INTRODUCTION TO SIGMA NOTATION
INTRODUCTION TO SIGMA NOTATION 1 The notation itself Sigma notation is a way of writing a sum of many terms, in a concise form A sum in sigma notation looks something like this: X5 k=1 3k The Σ (sigma) indicates that a sum is being taken The variable k is called the index of the sum The numbers at the top and bottom
sigma - mathcentreacuk
Sigma notation Sigma notation is a method used to write out a long sum in a concise way In this unit we look at ways of using sigma notation, and establish some useful rules In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature
Mathematics Learning Centre - University of Sydney
1 Sigma Notation 1 1 Understanding Sigma Notation The symbol Σ (capital sigma) is often used as shorthand notation to indicate the sum of a number of similar terms Sigma notation is used extensively in statistics For example, suppose we weigh five children We will denote their weights by x 1, x 2, x 3, x 4 and x 5 The sum of their weights
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sigma notation: § 7 2, p 144 cf E "commutes" with scalar multiplication: be brought outside the E For example, on the index of summation, then it can
Sigma notation - mathcentreacuk
Sigma notation mc-TY-sigma-2009-1 Sigma notation is a method used to write out a long sum in a concise way In this unit we look at ways of using sigma notation, and establish some useful rules In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature
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Introduction to Section 5 1: Sigma Notation, Summation Formulas Theory: Let a m, a m+1, a m+2,:::, a n be numbers indexed from m to n We abre-viate Xn j=m a j = a m + a m+1 + a m+2 + :::+ a n: For example X13 j=5 1 j = 1 5 + 1 6 + 1 7 + 1 8 + 1 9 + 1 10 + 1 11 + 1 12 + 1 13; Xn j=1 ( 1)j 1 j = 1 1 + 1 2 1 3 + :::+ ( 1)n 1 n; Xn j=1 c = c+ c+
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Sigma Notation De nition (Sigma Notation) We write the sum of nobservations as: More Xn i=1 x i = x 1 + x 2 + x 3 + :::+ x n 1 + x n The summation operator, P, is the greek letter, capital sigma, hence the name \Sigma notation " The operator, Xn i=1, is read as \the sum from i= 1 to n " You can use it to sum any number, not just observations
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Math 132 Area, Distance, and Sigma Notation Section 4 1 2 Above we looked at Right Hand Sums, meaning we used the right side of each rectangle for our approximation A Left Hand Sum is the same approximation process, except we use the
LEAN SIX SIGMA GREEN BELT CHEAT SHEET
• When to use what test: (The Six Sigma Memory Jogger II p 144) • If comparing a group to a specific value use a 1-sample t-test (The Lean Six Sigma Pocket Toolbook p 162) Tells us if a statistical parameter (average, standard deviation, etc ) is different from a value of interest
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INTRODUCTION TO SIGMA NOTATION
1.The notation itselfSigmanotation is a way of writing a sum of many terms, in a concise
form. A sum in sigma notation looks something like this: 5 k=13k The Σ (sigma) indicates that a sum is being taken. The variablek is called theindex of the sum. The numbers at the top and bottom of the Σ are called theupperandlowerlimits of the summation. In this case, the upper limit is 5, and the lower limit is 1. The notation means that we will take every integer value ofkbetween 1 and 5 (so1, 2, 3, 4, and 5) and plug them each into the summand formula (here
that formula is 3k). Then those are all added together. 5 k=13k= 3·1 + 3·2 + 3·3 + 3·4 + 3·5 = 45 Example 1.Write out what is meant by the following: 3 k=01k+ 1 Here, the indexktakes the values 0, 1, 2, and 3. We"ll plug those each into1k+1and add them together.
3 k=01k+ 1=10 + 1 +11 + 1 +12 + 1 +13 + 1 Example 2.Write out what is meant by the following: 8 i=1(-1)iDate: Wednesday March 29, 2017. 12 INTRODUCTION TO SIGMA NOTATION
The index variable here is written asiinstead ofk. That"s ok. The most common variables to use for indexes includei,j,k,m, andn. 8 i=1(-1)i= (-1)1+ (-1)2+ (-1)3+ (-1)4+ (-1)5+ (-1)6+ (-1)7+ (-1)8 =-1 + 1 +-1 + 1 +-1 + 1 +-1 + 1 = 0Try one on your own.
Example 3.Write out what is meant by the following (no need to simplify): 4? n=-1⎷n+ 1Let"s try going the other way around.
Example 4.Write the following sum in sigma notation.2 + 4 + 6 + 8 +...+ 22 + 24
Notice that we can factor a 2 out of each term to rewrite this sum as2·1 + 2·2 + 2·3 + 2·4 +...+ 2·11 + 2·12
That means that we are adding together 2 times every number between1 and 12. The sigma notation could be
12 k=12k There is no need to usekas our index variable. We could have just as easily usedmorjinstead. 12 k=12k=12 m=12m=12 j=12jNotice, that these are NOT the same as
12 k=12m Example 5.Write the following sum in sigma notation. 1-12 +14 -18 +...-164 +1128INTRODUCTION TO SIGMA NOTATION 3
This one is a little more complicated. We"ll worry about the signs later, first we"ll deal with the numbers themselves. Do you notice a pattern in the terms? Sure, we get to the next term by dividing by 2.That is:
1 = 12 0=?12 0 12 =12 1=?12 1 14 =12 2=?12 2 1128=12 7=?12 7 If we call our index variablek, thenkshould go from 0 to 7, and the numbers themselves are just?12 k. Now we need to deal with the signs. We say above that (-1)kwill alternate between +1 and-1. That is, if we multiply our terms from above by (-1)k, they will alternate between + and-. We are starting withk= 0, so (-1)0= +1 will give us the alternation starting at the sign we want. 7 k=0(-1)k?12 k =7 k=0? -12 k