# Difference between revisions of "Statistic"

A statistic is a calculation made on the basis of a set numbers derived as a sample from some probability distribution, and usually used in order to estimate something about the distribution from which the sample is taken.

For example, suppose a random sample of three children is chosen from a particular class, and their heights measured as 1.42cm., 1.54cm., and 1.48cm; then the arithmetic mean of these heights is 1.48cm. We might then go on to use this value of 1.48cm to represent the average height of a child in that class.

Clearly the validity and reliability of such estimations will depend enormously on a range of factors such as the type of distributions, the number in the sample, and on sampling methods used.

### Formal Definition:

Let X1, X2, X3, ...., Xn be a random sample of size n from some distribution. A statistic calculated on the sample is defined to be any function of the set of values X1, X2, X3, ...., Xn, involving no unknown quantities 

The point of this definition is to ensure that the process results in an actual numerical value, rather than a formula involving variables.