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Harmonic Mean Problems And Solutions Pdf

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Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. A harmonic mean is the reciprocal of the mean reciprocal of data, and is used to average rates.

HARMONIC MEAN - Quantitative Techniques for management

NEIL O. This paper investigates the properties of the harmonic mean method for the analysis of variance with unequal sample sizes for one- and two-way classifications. The test statistic is shown to be distributed as a ratio of linear combinations of chi-squared random variables. Under the null hypothesis, this distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the discrepancies in the sample size.

Simulation methods are used to show that the approximation is accurate over a range of conditions and that the test based on least squares is not uniformly more powerful than the test based on the harmonic mean procedure. Most users should sign in with their email address. If you originally registered with a username please use that to sign in. Oxford University Press is a department of the University of Oxford.

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Google Scholar. Select Format Select format. Permissions Icon Permissions. Abstract This paper investigates the properties of the harmonic mean method for the analysis of variance with unequal sample sizes for one- and two-way classifications.

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NEIL O. This paper investigates the properties of the harmonic mean method for the analysis of variance with unequal sample sizes for one- and two-way classifications. The test statistic is shown to be distributed as a ratio of linear combinations of chi-squared random variables. Under the null hypothesis, this distribution may be approximated by a central F distribution with the degrees of freedom of the numerator adjusted in accordance with the discrepancies in the sample size. Simulation methods are used to show that the approximation is accurate over a range of conditions and that the test based on least squares is not uniformly more powerful than the test based on the harmonic mean procedure.

Harmonic Mean

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. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals.

Show all documents Reverse arithmetic harmonic mean and mixed mean operator inequalities This note aims to present some scalar inequalities and operator inequalities on a Hilbert space. Firstly, the direct reverse weighted arithmetic- harmonic mean inequalities for scalars are obtained. Secondly, based on these scalar inequalities, the corresponding operator inequalities are established.

It is a type of average which is calculated by dividing the number of values by the sum of reciprocals of each value. Therefore, the harmonic mean is calculated by dividing the number of observations by the sum of reciprocals of each given number. Furthermore, we can notice that the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. The harmonic mean is often used in calculating the average of the ratios.

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