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Summation Notation
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Lecture notes of 4 pages for the course Basic Statistics at OU (Summation Notation)
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20/07/2022, 09:45 Summation NotationSummation Notation
Often mathematical formulae require the addition of many variables Summation or sigma notation is a
convenient and simple form of shorthand used to give a concise expression for a sum of the values of a
variable.
Let x1, x2, x3, …xn denote a set of n numbers. x1 is the first number in the set. xi represents the ith number
in the set.
Summation notation involves:
The summation sign
This appears as the symbol, S, which is the Greek upper case letter, S. The summation sign, S, instructs us
to sum the elements of a sequence. A typical element of the sequence which is being summed appears to the
right of the summation sign.
The variable of summation, i.e. the variable which is being summed
The variable of summation is represented by an index which is placed beneath the summation sign. The
index is often represented by i. (Other common possibilities for representation of the index are j and t.) The
index appears as the expression i = 1. The index assumes values starting with the value on the right hand side
of the equation and ending with the value above the summation sign.
The starting point for the summation or the lower limit of the summation
The stopping point for the summation or the upper limit of summation
Some typical examples of summation
This expression means sum the values of x, starting at x1 and ending with xn.
This expression means sum the values of x, starting at x1 and ending with x10.
This expression means sum the values of x, starting at x3 and ending with x10.
www.columbia.edu/itc/sipa/math/summation.html#:~:text=A typical element of the,is often represented by i. 1/4
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