Discussion on Meaning and Calculation Method of the Mean Through the Illustration of the Harmonic Mean

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  • 平均の意味と正確な計算方法に関する浅見 : 調和平均の例解を中心に
  • ヘイキン ノ イミ ト セイカク ナ ケイサン ホウホウ ニ カンスル センケン : チョウワ ヘイキン ノ レイカイ オ チュウシン ニ

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In this paper, meaning and calculation method of the mean were discussed through harmonic mean, because there were many freshmen who could not completely understand the concept of mean. Harmonic mean and weighted harmonic mean were derived, and it was confirmed that harmonic mean is equal to weighted arithmetic mean, by using the most familiar example of mean speed of a round trip. Harmonic mean of given numbers is equal to arithmetic mean of the reciprocal of the given numbers, the example is that the harmonic mean of “the population density” is equal to the arithmetic mean of “the acreage per person” which is the reciprocal number of the population density. Two kinds of analyses often used harmonic mean, one is that the analyses target must take the harmonic mean theoretically, such as the mean mileage of the cars. The other one is that the analyses emphasized the balance between the elements, such as the general evaluation of the contest or performance.

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