COURSE CODE : PAS 111
COURSE DESCRIPTION : Elementary Statistics
TARGET POPULATION : All 1st-year BSBA STUDENTS
COURSE FACILITATOR : Angelus M. Sanchez
Week 3:
Learning Objectives:
1. Understand the Summation Notation and its sign.
2. Understand the usage of summation notation.
3. Study how to compute different equations using summation.
Summation Notation
The summation sign
This appears as the symbol, Ʃ, which is the Greek upper case letter, S. The
summation sign, Ʃ, 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 of the summation or the upper limit of the 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.
The limits of summation are often understood to mean i = 1 through n. Then the
notation below and above the summation sign is omitted. Therefore this expression
means sum the values of x, starting at x1and ending with xn.
Ʃ
This expression means sum the squared values of x, starting at x1 and ending with xn.
Arithmetic operations may be performed on variables within the summation. For
example:
This expression means sum the values of x, starting at x1 and ending
with xn and then square the sum.
Arithmetic operations may be performed on expressions containing more than one
variable. For example:
This expression means form the product of x multiplied by y, starting at x 1 and y1 and
ending with xn and yn and then sum the products.
In this expression c is a constant, i.e. an element which does not involve the variable
of summation and the sum involves n elements.
Sample Problem:
Data value: x1 = 1, x2 = 2, x3 = 3, x4 = 4
Data value:
i xi
1 -1
2 3
3 7
3. Find
4. Find
5. Find
Data value: x1 = 10, x2 =8, x3 = 6, x4 =4
Y1 = 0 ,Y2= 3, Y3= 6, Y1 = 9
6. Find
7. Find
8. Find
9. Find
Reference:
Sirug, W (2015). Basic Probability Statistics, A Step by Step Approach, Revised Edition.
Mindshapers.,Inc
Cabrero, B (2013). Business Statistics.Anvil Publishing, Inc
Summation notation.(n.d.). Retrieved from http://www.columbia.edu/itc/sipa/math/summation.h
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