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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.​​

Subject:
Algebra
Mathematics
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
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Author:
Sal Khan
08/17/2023 Conditional Remix & Share Permitted
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This is a brief conditional probability examplediscussing probabilities like P(A | B) using breakfast and lunch as examples.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Sal Khan
08/21/2023 Conditional Remix & Share Permitted
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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.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Economics
Social Science
Material Type:
Lesson
Provider:
Author:
Sal Khan
08/21/2023 Conditional Remix & Share Permitted
CC BY-NC-SA
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Understanding alternate coordinate systems. Created by Sal Khan.

Subject:
Algebra
Mathematics
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Understanding why correlation does not imply causality (even though many in the press and some researchers often imply otherwise).

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.

Subject:
Algebra
Mathematics
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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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.

Subject:
Social Science
Sociology
Material Type:
Lesson
Provider:
Author:
Sydney Brown
02/28/2018 Conditional Remix & Share Permitted
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Dimension of the Column Space or Rank. Created by Sal Khan.

Subject:
Algebra
Mathematics
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
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Dimension of the Null Space or Nullity. Created by Sal Khan.

Subject:
Algebra
Mathematics
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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This video defines the differences between discrete and continuous random variables, then works through examples of each.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
02/28/2018 Conditional Remix & Share Permitted
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Where we live in society plays a huge role in the environmental benefits and risks that we're exposed to.

Subject:
Social Science
Sociology
Material Type:
Lesson
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Author:
02/28/2018 Conditional Remix & Share Permitted
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Compare distributions using the features of shape, center, spread, and outliers.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
02/28/2018 Conditional Remix & Share Permitted
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Overview of the Intermediate Value Theorem, the Extreme Value Theorem and the Mean Value Theorem.

Subject:
Algebra
Mathematics
Material Type:
Lesson
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Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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Short video which describes the difference between a sample and a population.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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Sal shows examples of intersection and union of sets and introduces some set notation.

Subject:
Mathematics
Statistics and Probability
Material Type:
Lesson
Provider:
Author:
Salman Khan
02/28/2018 Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Algebra
Mathematics
Material Type:
Lesson
Provider: