# Finite and Infinite Statistics

Statistics Definitions > Finite and Infinite Statistics

## 1. Finite 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.

## 2. Infinite Statistics

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.

## Finite and Infinite Statistics Examples

The normal distribution is one 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: 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.

## References

Hildebrand, F. H. and Johnson, C. G. Finite Mathematics. Boston, MA: Prindle, Weber, and Schmidt, 1970.
Kemeny, J. G.; Snell, J. L.; and Thompson, G. L. Introduction to Finite Mathematics, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1974
Triola, M. (2018). Elementary Statistics with Finite Mathematics (Math 121 & 122) Fifth Custom For Syracuse University.

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Stephanie Glen. "Finite and Infinite Statistics" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/finite-set-infinite-statistics/
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