Course Navigator

Back To Course

Math 101: College Algebra11 chapters | 81 lessons

Watch short & fun videos
**Start Your Free Trial Today**

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 eighteenth 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.

We also recommend watching Summation Notation and Mathematical Series and How to Calculate an Arithmetic Series

**Sigma** is the eighteenth 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 their 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 I'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 I 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, my 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, I only have four numbers and so my *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 I have done is plug and play. I've plugged my numbers into the equation where they belong and I solve it step by step, simplifying as I go.

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.

To unlock this lesson you must be a Study.com Member.

Create your account

Your Score:
{{(quiz.score / quiz.totalQuestions) * 100 | number:0}}%

(To pass you need a perfect score. You can retake the quiz at anytime.)

(You passed! You can still retake the quiz if you'd like to.)

Saving your score...
##### Email your results. (optional)

Oops, you didn't pass. But, that's okay! You can retake the quiz at any time.

Congratulations, you got a perfect score!

Start Your Free Trial To Take This Quiz

Free 5-day trial
Start your free trial to access this entire worksheet

A premium account that givies you access to all lesson, practice exams, quizzes & worksheets

Access to all video lessons

Quizzes, practice exams & worksheets

Certificate of completion

Access to instructors

Create an account to get started
Create Account

Did you know… We have over 100 college courses that prepare you to earn credit by exam that is accepted by over 2,900 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

- Go to Inequalities

- Go to Functions

- What is a Mathematical Sequence? 5:37
- How to Find and Classify an Arithmetic Sequence 9:09
- Finding and Classifying Geometric Sequences 9:17
- Summation Notation and Mathematical Series 6:01
- How to Calculate a Geometric Series 9:15
- Arithmetic and Geometric Series: Practice Problems 10:59
- Go to Sequences and Series

Browse by subject