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Harmonic Average

Definition

In mathematics, the harmonic mean is one of several kinds of average, and in particular one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired.

What is 'Harmonic Average'

The mean of a set of positive variables. Calculated by dividing the number of observations by the reciprocal of each number in the series.

Also known as "harmonic mean".

Explaining 'Harmonic Average'

Alternately, the harmonic average could be thought of as the reciprocal of the arithmetic mean of inverse values.


Further Reading


Asian options on the harmonic average
www.tandfonline.com [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

Difference Between Arithmetic Average and Harmonic Average and the Discrimination of Those Related ProblemsDifference Between Arithmetic Average and Harmonic Average and the Discrimination of Those Related Problems
en.cnki.com.cn [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

Using the price-to-earnings harmonic mean to improve firm valuation estimatesUsing the price-to-earnings harmonic mean to improve firm valuation estimates
www.jstor.org [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

Stabilizing high‐order, non‐classical harmonic analysis of NDVI data for average annual models by damping model roughnessStabilizing high‐order, non‐classical harmonic analysis of NDVI data for average annual models by damping model roughness
www.tandfonline.com [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

A Hybrid Autoregressive Integrated Moving Average-phGMDH Model to Forecast Crude Oil PriceA Hybrid Autoregressive Integrated Moving Average-phGMDH Model to Forecast Crude Oil Price
search.proquest.com [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

From harmonically modulated structures to quasicrystalsFrom harmonically modulated structures to quasicrystals
www.tandfonline.com [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

Angular average of time-harmonic transport solutionsAngular average of time-harmonic transport solutions
www.tandfonline.com [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …

Forecast model for financial time series: An approach based on harmonic oscillatorsForecast model for financial time series: An approach based on harmonic oscillators
www.sciencedirect.com [PDF]
… However, we shall present a few links with the field of finance … average (see Chen and Wan [8]). Moreover, there is a link between the options on harmonic average and the … It is worth noting that there is more financial intuition related to the harmonic average rather than to the …



Q&A About Harmonic Average


Is there another way to think about this type of average?

Yes, it could be thought as reciprocal arithmetic mean inverse values.

What is the harmonic mean?

The harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means.

How do you calculate the harmonic average?

You divide the number of observations by the reciprocal each number in the series.

How can you express it as a reciprocal?

You can express it as the reciprocal of the arithmetic mean of reciprocals. As a simple example, the harmonic mean of 1, 4, and 4 is .

What does it typically refer to?

It typically refers to situations when the average of rates is desired.

What is another name for this type of average?

It could also be thought as "harmonic mean".

What is the mean of a set of positive variables?

The mean of a set of positive variables is called the harmonic average.

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