# 0.1.2 - Summations

$$\Sigma$$

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 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 $$8.75$$