To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components …

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 …

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 …

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.

The most common way to calculate the correlation coefficient (r) is by …

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 …

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 …

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.

Sociology often looks at different age cohorts. A cohort is simply a …

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.

We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might …

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.

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