To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.​​

Describe a bivariate relationship's linearity, strength, and direction. In other words, plotting things that take two variables into consideration and trying to see whether there's a pattern with how they relate.

The most common way to calculate the correlation coefficient (r) is by using technology, but using the formula can help us understand how r measures the direction and strength of the linear association between two quantitative variables.

This is a brief conditional probability examplediscussing probabilities like P(A | B) using breakfast and lunch as examples.

The most common way to calculate the correlation coefficient (r) is by using technology, but using the formula can help us understand how r measures the direction and strength of the linear association between two quantitative variables.

This video talka about what is easily one of the most fundamental and profound concepts in statistics and maybe in all of mathematics. And that's the central limit theorem.

Overview of Communism and Marxist-Leninist states. For extra coverage of the Cold War outside the scope of the AP course, click here. Created by Sal Khan.

Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise).

Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

Sociology often looks at different age cohorts. A cohort is simply a group of people, but here we're looking specifically at different age groups or generations, because these people all lived through the same certain events through a certain time that affected their lives similarly.

This video defines the differences between discrete and continuous random variables, then works through examples of each.

Where we live in society plays a huge role in the environmental benefits and risks that we're exposed to.

Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.

Sal shows examples of intersection and union of sets and introduces some set notation.

We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might be wondering, is there the equivalent of matrix division? And before we get into that, let me introduce some concepts to you. And then we'll see that there is something that maybe isn't exactly division, but it's analogous to it.