This is from my lecture notes and I should have clarified before leaving class.

How do you find the summation (xi - x bar) (yi - y bar) = 6640 summation (xi - xbar)2= 1239.88

x: 2 8 16 22 25 34 35 39
y: 30 75 165 200 110 250 225 225

Do you mean two separate things here?

\Sigma (x_i - \bar{x})(y_i - \bar{y}) = 6640

and

\Sigma (x_i - \bar{x})^2 = 1239.88

?

Because that seems as: \Sigma (x_i - \bar{x})(y_i - \bar{y}) = 6640 \Sigma (x_i - \bar{x})^2 = 1239.88

If I'm right, then what you have to do is:
1. Find x bar and y bar, the mean of x and y respectively.
2. x_i is each value that x contains. x_i - x bar is (2 - x bar) or (8 - x bar), etc.
Summation of (x_i - x bar) is the mean, removed from each of the terms in x.

Here, it is:
(2 - x bar) + (8 - x bar) + (16 - x bar) + (22 - x bar) + (25 - x bar) +... + (39 - x bar)

3. The same goes for (y_i - y bar).

For the first one, multiply each result of (x_i - x bar) with (y_i - y bar) then add them together.

For example, do (2 - x bar)(30 - y bar) + ( 8 - x bar)(75 - y bar)

For the second one, square each (x_i - x bar) then add them up.

I just checked them, and I got the answers right :)