Page:Online Statistics Education.pdf/52

 by David M. Lane

Prerequisites • None

Learning Objectives Many statistical formulas involve summing numbers. Fortunately there is a convenient notation for expressing summation. This section covers the basics of this summation notation.
 * 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

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 “Xi” indicates that X is the variable to be summed as i goes from 1 to 4. Therefore, 52