Why gemoateric mean arithmeticmean harmonic mean are used?
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The geometric mean applies only to positive numbers. It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.
In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
The geometric mean applies only to positive numbers. It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.
In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
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Use the geometric mean when your sample contains fractions. Use the harmonic mean when your sample contains fractions and/or extreme values (either too big or too small). It is more stable regarding outliers. For example: the arithmetic mean of (1,2,3,4,5,100) is 19.2 whereas the harmonic one is 2.58.
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