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High School Precalculus: Homework Help Resource32 chapters | 273 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In addition to being the 18th letter of the Greek alphabet, sigma also means 'sum' and 'deviation' in the mathematics world. Learn what each symbol looks like and how each formula works.

**Sigma** is the 18th letter of the Greek alphabet and is equivalent to our letter 'S'. In mathematics, the upper case sigma is used for the summation notation. The lower case sigma stands for standard deviation. Each has its own unique formula, and yes, both the upper case and lower case look vastly different from each other.

Neither of them looks like our letter 'S', but they are both the Greek equivalent of it. If you notice, the two formulas that use these two symbols both start with the letter 's'.

The upper case sigma is used in the summation notation. This particular notation is also called sigma notation.

This particular formula, as its name denotes, tells you to sum up the function evaluated at particular points determined by the little numbers on top and below the big sigma. It is used to add a series of numbers.

You will most likely see this used to sum up a function evaluated at certain points. In the real world, this can be used to figure out the interest you earn over a period of time if you have money saved in an interest-bearing account at a financial institution.

When performing math problems, you will most often see this in association with functions of various types. An example is the summation of *f(n)* = 1/*n* evaluated at 1, 2, 3, and 4.

The little numbers on top and below the big sigma determine the starting and ending evaluation values. You can see that we've plugged in the values 1, 2, 3, and 4 into the *n* in the formula to evaluate at each of the values and then summed it all up.

The summation or sigma notation is fairly straightforward and easy to follow. Try it out with a few functions you are familiar with so you can get a better feel for how it works. Try different starting and ending values as well.

The lower case sigma is used for the standard deviation formula in statistics.

If you haven't delved into statistics before, welcome! Don't let this huge formula scare you. The letter that looks like the letter 'u' but with a longer line is the Greek letter 'mu', and in this formula it stands for the mean, or average, of a series of numbers. The *x* with the subscript *i* stands for each number in the series. Say, for example, the series of numbers goes like this: 5, 2, 8, and 1. The *x* sub 1 number is 5 and the *x* sub 3 number is 8. Do you see how it works? In this particular series, we only have four numbers and so our *N* is 4.

While the above example might look scary, it really isn't. If you break it down into its parts you will see that all we have done is plug and play. We've plugged our numbers into the equation where they belong, and we solve it step by step, simplifying as we go.

Let's review. The first and most common formula related to the **sigma** symbol is the summation notation using the upper case sigma. The less common formula is the one for standard deviation used in statistics. This second formula uses the lower case sigma.

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High School Precalculus: Homework Help Resource32 chapters | 273 lessons

- What is a Mathematical Sequence? 5:37
- Introduction to Sequences: Finite and Infinite 4:57
- How to Use Factorial Notation: Process and Examples 4:40
- Summation Notation and Mathematical Series 6:01
- How to Use Series and Summation Notation: Process and Examples 4:16
- Understanding Arithmetic Series in Algebra 6:17
- How to Calculate an Arithmetic Series 5:45
- Arithmetic Sequences: Definition & Finding the Common Difference 5:55
- How and Why to Use the General Term of an Arithmetic Sequence 5:01
- The Sum of the First n Terms of an Arithmetic Sequence 6:00
- How to Find and Classify an Arithmetic Sequence 9:09
- Working with Geometric Sequences 5:26
- Finding and Classifying Geometric Sequences 9:17
- How and Why to Use the General Term of a Geometric Sequence 5:14
- The Sum of the First n Terms of a Geometric Sequence 4:57
- Understand the Formula for Infinite Geometric Series 4:41
- How to Calculate a Geometric Series 9:15
- Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences 5:52
- Arithmetic and Geometric Series: Practice Problems 10:59
- Using Sigma Notation for the Sum of a Series 4:44
- Mathematical Induction: Uses & Proofs 7:48
- How to Find the Value of an Annuity 4:49
- How to Use the Binomial Theorem to Expand a Binomial 8:43
- Special Sequences and How They Are Generated 5:21
- Mathematical Series: Formula & Concept
- Summation Notation: Rules & Examples 3:36
- What is Sigma? - Definition & Concept 3:15
- Go to Mathematical Sequences and Series: Homework Help

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