0.1.2 - Summations


This is the Greek capital letter "sigma." In math, this symbol is also known as a summation. This tells us that we should add a series of numbers (i.e., take the sum).

Example: Candy Section

Candy Corn

Four children are comparing how many pieces of candy they have:

ID Child Pieces of Candy
1 Marty 9
2 Harold 8
3 Eugenia 10
4 Kevi 8

We could say that: \(x_{1}=9\),\(x_{2}=8\), \(x_{3}=10\), and \(x_{4}=8\).

If we wanted to know how many total pieces of candy the group of children had, we could add the four numbers. The notation for this is:

\[\sum x_{i}\]

So, for this example, \(\sum x_{i}=9+8+10+8=35\)

To conclude, combined, the four children have \(35\) pieces of candy.

You will first see a summation in Lesson 2 when you learn to compute a sample mean (\(\overline{x}\)). This is also known as the average. You will learn that \(\overline{x}=\frac{\Sigma{X}}{n}\); in other words, the sum of all of the observations divided by the number of observations. 

In this example, \(\overline{x}=\frac{\Sigma{X}}{n}=\frac{9+8+10+8}{4}=\frac{35}{4}=8.75\)

In this sample of four children, the average number of pieces of candy is \(8.75\)