The difference between Average and Harmonic mean

When used as nouns, average means the arithmetic mean, whereas harmonic mean means a type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, h = { n \over {1 \over x_1} + {1 \over x_2} + \cdots {1 \over x_n} }.

Average is also verb with the meaning: to compute the average of, especially the arithmetic mean.

Average is also adjective with the meaning: constituting or relating to the average.

check bellow for the other definitions of Average and Harmonic mean

  1. Average as a noun (mathematics):

    The arithmetic mean.

    Examples:

    "The average of 10, 20 and 24 is (10 + 20 + 24)/3 = 18."

  2. Average as a noun (statistics):

    Any measure of central tendency, especially any mean, the median, or the mode.

  3. Average as a noun (legal, marine):

    Financial loss due to damage to transported goods; compensation for damage or loss.

  4. Average as a noun:

    Customs duty or similar charge payable on transported goods.

  5. Average as a noun:

    Proportional or equitable distribution of financial expense.

  6. Average as a noun (sports):

    An indication of a player's ability calculated from his scoring record, etc.

    Examples:

    "batting average'"

  7. Average as a noun (UK, in the plural):

    In the corn trade, the medial price of the several kinds of grain in the principal corn markets.

  1. Average as an adjective (not comparable):

    Constituting or relating to the average.

    Examples:

    "The average age of the participants was 18.5."

  2. Average as an adjective:

    Neither very good nor very bad; rated somewhere in the middle of all others in the same category.

    Examples:

    "I soon found I was only an average chess player."

  3. Average as an adjective:

    Typical.

    Examples:

    "The average family will not need the more expensive features of this product."

  4. Average as an adjective (informal):

    Not outstanding, not good, banal; bad or poor.

  1. Average as a verb (transitive):

    To compute the average of, especially the arithmetic mean.

    Examples:

    "If you average 10, 20 and 24, you get 18."

  2. Average as a verb (transitive):

    Over a period of time or across members of a population, to have or generate a mean value of.

    Examples:

    "The daily high temperature last month averaged 15°C."

    "I averaged 75% in my examinations this year."

  3. Average as a verb (transitive):

    To divide among a number, according to a given proportion.

    Examples:

    "to average a loss"

  4. Average as a verb (intransitive):

    To be, generally or on average.

  1. Average as a noun (UK, legal, obsolete):

    The service that a tenant owed his lord, to be done by the animals of the tenant, such as the transportation of wheat, turf, etc.

  1. Harmonic mean as a noun (mathematics):

    A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, H = { n \over {1 \over x_1} + {1 \over x_2} + \cdots {1 \over x_n} }

    Examples:

    "If ''a''<sub>''n''</sub> and ''b''<sub>''n''</sub> denote the perimeters of inscribed and circumscribed regular ''n''-gons, respectively, along some circle then the harmonic mean and geometric mean of those two perimeters yield the perimeters of the inscribed and circumscribed regular 2''n''-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)"

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