What is Sigma? - Definition, Lesson & Quiz

Supplemental Lesson
Share Feedback Rate
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 Using Sigma Notation for the Sum of a Series and What is Temperature? - Definition, Lesson & Quiz

What is Sigma?

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.

The Greek letter sigma.
sigma letters

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.

Upper Case Sigma

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

Summation notation formula.
sigma summation

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.

An example of the summation formula.
sigma summation example

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.

Lower Case Sigma

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

The standard deviation formula.
sigma std dev

Continue reading...
Create An Account
To Start This Course Today
Used by over 10 million students worldwide
Create An Account
Try it free for 5 days
Start Your Free Trial To Take This Quiz

As a member, you'll also get unlimited access to over 8,500 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
It only takes a few minutes to set up and you can cancel at any time.
Already registered? Login here for access

Earning College Credit

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

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Education Portal 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.


Watch all the video lessons you want free for 5 days
Select a plan to try & see why over 10 million users love Education Portal
Start Free Trial