This is the upper-case Greek letter sigma. A sigma tells us that we need to sum (i.e., add) a series of numbers.

$$\sum$$

For example, four children are comparing how many pieces of candy they have:

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.

In statistics, some equations include the sum of all of the squared values (i.e., square each item, then add). The notation is:

$$\sum x_i^2$$

or

$$\sum (x_i^2)$$

Here, $\sum x_i^2=9^2+8^2+{10}^2+8^2=81+64+100+64=309$.

Sometimes we want to square a series of numbers that have already been added. The notation for this is:

$$(\sum x_i{)}^2$$

Here,$(\sum x_i{)}^2=(9+8+10+8{)}^2={35}^2=1225$

Note that $\sum x_i^2$ and $(\sum x_i{)}^2$ are different.