Correct Use of Four Kinds of Mean Commonly Used in Data Analysis : Arithmetic Mean, Geometric Mean, Harmonic Mean and Quadratic Mean

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  • データ分析で常用される４種類の平均の使い分け : 算術平均・幾何平均・調和平均・平方平均
  • データ ブンセキ デ ジョウヨウ サレル 4シュルイ ノ ヘイキン ノ ツカイワケ : サンジュツ ヘイキン ・ キカ ヘイキン ・ チョウワ ヘイキン ・ ヘイホウ ヘイキン

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According to the author's teaching experience in mathematics, and the results of the “Investigation into University Students' Basics of Mathematics" involving about 6,000 people in 2011, it is clear that many of the university students and graduates do not have sufficient understanding of mean. This paper discusses four kinds of mean commonly used in data analysis: the arithmetic mean, the geometric mean, the harmonic mean and the quadratic mean. The necessity of each kind and the distinctions between how to use them, followed by the calculation methods, are shown through specific examples. Via geometric interpretations of the four types of mean, the inequality relations between them are clarified.Moreover, by the general definition of mean and the expression of the generalized mean, common features of every type and unique properties of each type are made explicit. The author hopes that these means can be correctly used according to the users' purposes.

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