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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)

ΣY = 8 + 3 + 1 = 12

ΣX + ΣY = 9 + 12 =

For an example, let a = 2.

ΣaX = (2)(3) + (2)(2) + (2)(4) =

a ΣX = (2)(9) =

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 =

ΣX² = 3²+ 2²+ 4²= 29

(ΣX)²/N = 9²/3 = 27

ΣX² - (ΣX)²/N = 29 - 27 =

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