Statistical Inference: A Short Course

1.5 Let Us Add

Quite often throughout this text the reader will be asked to total or form the sum of the values appearing in a variety of data sets. We have a special notation for the operation of addition. We will let the Greek capital sigma or Σ serve as our “summation sign.” Specifically, for a variable X with values X₁, X₂, . . ., X_n,

(1.1)

Here the right-hand side of this expression reads “the sum of all observations X_i as i goes from 1 to n.” In this regard, Σ is termed an operator—it operates only on those items having an i index, and the operation is addition. When it is to be understood that we are to add over all i values, then Equation (1.1) can be rewritten simply as .