A1.1 SUMMATION AND ITS PROPERTIES
The addition of numbers is basic to our study of statistics. To avoid a detailed and repeated writing of this operation, the symbol Σ (the Greek capital letter sigma) is used as mathematical shorthand for the operation of addition.
Summation Notation Σ
The notation represents the sum of n numbers x1, x2, …, xn and is read as the sum of all xi with i ranging from 1 to n.
The term following the sign Σ indicates the quantities that are being summed, and the notations on the bottom and the top of the Σ specify the range of the terms being added. For instance,
Suppose that the four measurements in a data set are given as x1 = 2, x2 = 5, x3 = 3, x4 = 4. Compute the numerical values of
Alternatively, noting that (xi − 3)2 = − 6xi + 9, we can write
A few basic properties of the summation operation are apparent ...