When summarizing a data set (either from a population or a sample) we will often need to add (i.e. sum) all of these number up. To make an easier way to express the process of adding a bunch of number in a pile we use the summation notation, which we use the capital Greek letter sigma: \(\sum\)

The notation we will use for this is:

This notation means that we sum \(x\) for every \(x\) in ("\(\in\)") our pile.

---

In statistics we will not be summing random piles but instead we will be summing data taken from subjects of either a population or a sample. So to denote this we will always number of our subjects and for each \(i^{\text{th}}\) subject we will denote their data as \(x_i\). That is if we have \(n\) subjects in our sample we list their data as: \(\{x_1,x_2,..., x_n\}\), to sum this we will use the notation:

\[\sum_{i=1}^nx_i\]

The notation means we sum \(\sum\) for \(i=1\) up to \(i=n\) the values \(x_i\).

Note that the \(x_i\) is just a notation to mean that we have a data value numbered by \(i\).