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 [[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.
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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.
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Clearly the [[validity]] and [[reliability]] of such [[estimation]]s will depend enormously on a range of factors such as the type of distributions, the number in the sample, and on sampling methods used.
  
  

Revision as of 04:58, 14 May 2007

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