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 = x_{1} = 12
Age of second student = x_{2} = 14
Age of third student = x_{3} = 15
Age of fourth student = x_{4} = 10
Age of fifth student = x_{5} = 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.
x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 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 = x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 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.
x_{1} + x_{2} + x_{3} + x_{4} + ... + x_{50} + ... + x_{100}
Meaning of Σx^{2}
Square each value of x and then take the sum.
Σx^{2} = x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} + x_{5}^{2} + ... + x_{n}^{2}
Meaning of (Σx)^{2}
Add the values of x and then square the result.
(Σx)^{2} = (x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + ... + x_{n} )^{2}
Meaning of Σxy
Multiply each value of x by each value of y and then take the sum.
Σxy = x_{1} × y_{1} + x_{2} × y_{2} + x_{3} × y_{3} + ... + x_{n} × y_{n}
Meaning of Σxy^{2}
Multiply each value of x by the square of each value of y and then take the sum.
Σxy^{2} = x_{1} × y_{1}^{2} + x_{2} × y_{2}^{2} + x_{3} × y_{3}^{2} + ... + x_{n} × y_{n}^{2}
At this point, most likely you understood how to work with summation notation.
Jun 06, 23 07:32 AM
May 01, 23 07:00 AM