Summation Notation (4 of 4)
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Basic Theorems:
The following data will be used to illustrate the theorems:
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
Next Section: Measurement Scales