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.   
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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 [[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>
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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 Mean
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* [[Arithmetic mean]]
* Median
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* [[Median]]
* Standard Deviation
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* [[Standard deviation]]
* Pearson's Measure of Skewness '' = 3*(mean - median)/standard  deviation
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* [[Pearson's measure of skewness]] '' = 3*(mean - median)/standard  deviation
  
 
===References===
 
===References===
  
 
<references/>
 
<references/>
 
  
 
[[Category:Science]]
 
[[Category:Science]]
[[Category:Mathematics]]
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[[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 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:

References

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