Journal article Open Access

Central Limit Theorem and Its Applications

Sutanapong. Chanoknath; Louangrath, P.


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  <identifier identifierType="DOI">10.5281/zenodo.1321357</identifier>
  <creators>
    <creator>
      <creatorName>Sutanapong. Chanoknath</creatorName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0001-8064-0152</nameIdentifier>
      <affiliation>International Journal of Research and Methodology in Social Science</affiliation>
    </creator>
    <creator>
      <creatorName>Louangrath, P.</creatorName>
      <givenName>P.</givenName>
      <familyName>Louangrath</familyName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0001-5272-5159</nameIdentifier>
      <affiliation>Bangkok University - International College</affiliation>
    </creator>
  </creators>
  <titles>
    <title>Central Limit Theorem and Its Applications</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2018</publicationYear>
  <subjects>
    <subject>central limit theorem, distribution</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2018-09-30</date>
  </dates>
  <language>en</language>
  <resourceType resourceTypeGeneral="Text">Journal article</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/1321357</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.1321356</relatedIdentifier>
  </relatedIdentifiers>
  <version>1</version>
  <rightsList>
    <rights rightsURI="http://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;The purpose of this paper is to explain the central limit theorem and its application in research. Two concepts are constant companions in statistics: Central Limit theorem and distribution. The central limit theorem states that the arithmetic mean of sufficiently large number of iterations of independently random variable is the expected value of the iterations, and it is normally distributed with the mean equal to the expected value. Distribution is the probability of occurrence of a certain value within a defined range of values. The distribution type that describes the central limit theorem is the normal distribution curve. A normal distribution curve describes the probability distribution of continuous data. A normal distribution curve has the following properties: (i) it is symmetric around the point where &lt;em&gt;x = mu&lt;/em&gt;; (ii) unimodal; (iii) it has two inflection points at &lt;em&gt;x = mu - s&lt;/em&gt; and&lt;em&gt; x = mu + s&lt;/em&gt;; (iv) it is log-concave in shape; and (v) it is infinitely differentiable.&lt;/p&gt;</description>
  </descriptions>
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