Difference between revisions of "Statistic"
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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 random sample of size n from some distribution. 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. | ||
Revision as of 13:15, February 28, 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 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
- ↑ Francis, A. (2005) Advanced Level Statistics, Stanley Thornes