# APPENDIX A1

# Summation Notation

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 *x*_{1}, *x*_{2}, …, *x _{n}* and is read as

**the sum of all**.

*x*with_{i}*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,

Example

Suppose that the four measurements in a data set are given as *x*_{1} = 2, *x*_{2} = 5, *x*_{3} = 3, *x*_{4} = 4. Compute the numerical values of

SOLUTION

Alternatively, noting that (*x _{i}* − 3)

^{2}= − 6

*x*+ 9, we can write

_{i}A few basic properties of the summation operation are apparent ...

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