments" than poring all your money into the Powerball Lottery.

** Keywords: **Probability and combinatorics

Making decisions with probability from Khan Academy Statistics

** Keywords: **Probability and combinatorics

Can I pick a red frog out of a bag that only contains marbles? Is it smart to buy a lottery ticket? Even if we are unsure about whether something will happen, can we start to be mathematical about the "chances" of an event (essentially realizing that some things are more likely than others). ...

** Keywords: **Independent and dependent events

What is the probability of getting a diamond or an ace from a deck of cards? Well I could get a diamond that is not an ace, an ace that is not a diamond, or the ace of diamonds. This tutorial helps us think these types of situations through a bit better (especially with the help of our good...

** Keywords: **Independent and dependent events

What is the probability of making three free throws in a row (LeBron literally asks this in this tutorial). In this tutorial, we'll explore compound events happening where the probability of one event is not dependent on the outcome of another (compound, independent, events).

** Keywords: **Independent and dependent events

What's the probability of picking two "e" from the bag in scrabble (assuming that I don't replace the tiles). Well, the probability of picking an 'e' on your second try depends on what happened in the first (if you picked an 'e' the first time around, then there is one less 'e' in the bag). ...

** Keywords: **Independent and dependent events

Whether you are learning computer science, logic, or probability (or a bunch of other things), it can be very, very useful to have this "set" of skills. From what a set is to how we can operate on them, this tutorial will have you familiar with the basics of sets!

** Keywords: **Independent and dependent events