281
edits
Changes
Jump to navigation
Jump to search
create entry
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 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.
===Examples of Statistics:===
* Arithmetic Mean
* Median
* Standard Deviation
* Pearson's Measure of Skewness '' = 3*(mean - median)/standard deviation
===References===
<references/>
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<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.
===Examples of Statistics:===
* Arithmetic Mean
* Median
* Standard Deviation
* Pearson's Measure of Skewness '' = 3*(mean - median)/standard deviation
===References===
<references/>