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Basic Mathematics - Statistics

I will be blunt: I am not a big fan of statistics. As a matter of fact, of all the science related courses I have taken, Statistics was (and is) my Achilles Heel.

Statistics is basically the collection of empirical data used to generate probability. Data is collected, including random errors, and distributions plots are generated. These plots provide probability of a given event.

We see statistics on an almost daily basis: weather reports, stock market reports, and Monday mornings (call in sick or not - probability based on weather or feelings towards work in general).

We have also heard of statistics in airline safety - its safer to fly than to drives since the occurrences of plane crashes is far less than automobile crashes.

This is all based on Statistics. By using data plots, the sum of events can be observed.

Probability is another form of statistics that is based on experimentation and outcomes.



In order to generate plots, a data set must be gathered. The data set is a series of observations ordered by class - for example, test grades from 6 different courses, each course is a class and each grade is an observation.

The image above is an example of a bar graph. This is also called a histogram.

To center the data, we can use mean, median, and mode.

The mean:

The median:

Arrange the data in order. For example, your grades are 60, 62, 58, 75, 99, and 47, the order will be:

47, 58, 60, 62, 75, and 99

The mean is between 60 and 62, so its 61.

Another example:

10, 100, 5000, 1000000, 5000000000 (the latter two are one million and five billion)

The median is 5000

The mode:

Any value that appears more than once will be the mode. There are no duplicate values in the grades above, so there is no mode for this data set. If the grades were:

47, 58, 60, 75, 75, and 99

The mode will be 75.

The histogram created will generate a curved plot.
A natural bell shape to a histogram is said to have a normal distribution. The area that is spread out is called the standard deviation. The numbers along the axis are called z-scores.

If a value does not fall on a z-score line, the unknown z-score can be determined by:

For an unknown observation value:

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In order to study uncertain events, we use probability. There are four steps involved:

  • Experiment - actions that cannot be predicted

  • Outcomes - possible results

  • Sample Space - collection of all possible outcomes

  • Event - sub-collection of the sample space

The result P(E) can be 0 or 1 or anything in between.

P(E) = 0 means the event (E) will never occur
P(E) = 1 means the event (E) will always occur

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