# 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 X_{1}, X_{2}, X_{3}, ...., X_{n} 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 X_{1}, X_{2}, X_{3}, ...., X_{n}, involving no unknown quantities ^{[1]}

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

### Examples of Statistics:

- Arithmetic mean
- Median
- Standard deviation
- Pearson's measure of skewness
*= 3*(mean - median)/standard deviation*

### References

- ↑ Francis, A. (2005) Advanced Level Statistics, Stanley Thornes