Summation Notation

Prerequisites
None

Learning Objectives

  1. Use summation notation to express the sum of all numbers
  2. Use summation notation to express the sum of a subset of numbers
  3. Use summation notation to express the sum of squares

Many statistical formulas involve summing numbers. Fortunately there is a convenient notation for expressing summation. This section covers the basics of this summation notation.
The following formula means to sum up four numbers:

The Greek letter Σ indicates summation. The "i = 1" at the bottom indicates that the summation is to start with X1 and the 4 at the top indicates that the summation will end with X4. The Xi indicates that X is the variable to be summed as i goes from 1 to 4.

When all the scores of a variable (such as X) are to be summed, it is often convenient to use the following abbreviated notation:

Thus when no values of i are shown, it means to sum all the values of X.