# Difference between revisions of "Statistic"

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− | 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. | + | 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. | 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. | ||

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===Formal Definition:=== | ===Formal Definition:=== | ||

− | Let X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, ...., X<sub>n</sub> be a | + | Let X<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, ...., X<sub>n</sub> 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<sub>1</sub>, X<sub>2</sub>, X<sub>3</sub>, ...., X<sub>n</sub>, involving no unknown quantities <ref> Francis, A. (2005) Advanced Level Statistics, Stanley Thornes </ref> |

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

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===Examples of Statistics:=== | ===Examples of Statistics:=== | ||

− | * Arithmetic | + | * [[Arithmetic mean]] |

− | * Median | + | * [[Median]] |

− | * Standard | + | * [[Standard deviation]] |

− | * Pearson's | + | * [[Pearson's measure of skewness]] '' = 3*(mean - median)/standard deviation |

===References=== | ===References=== | ||

<references/> | <references/> | ||

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[[Category:Science]] | [[Category:Science]] | ||

− | [[Category: | + | [[Category:Statistics]] |

## Revision as of 08:12, 28 February 2009

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