# A.2 Summations

A.2 Summations

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:

 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.

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.

#### Summations

Here is a brief review of summations as they will be applied in STAT 200:

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