A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences

A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences

The basic formula to calculate sample variance is based on the sum of squared differences from mean. From computational perspective, mean calculation is nondesired as it can introduce computing errors. Previous researches have proposed to use weighted formula of the successive differences to calcula...

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Main Authors: Kuo-Hung Lo, Tien-Lung Sun, Juei-Chao Chen
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2014/210761
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spelling doaj-ba4add2d63864fba8b333634bc3835e92020-11-24T22:52:36ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/210761210761A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive DifferencesKuo-Hung Lo0Tien-Lung Sun1Juei-Chao Chen2Department of Industrial Engineering and Management, Yuan Ze University, Zhongli 32003, TaiwanDepartment of Industrial Engineering and Management, Yuan Ze University, Zhongli 32003, TaiwanDepartment of Statistics and Information Science, Fu Jen Catholic University, New Taipei City 24205, TaiwanThe basic formula to calculate sample variance is based on the sum of squared differences from mean. From computational perspective, mean calculation is nondesired as it can introduce computing errors. Previous researches have proposed to use weighted formula of the successive differences to calculate sample variance to avoid mean calculation. But their weighted formula is not in a unified format in the sense that it has to be represented as two formulas. This paper proposes a unified weight formula for sample variance calculation from weighted successive differences. A proof is provided to show that sample variance calculated using the proposed unified weighted formula is mathematically equivalent to the basic definition.http://dx.doi.org/10.1155/2014/210761
collection DOAJ
language English
format Article
sources DOAJ
author Kuo-Hung Lo
Tien-Lung Sun
Juei-Chao Chen
spellingShingle Kuo-Hung Lo
Tien-Lung Sun
Juei-Chao Chen
A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
Discrete Dynamics in Nature and Society
author_facet Kuo-Hung Lo
Tien-Lung Sun
Juei-Chao Chen
author_sort Kuo-Hung Lo
title A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
title_short A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
title_full A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
title_fullStr A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
title_full_unstemmed A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences
title_sort unified weight formula for calculating the sample variance from weighted successive differences
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2014-01-01
description The basic formula to calculate sample variance is based on the sum of squared differences from mean. From computational perspective, mean calculation is nondesired as it can introduce computing errors. Previous researches have proposed to use weighted formula of the successive differences to calculate sample variance to avoid mean calculation. But their weighted formula is not in a unified format in the sense that it has to be represented as two formulas. This paper proposes a unified weight formula for sample variance calculation from weighted successive differences. A proof is provided to show that sample variance calculated using the proposed unified weighted formula is mathematically equivalent to the basic definition.
url http://dx.doi.org/10.1155/2014/210761
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AT jueichaochen aunifiedweightformulaforcalculatingthesamplevariancefromweightedsuccessivedifferences
AT kuohunglo unifiedweightformulaforcalculatingthesamplevariancefromweightedsuccessivedifferences
AT tienlungsun unifiedweightformulaforcalculatingthesamplevariancefromweightedsuccessivedifferences
AT jueichaochen unifiedweightformulaforcalculatingthesamplevariancefromweightedsuccessivedifferences
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