The Root Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality

1989 ◽  
Vol 20 (3) ◽  
pp. 231
Author(s):  
Roger B. Nelsen
Keyword(s):  
Root Mean Square ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Mean Square

scholarly journals Impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method

2020 ◽  
Vol 6 (4) ◽  
pp. 124 ◽  
Author(s):  
Oluyori P. Dare ◽  
Eteje S. Okiemute
Keyword(s):  
Root Mean Square ◽  
Arithmetic Mean ◽  
Orthometric Height ◽  
Harmonic Mean ◽  
Geometric Method ◽  
Mean Square ◽  
Geoid Model ◽  
Microsoft Excel ◽  
Orthometric Heights ◽  
The Impact

<p class="abstract"><strong>Background:</strong> Orthometric height, as well as geoid modelling using the geometric method, requires centroid computation. And this can be obtained using various models, as well as methods. These methods of centroid mean computation have impacts on the accuracy of the geoid model since the basis of the development of the theory of each centroid mean type is different. This paper presents the impact of different centroid means on the accuracy of orthometric height modelling by geometric geoid method.</p><p class="abstract"><strong>Methods:</strong> DGPS observation was carried out to obtain the coordinates and ellipsoidal heights of selected points. The centroid means were computed with the coordinates using three different centroid means models (arithmetic mean, root mean square and harmonic mean). The computed centroid means were entered accordingly into a Microsoft Excel program developed using the Multiquadratic surface to obtain the model orthometric heights at various centroid means. The root means square error (RMSE) index was applied to obtain the accuracy of the model using the known and the model orthometric heights obtained at various centroid means.  </p><p class="abstract"><strong>Results:</strong> The computed accuracy shows that the arithmetic mean method is the best among the three centroid means types.</p><p class="abstract"><strong>Conclusions:</strong> It is concluded that the arithmetic mean method should be adopted for centroid computation, as well as orthometric height modelling using the geometric method.</p>

Empirical Investigation of Alternative Measures of Central Tendency

2020 ◽  
Author(s):  
William H Black ◽  
Lari B Masten
Keyword(s):  
Geometric Mean ◽  
Predictive Performance ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Central Tendency ◽  
Business Valuation ◽  
Alternative Measures ◽  
Data Points ◽  
Using Data ◽  
Performance Results

There is ongoing controversy in the business valuation literature regarding the preferability of the arithmetic mean or the harmonic mean when estimating ratios for use in business valuation. This research conducts a simulation using data reported from actual market transactions. Successive random samples were taken from data on valuation multiples and alternative measures of central tendency were calculated, accumulating more than 3.7 million data points. The measures (arithmetic mean, median, harmonic mean, geometric mean) were compared using hold-out sampling to identify which measure provided the closest approximation to actual results, evaluated in terms of least squares differences. Results indicated the harmonic mean delivered superior predictions to the other measures of central tendency, with less overstatement. Further, differences in sample size from 5 to 50 observations were evaluated to assess their impact on predictive performance. Results showed substantial improvements up to sample sizes of 20 or 25, with diminished improvements thereafter.

scholarly journals Unification Theories: Means and Generalized Euler Formulas

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 144
Author(s):  
Radu Iordanescu ◽  
Florin Felix Nichita ◽  
Ovidiu Pasarescu
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Current Paper ◽  
Baxter Equation ◽  
Quadratic Mean ◽  
Euler’S Formula ◽  
Associative Structures ◽  
Generalized Mean

The main concepts in this paper are the means and Euler type formulas; the generalized mean which incorporates the harmonic mean, the geometric mean, the arithmetic mean, and the quadratic mean can be further generalized. Results on the Euler’s formula, the (modified) Yang–Baxter equation, coalgebra structures, and non-associative structures are also included in the current paper.

scholarly journals Comparison of different ways of computing grades in continuous assessment into the final grade

2017 ◽  
Vol 8 ◽  
pp. 1
Author(s):  
Juan A. Marin-Garcia ◽  
Julien Maheut ◽  
Julio J. Garcia Sabater
Keyword(s):  
Learning Outcomes ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Harmonic Mean ◽  
Alternative Methods ◽  
Continuous Assessment ◽  
Final Grade ◽  
Weighted Arithmetic ◽  
Student’S Performance ◽  
The Subject

<p>We present the results of comparing various ways of calculating students' final grades from continuous assessment grades. Traditionally the weighted arithmetic mean has been used and we compare this method with other alternatives: arithmetic mean, geometric mean, harmonic mean and multiplication of the percentage of overcoming of each activi-ty. Our objective is to verify, if any of the alternative methods, agree with the student’s performance proposed by the teacher of the subject, further discriminating the grade be-tween high and low learning outcomes and reducing the number of approved opportunists.</p><p> </p><p>[Comparación del efecto de diferentes modos de agregar las califica-ciones de evaluación continua en la nota final]</p>

scholarly journals Determination of the distance between dots at band scheme of sowing onion seeds

2021 ◽  
pp. 53-56
Author(s):  
Vusala Sabir gyzy Alekberova
Keyword(s):  
Root Mean Square ◽  
Coefficient Of Variation ◽  
Field Tests ◽  
Arithmetic Mean ◽  
Mathematical Statistics ◽  
Technological Scheme ◽  
Mean Square

The article presents the results of field tests of an experimental seeder when sowing seeds of onion varieties “Bereketli” with a ribbon-dotted pattern. At the same time, the developed technological scheme and the principle of operation of the experimental machine are presented. The experimental machine is based on the SZS-2,1 seeder with a reel-to-reel sowing device. The experimental seeder is additionally equipped with Romanian-made "HRC" seed drills.Processing the results of experiments of mathematical statistics show that with an increase in the speed of the tractor movement, the coefficient of variation, the arithmetic mean and root-mean-square value increases.

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