Statistics Definitions > Finite and Infinite Statistics
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:
- Space: there simply isn’t room on any page in existence for a table of infinite values!
- 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.