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).