Category: Mathematics

Mathematics uses many concepts in threes. The first structure mathematically is a triangle. There are acute, right, and obtuse angles. Trigonometry is the study of the relationship of the sides of a triangle. Have your heard of Pascal's Triangle?

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Empirical rule – The 68-95-99.7 Rule

Empirical rule

Empirical rule

The 68-95-99.7 Rule
For Normal Distributions

This rule applies generally to a variable X having normal (bell-shaped or mound-shaped) distribution with mean "mu" (the greek letter) and standard deviation "sigma" (the greek letter). However, this rule does not apply to distributions that are not normal.

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Hypothesis testing

There are three possible pairs of null and alternative hypotheses

The null hypothesis (denoted $ H_0$) is a statement about the population statistic, such as $ mu$.

The alternate hypothesis (denoted $ H_1$) is a claim to be tested.

There are three ways to set up a the null and alternate hypothesis.

 

  1. Equal hypothesis verses not equal hypothesis (two-tailed test)
    $ H_0$:$ mu$ = some value
    $ H_1$:$ mu$ ?some value
  2. Equal hypothesis verses less than hypothesis (left-tailed test)
    $ H_0$:$ mu$ = some value
    $ H_1$:$ mu <$ some value
  3. Equal hypothesis verses greater than hypothesis (right-tailed test)
    $ H_0$:$ mu$ = some value
    $ H_1$:$ mu >$ some value
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Pythagoras – three is the perfect number

Pythagoras

Pythagoras
 
Pythagoras calls three the perfect number, expressive of “beginning, middle, and end,” wherefore he makes it a symbol of Deity. The world was supposed to be under the rule of three gods, viz. Jupiter (heaven), Neptune (sea), and Pluto (Hades). 

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