 SIGMA

Essentials: Sigma -  (Yeah, I got this – so everyone thinks, but it isn’t as easy as it looks.) Understand what Sigma (  means and how it is used. Be able to interpret what  is telling you to do in a given formula. When you think you’ve got it, practice some more.

ANATOMY OF SIGMA: s ummation notation This is Sigma. It is the Greek symbol for uppercase “S.” Sigma is not unique to statistics, but is a notation used in many areas of mathematics. When you see this notation, you will take the sum of whatever follows it. It is read as “the sum of.” Here, in words, it is “the sum as i goes from one to n of x sub i.” This is a subscript (or index). When x, and its subscript are replaced by actual numbers, it will denote a unique value in a data set. This is the lower index of the sum. This is the upper index of the sum. Two examples will prove very helpful here. Let: Then, The expression to the left is read as, “Sum the x sub-i as i goes from 1 (the first value) to n (the last value).” = (6 - 8) 2 + (3 - 8) 2 + (17 – 8) 2 + (12 – 8) – 8) 2 = (-2) 2 + (-5) 2 + (9) 2 +(4) 2 + (-6) 2 = = 162 The expression to the left is read as, “Sum the values obtained from the x sub-i minus the mean, quantity squared as i goes from 1 to n.”

Summation Practice: Let the variable X represent the numbers: Let the variable Y represent the numbers:

Summation Practice: Let the variable X represent the numbers: Let the variable Y represent the numbers:

Summation Practice: Let the variable X represent the numbers: Let the variable Y represent the numbers: