Summation Notation (4 of 4)

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Basic Theorems:

The following data will be used to illustrate the theorems:

X
Y
3 8
2 3
4 1

Σ(X + Y) = ΣX + ΣY
Σ(X + Y) = 11 + 5 + 5 = 21
ΣX = 3 + 2 + 4 = 9
ΣY = 8 + 3 + 1 = 12
ΣX + ΣY = 9 + 12 = 21

ΣaX = aΣX (a is a constant)
For an example, let a = 2.
ΣaX = (2)(3) + (2)(2) + (2)(4) = 18
a ΣX = (2)(9) = 18

Σ(X-M)² = ΣX² - (ΣX)²/N
(N is the number of numbers, 3 in this case, and M is the mean which is also equal to 3 in this case.
Σ(X-M)² = (3-3)² + (2-3)² + (4-3)² = 2
ΣX² = 3²+ 2²+ 4²= 29
(ΣX)²/N = 9²/3 = 27
ΣX² - (ΣX)²/N = 29 - 27 = 2



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