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1. #How to find standard deviation pasco capstone how to#
2. #How to find standard deviation pasco capstone registration#
3. #How to find standard deviation pasco capstone series#

That gives us a variance-measured in square units (square dollars, say, whatever those are). We always calculate variability by summing squared deviations from the mean. Question 1: Why add variances instead of standard deviations? Let’s have a look at some arguments you can make in class that show your students the theorem makes sense.

Teaching the TheoremĪlthough that proof may make you feel better about the theorem (or not), it’s not likely to warm the hearts of most of your students. And independence was why part of the expression vanished, leaving us with the sum of the variances. Variances add for the sum and for the difference of the random variables because the plus-or-minus terms dropped out along the way.

Note that this proof answers all three questions we posed. If X and Y are independent, each term in the first sum is equal to the corresponding term in the second sum hence that middle term is 0. The product µ xµ y is the sum of all terms of the form x iP( x i) The proof uses the fact that, because expected values are basically summations, they are additive:Īnd now, the Pythagorean theorem of statistics:Ĭonsider that middle term: E(xy) - µ xµ y.Į(xy) is the sum of all terms of the form x iy j It’s a rule of mathematics that no proof should be taken seriously unless there’s a lemma, so here’s ours. Proving the Theorem: The Mathįirst, then, let’s have a look at a formal proof.

#How to find standard deviation pasco capstone series#

By that I mean a series of justifications that stop short of being formal proofs yet give students clear examples that make the theorem something believable and vital, not simply a meaningless rule to memorize. Instead, a plausibility argument should suffice. Although some teachers may decide to show this proof to their classes, most won’t inflict it on AP Statistics students. On one level is the proof, just to make you feel better. I’ll answer these questions on two levels. Why do the variables have to be independent?.Why do we add even when working with the difference of the random variables?.Let’s start by taking a look at the theorem itself. They gain important insights in dealing with binomial probabilities, inference, and even the CLT itself - and they gain an important problem-solving skill sure to pay off on the AP Exam. When your students understand and learn to use this theorem, many doors open. You probably won’t discuss orthogonal vectors with your AP Statistics students, but that’s no excuse for not giving the Pythagorean theorem the emphasis it deserves. Then the standard deviation of the sum or difference of the variables is the hypotenuse of a right triangle. When the variables are independent, the vectors are orthogonal. There’s a nice geometric model that represents random variables as vectors whose lengths correspond to their standard deviations. The name helps students remember both the relationship and the restriction.Īs you may suspect, this analogy is more than a mere coincidence.Just as the Pythagorean theorem applies only to right triangles, this relationship applies only to independent random variables.When written in terms of standard deviations, it looks like the Pythagorean theorem:.I like to refer to this statement as the Pythagorean theorem of statistics for several reasons: Learning Opportunities for AP Coordinators.AP World Language and Cultures Webinars.AP History and Social Sciences Webinars.AP Computer Science Female Diversity Award.Score Reports and Services for Colleges.

#How to find standard deviation pasco capstone how to#

How to Access Score Reports for Educators.Rebates for Schools with Large AP Programs.What Students Should & Should Not Bring.Transfer Students To or Out of Your School.Schools That Administer AP Exams but Don’t Offer AP Courses.Homeschooled, Independent Study, and Virtual School Students and Students from Other Schools.AP Exam Fee Collection Provider Program.

#How to find standard deviation pasco capstone registration#