FOCUS ON PROBLEM SOLVING It may help to simplify summation notation if you observe that the summation sign is always followed by a symbol or symbolic expression-for example, EX or E(X + 3). This symbol specifies which values you are to add. If you use the symbol as a column heading and list all the appropriate values in the column, your task is simply to add up the numbers in the column. To find E(X + 3) for example, start a column headed with (X + 3) next to the column of Xs. List all the (X + 3) values; then find the total for the column. Often, summation notation is part of a relatively complex mathematical expression that requires several steps of calculation. The series of steps must be performed according to the order of mathematical operations (see page 26). The best procedure is to use a computational table that begins with the original X values listed in the first column. Except for summation, each step in the calculation creates a new column of values. For example, computing E(X + 1)? involves three steps and produces a computational table with three columns. The final step is to add the values in the third column (see Example 1.4). DEMONSTRATION 1.1 SUMMATION NOTATION A set of scores consists of the following values: 7 3 9 5 4 For these scores, compute each of the following: EX (EX) EX + 5 E(X - 2) X X Compute EX To compute EX, we simply add all of the scores in the group. 49 EX = 7 +3 +9 +5+4= 28 81 Compute (EX) The first step, inside the parentheses, is to compute EX. The second step is 25 to square the value for EX. 16 EX = 28 and (EX)? = (28) = 784