Here's a tip for working with formulas involving summations. I was working with a student yesterday who was getting confused with squaring a sum of values and squaring each individual value and then summing. This caused numerous errors when calculating the value of the correlation coefficient.
If the formula asks for sum x^2 then you square each x value and then take the sum.
For example, if the x values are 2, 3, 5, 6, 9 square each value first
2^2 = 4
3^2 = 9
5^2 = 25
6^2 = 36
9^2 = 81
Now get the sum of these values
4 + 9 + 25 + 36 + 81 = 155
If the formula asks for (sum x)^2, you get the sum of the x values, then square the result. In the above data set, we get
2 + 3 + 5 + 6 + 9 = 25, then square 25 to get 625.
The key to remember is to perfom everything inside the parentheses first. Recall the order of operations is
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
You can remember this by remembering the phrase "Please Excuse My Dear Aunt Sally"
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