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Improved frequency table with application to environmental data

This paper proposes three different statistics to be used to represent the magnitude observations in each class when estimating the statistical measures from the frequency table for continuous data. The existing frequency tables use the midpoint as the magnitude of observations in each class, which...

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Main Authors:	Mohammed, M. B., Adam, Mohd Bakri, Zulkafli, Hani Syahida, Ali, Norhaslinda
Format:	Article
Language:	English
Published:	Horizon Research Publishing 2020
Online Access:	http://psasir.upm.edu.my/id/eprint/89315/1/TABLE.pdf http://psasir.upm.edu.my/id/eprint/89315/ https://www.hrpub.org/journals/article_info.php?aid=8927
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spelling	my.upm.eprints.893152021-09-03T08:44:31Z http://psasir.upm.edu.my/id/eprint/89315/ Improved frequency table with application to environmental data Mohammed, M. B. Adam, Mohd Bakri Zulkafli, Hani Syahida Ali, Norhaslinda This paper proposes three different statistics to be used to represent the magnitude observations in each class when estimating the statistical measures from the frequency table for continuous data. The existing frequency tables use the midpoint as the magnitude of observations in each class, which results in an error called grouping error. Using the midpoint is due to the assumption that the observations in each class are uniformly distributed and concentrated around their midpoint, which is not always valid. In this research, construction of the frequency tables using the three proposed statistics, the arithmetic mean, median, and midrange and midpoint are respectively named, Method 1, Method 2, Method 3, and the Existing method. The four methods are compared using root-mean-squared error (RMSE) by performing simulation studies using three distributions, normal, uniform, exponential distributions. The simulation results are validated using real data, Glasgow weather data. The ﬁndings indicated that using the arithmetic mean to represent the magnitude of observations in each class of the frequency table leads to minimal error relative to other statistics. It is followed by using the median, for data simulated from normal and exponential distributions, and using midrange for data simulated from uniform distribution. Meanwhile, in choosing the appropriate number of classes used in constructing the frequency tables, among seven different rules used, the freedman and Diaconis rule is the recommended rule. Horizon Research Publishing 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/89315/1/TABLE.pdf Mohammed, M. B. and Adam, Mohd Bakri and Zulkafli, Hani Syahida and Ali, Norhaslinda (2020) Improved frequency table with application to environmental data. Mathematics and Statistics, 8 (2). 201 - 210. ISSN 2332-2071; ESSN: 2332-2144 https://www.hrpub.org/journals/article_info.php?aid=8927 10.13189/ms.2020.080216
institution	Universiti Putra Malaysia
building	UPM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Putra Malaysia
content_source	UPM Institutional Repository
url_provider	http://psasir.upm.edu.my/
language	English
description	This paper proposes three different statistics to be used to represent the magnitude observations in each class when estimating the statistical measures from the frequency table for continuous data. The existing frequency tables use the midpoint as the magnitude of observations in each class, which results in an error called grouping error. Using the midpoint is due to the assumption that the observations in each class are uniformly distributed and concentrated around their midpoint, which is not always valid. In this research, construction of the frequency tables using the three proposed statistics, the arithmetic mean, median, and midrange and midpoint are respectively named, Method 1, Method 2, Method 3, and the Existing method. The four methods are compared using root-mean-squared error (RMSE) by performing simulation studies using three distributions, normal, uniform, exponential distributions. The simulation results are validated using real data, Glasgow weather data. The ﬁndings indicated that using the arithmetic mean to represent the magnitude of observations in each class of the frequency table leads to minimal error relative to other statistics. It is followed by using the median, for data simulated from normal and exponential distributions, and using midrange for data simulated from uniform distribution. Meanwhile, in choosing the appropriate number of classes used in constructing the frequency tables, among seven different rules used, the freedman and Diaconis rule is the recommended rule.
format	Article
author	Mohammed, M. B. Adam, Mohd Bakri Zulkafli, Hani Syahida Ali, Norhaslinda
spellingShingle	Mohammed, M. B. Adam, Mohd Bakri Zulkafli, Hani Syahida Ali, Norhaslinda Improved frequency table with application to environmental data
author_facet	Mohammed, M. B. Adam, Mohd Bakri Zulkafli, Hani Syahida Ali, Norhaslinda
author_sort	Mohammed, M. B.
title	Improved frequency table with application to environmental data
title_short	Improved frequency table with application to environmental data
title_full	Improved frequency table with application to environmental data
title_fullStr	Improved frequency table with application to environmental data
title_full_unstemmed	Improved frequency table with application to environmental data
title_sort	improved frequency table with application to environmental data
publisher	Horizon Research Publishing
publishDate	2020
url	http://psasir.upm.edu.my/id/eprint/89315/1/TABLE.pdf http://psasir.upm.edu.my/id/eprint/89315/ https://www.hrpub.org/journals/article_info.php?aid=8927
_version_	1710677180081504256
score	13.211869

Improved frequency table with application to environmental data

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