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Summation Notation
by David M. Lane

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.

Let's say we have a variable X that represents the weights (in grams) of 4 grapes. The data are shown in Table 1.

Table 1. Weights of 4 grapes.

We label Grape 1's weight X₁, Grape 2's weight X₂, etc. The following formula means to sum up the weights of the four grapes:

$\sum _{i=1}^{4}X_{i}$

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 “X_i” indicates that X is the variable to be summed as i goes from 1 to 4. Therefore,

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