# Statistic

A statistic is a calculation made on the basis of a set numbers derived as a sample from some 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 [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

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