Summation notation
Summation notation is used to denote the sum of values. Suppose you have a sample consisting of the ages of 5 students in a middle school. Suppose the ages of these five students are 12, 14, 15, 10, and 9.
The variable age of a student can be denoted by x.
You could write the ages of the five students as follows.
Age of first student = x1 = 12
Age of second student = x2 = 14
Age of third student = x3 = 15
Age of fourth student = x4 = 10
Age of fifth student = x5 = 9
In the notation above, x represents students and the subscript denotes a particular student.
Meaning of Σx
Suppose you want to add the ages of all five students.
x1 + x2 + x3 + x4 + x5 = 12 + 14 + 15 + 10 + 9 = 60
The upper case Greek letter Σ is used to denote the sum of all values (2 values, 5, values, 200 values, or more). Σ is pronounced sigma.
Using Σ notation, we can instead write Σx = x1 + x2 + x3 + x4 + x5 = 60
In the example above, you only had 5 terms to add. Imagine you had 100. You could just use Σx to represent the addition of 100 terms. Therefore, Σx is a handy shortcut because it makes sense to write Σx as opposed to writing the following 100 terms down.
x1 + x2 + x3 + x4 + ... + x50 + ... + x100
Meaning of Σx2
Square each value of x and then take the sum.
Σx2 = x12 + x22 + x32 + x42 + x52 + ... + xn2
Meaning of (Σx)2
Add the values of x and then square the result.
(Σx)2 = (x1 + x2 + x3 + x4 + x5 + ... + xn )2
Meaning of Σxy
Multiply each value of x by each value of y and then take the sum.
Σxy = x1 × y1 + x2 × y2 + x3 × y3 + ... + xn × yn
Meaning of Σxy2
Multiply each value of x by the square of each value of y and then take the sum.
Σxy2 = x1 × y12 + x2 × y22 + x3 × y32 + ... + xn × yn2
At this point, most likely you understood how to work with summation notation.
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