Summation Notation (1 of 4)

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The Greek letter Σ (a capital sigma) is used to designate summation. For example, suppose an experimenter measured the performance of four subjects on a memory task. Subject 1's score will be referred to as X 1 , Subject 2's as X 2 , and so on. The scores are shown below:

Subject
Score
1
X1
7
2
X2
6
3
X3
5
4
X4
8


The way to use the summation sign to indicate the sum of all four X's is:



This notation is read as follows:

Sum the values of X from X1 through X4 .

The index i (shown just under the Σ sign) indicates which values of X are to be summed. The index i takes on values beginning with the value to the right of the "=" sign (1 in this case) and continues sequentially until it reaches the value above the Σ sign (4 in this case). Therefore i takes on the values 1, 2, 3, and 4 and the values of X1, X2, X3, and X4 are summed (7 + 6 + 5 + 8 = 26).
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