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Finite and Infinite Statistics

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Finite and Infinite Statistics

Finite statistics are statistics calculated from finite sets. Basically, you have a sample that you’re using to make a calculation (like the sample variance). If you have a countable number of data points in your sample, what you end up with is a finite statistic.

On the other hand, infinite statistics are those calculated from infinite sets. For example, a probability density function has, for practical purposes, an infinite number of data points under its curve.

The normal distribution is another example of an area that uses infinite statistics: the z-table on this site lists just a few hundred points, but technically the table has an uncountable number of points on it (e.g. z=2.1 is listed, but z = 2.1249865 is not). This is for a couple of reasons:

  1. Space: there simply isn’t room on any page in existence for a table of infinite values!
  2. Practical Purposes: Even if you could list every possible z-value, there comes a point where the values are so similar, a finite set is “good enough”. Take a look at this snapshot from the table:
    infinite set

    Any value between 3.7 and 3.8 would also be an area of 0.4999, so there’s really no point in listing them all.

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Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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