Average and Harmonic mean

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Difference between Average and Harmonic mean

Average vs. Harmonic mean

In colloquial language, an average is a middle or typical number of a list of numbers. In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

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Average

In colloquial language, an average is a middle or typical number of a list of numbers.

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Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Generalized mean

In mathematics, generalized means are a family of functions for aggregating sets of numbers, that include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means).

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Geometric mean

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

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Inequality of arithmetic and geometric means

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

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Log-normal distribution

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Weighted arithmetic mean

The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others.

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