Summation Algebra Proofs

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Presentation transcript:

Summation Algebra Proofs James H. Steiger

Sum of Deviation Scores Prove that, in any list of numbers, the sum of the deviation scores is zero, that is,

Linear Transformation Rule for Means If, a group of X’s with mean is transformed into a group of Y’s via the rule then the new mean must follow the rule

Linear Transformation Rule for Deviation Scores If, a group of X’s with mean is transformed into a group of Y’s via the rule then the deviation scores must follow the rule

Definition – Sample Variance The sample variance of a set of numbers is

Linear Transformation Rule for Variances If, a group of X’s with variance is transformed into a group of Y’s via the rule then the new variance must follow the rule