# 0.1.2 - Summations

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

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 $8.75$

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