• The Mathematical Education
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• v.49 no.2
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• pp.199-221
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• 2010

The purpose of the study were to investigate how secondary pre-service teachers conceptualize arithmetic mean and how their conceptualization was formed for solving the problems involving arithmetic mean. As a result, pre-service teachers' conceptualization of arithmetic mean was categorized into conceptualization by "mathematical knowledge(mathematical procedural knowledge, mathematical conceptual knowledge)", "analog knowledge(fair-share, center-of-balance)", and "statistical knowledge". Most pre-service teachers conceptualized the arithmetic mean using mathematical procedural knowledge which involves the rules, algorithm, and procedures of calculating the mean. There were a few pre-service teachers who used analog or statistical knowledge to conceptualize the arithmetic mean, respectively. Finally, we identified the relationship between problem types and conceptualization of arithmetic mean.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.285-289
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• 2000

An additional term between the arithmetic mean and the geometric mean is presented.

• The Mathematical Education
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• v.57 no.3
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• pp.311-328
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• 2018

In school mathematics, the concept of an average is not a concept that is limited to a unit of statistics. In particular, high school students will learn about arithmetic mean and geometric mean in the process of learning absolute inequality. In calculus learning, the concept of average is involved when learning the concept of average speed. The arithmetic mean is the same as the procedure used when students mean the test scores. However, the procedure for obtaining the geometric mean differs from the procedure for the arithmetic mean. In addition, if the arithmetic mean and the geometric mean are the discrete quantity, then the mean rate of change or the average speed is different in that it considers continuous quantities. The average concept that students learn in school mathematics differs in the quantitative nature of procedures and objects. Nevertheless, it is not uncommon to find out how students construct various mathematical concepts into mathematical knowledge. This study focuses on this point and conducted the interviews of the students(three) in the second grade of high school. And the expression of students in the process of average concept formation in arithmetic mean, geometric mean, average speed. This study can be meaningful because it suggests practical examples to students about the assertion that various scholars should experience various properties possessed by the average. It is also meaningful that students are able to think about how to construct the mean conceptual properties inherent in terms such as geometric mean and mean speed in arithmetic mean concept through interview data.

• Research in Mathematical Education
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• v.18 no.1
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• pp.31-40
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• 2014

Working with dynamic visual representations can help students-with-computer discover new mathematical ideas. Students translate among multiple representations as a strategy to investigate non-routine problems to explore possible solutions in mathematics classrooms. In this paper, we use the area models as new representations for our secondary students to investigate three problems related to the average speed of a particle. Students show their ideas in the process of investigating arithmetic mean, harmonic mean, and average speed through their created dynamic figures. These figures really utilize dynamic geometry software.

• Kyungpook Mathematical Journal
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• v.54 no.4
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• pp.521-529
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• 2014

In this paper we derive some optimal convex combination bounds related to arithmetic mean. We find the greatest values ${\alpha}_1$ and ${\alpha}_2$ and the least values ${\beta}_1$ and ${\beta}_2$ such that the double inequalities $${\alpha}_1T(a,b)+(1-{\alpha}_1)H(a,b)<A(a,b)<{\beta}_1T(a,b)+(1-{\beta}_1)H(a,b)$$ and $${\alpha}_2T(a,b)+(1-{\alpha}_2)G(a,b)<A(a,b)<{\beta}_2T(a,b)+(1-{\beta}_2)G(a,b)$$ holds for all a,b > 0 with $a{\neq}b$. Here T(a,b), H(a,b), A(a,b) and G(a,b) denote the second Seiffert, harmonic, arithmetic and geometric means of two positive numbers a and b, respectively.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.95-100
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• 2016

In this paper, we establish a new refinement of the arithmetic-geometric mean inequality. Applying this result in information theory, we obtain a more precise upper bound for Shannon's entropy.

• Research in Mathematical Education
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• v.12 no.1
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• pp.49-66
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• 2008

In this paper we present a cognitive developmental analysis of the arithmetic mean concept. This analysis leads us to a hierarchical classification at different levels of understanding of the responses of 227 students to a questionnaire which combines open-ended and multiple-choice questions. The SOLO theoretical framework is used for this analysis and we find five levels of students' responses. These responses confirm different types of difficulties encountered by students regarding their conceptualization of the arithmetic mean. Also we have observed that there are no significant differences between secondary school and university students' responses.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.10a
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• pp.292-299
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• 1998

The effect of characteristic of surface roughness on friction and sliding wear was studied experimentally with ball-on-disk type wear tester. The test was conducted with specimens those have varying arithmetic mean value, skewness and kurtosis under the condition of different load, sliding speed and lubricant viscosity. The surface of the lower skewness in negative value or the highel kurtosis tends to have low friction for the same arithmetic mean value. There is optimum arithmetic mean value surface roughness for operating variables have load, speed, etc.

• Journal of Korean Society for Atmospheric Environment
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• v.3 no.2
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• pp.11-17
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• 1987

Atmospheric particulate matter (A.P.M.) was collected on quartz fiber filters from March 1985 to February 1986 at Chung-Ang University according to particle size using Andersen high-volume air smapler, and benzo (a) pyrene concentration in these particulates were analyzed by high performance liquid chromatography. The annual arithmetic mean concentration of A.P.M. was 115.50$\mug/m^3$. The annual arithmetic mean concentrations of coarse particles and fine particles in A.P.M. were 52.54$\mum/m^3$ and 62.96$\mum/m^3$ respectively. THe annual arithmetic mean concentration of benzo(a)pyrene in A.P.M. was 1.44$ng/m^3$. THe annual arithmetic mean concentrations of benzo(a)pyrene in coarse particles and fine particles were 0.05 $ng/m^3$ and 1.39 $ng/m^3$ respectively. Thus, the concentration of benzo(a)pyrene showed maldistribution of 96.53% in fine particle. A.P.M. showed wide fluctuation according to the season. The concentration of A.P.M. was lowest in summer and high in spring and winter. Coarse and fine particle concentrations in A.P.M. were highest in spring and winter, respectively. The concentrations of benzo(a)pyrene was highest in winter and lowest in summer. The concentrations of benzo(a)pyrene in fine and coarse particles were highest in winter and spring, respectively.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.759-768
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• 2005

K-means clustering has been widely used in many applications, such that pattern analysis, data analysis, market research and so on. It can identify dense and sparse regions among data attributes or object attributes. But k-means algorithm requires many hours to get k clusters, because it is more primitive and explorative. In this paper we propose a new method of k-means clustering using the grid-based representative value(arithmetic and trimmed mean) for sample. It is more fast than any traditional clustering method and maintains its accuracy.