Harmonic mean problems and solutions pdf
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The harmonic mean of n observations, none of which is zero, is defined as the reciprocal of the arithmetic mean of their reciprocals.
Scientific Research An Academic Publisher. In this paper, we have suggested a new technique to transform multi-objective linear programming problem MOLPP to the single objective linear programming problem by using Harmonic mean for values of function and an algorithm is suggested for its solution, the computer application of algorithm has been demonstrated by solving some numerical examples. We have used some other techniques, such as sen, arithmetic mean, median to solve the same problems, the results in Table 3 indicate that the new technique in general is promising. Linear programming is a relatively new mathematical discipline, dating from the invention of the simplex method by G.
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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. In other words, for resistors in parallel, the harmonic mean resistance is the mean value of each individual resistance.
For the case when the mean value of a Pareto distribution is undefined, three other statistical measures are defined; median, geometric mean, and the harmonic mean, all three of which are also defined when the first moment is also defined.
That is another point in favor of using the harmonic mean instead of one of the other statistics. Sign up to join this community.
The best answers are voted up and rise to the top. Harmonic mean of random variables Ask Question. Asked 3 years, 11 months ago. Active 3 years, 11 months ago. Viewed 2k times. Improve this question. Diogo Santos Diogo Santos 7 7 silver badges 19 19 bronze badges. I just took it to ask about what the continuous variable harmonic mean is for those distributions.
The question is too general to be answered. Add a comment. Active Oldest Votes. Improve this answer. Carl Carl If anything, they add as the reciprocal of the sum of reciprocals. I think the important point is that when the measurement system is reciprocal one has to use reciprocation. For example, the total electrical conductance in siemens or mhos of parallel resistors is the sum of the conductances of each resistor. But the total resistance of series resistors is the sum of the resistances in ohms.
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. In other words, for resistors in parallel, the harmonic mean resistance is the mean value of each individual resistance. For the case when the mean value of a Pareto distribution is undefined, three other statistical measures are defined; median, geometric mean, and the harmonic mean, all three of which are also defined when the first moment is also defined.
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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. Finally, we present the mixed arithmetic-geometric and geometric- harmonic means inequalities for two positive operators.
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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. Application of harmonic speed is in most cases in the problems of average speed. Intuitively, looking at the picture above, we can anticipate that the arithmetic mean is greater than or equal to geometric mean, which is greater than or equal to 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. It is the reciprocal dual of the arithmetic mean for positive inputs:. Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones while having at least one value unchanged.
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