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Summation Handout

Summation Handout - Summation Average and Standard...

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Summation, Average, and Standard Deviation Statistics 21, Hank Ibser Definitions and Formulas Lists of numbers are often written as x i . Each number on the list is one of these x i values. Thus the list 1 , 4 , 6 would have x 1 = 1 ,x 2 = 4 , and x 3 = 6. Here are a few formulas we will use: 5) and 6) are useful for the homework but you don’t need to know them. 1) The sum of a list of n numbers is x 1 + x 2 + · · · + x n or n i =1 x i 2) The sum of the squares can be written x 1 2 + x 2 2 + · · · + x n 2 or n i =1 x i 2 3) The average of a list of n numbers is the sum divided by n : ¯ x = 1 n n summationdisplay i =1 x i 4) The SD is either radicalBigg n i =1 ( x i - ¯ x ) 2 n or radicaltp radicalvertex radicalvertex radicalbt parenleftBigg 1 n n summationdisplay i =1 x 2 i parenrightBigg - ¯ x 2 5) The sum of the first n integers is 1 + 2 + 3 + · · · + n = n summationdisplay i =1 i = n ( n + 1) 2 6) The sum of the first n squared integers is 1 2 + 2 2 + 3 2 + · · · + n 2 = n summationdisplay i =1 i 2 = n ( n + 1)(2 n + 1) 6 Basic Properties of Sums
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