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Summation notation

# Summation notation - THE SUMMATION NOTATION In statistics...

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THE SUMMATION NOTATION 01/31/10 In statistics and in other math courses the Greek capital letter Σ (“sigma”) is used as a summation symbol which indicates the sum of related terms. For example, 5 Σ i = 1 + 2 + 3 + 4 + 5 = 15 i =1 means “the sum of the integers designated by i , from i = 1 to i = 5 . The letter i is called the index of summation; i is replaced by a series of consecutive numbers, starting with the lower limit of summation (its numerical value is placed below the summation symbol ) and ending with the upper limit of summation (its numerical value is placed above the summation symbol). In the discussed example, the lower limit is 1 , and the upper limit is 5 . ( Any letter may be used as a summation symbol. The lower and upper indices of summation are called also the bounds of summation .) If a variable quantity is denoted by x , then the successive values of that variable can be indicated by using a subscripted variable , as in x 1 , x 2 , x 3 , … (read as “x-sub- one ”, “x-sub- two ”, “x-sub- three

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