This paper intends to cover various types of relationships in the mathematical model and also explore the strengths and weaknesses of the same from the data of several married men and women and divorced men and women.
The relationships between systems and variables cannot be easily represented by the use of physical representation since this may be cumbersome and may lead to loss of time. Mathematics model is a type of a model that often utilizes mathematical language to describe the behavior of a given system. These models can often take many forms such as statistical models, dynamic systems, and differential equations. The models translate our beliefs of how systems functions and convert them into mathematical language. Most science analysis of operations is executed using mathematics models which in most cases if not all utilize mathematical symbols. Most of the models are general and can easily be manipulated for the various purposes of prediction and experimentation.
The math models are mainly in the form of mathematical equations or statements, and the components of a given relationship are given in terms of variables.
Strengths of the Mathematics Model
Models are straightforward to come up with given the variables to consider and with no doubt can make a complicated situation a simple one. Also, the greatly save on time since once developed, the time it takes to obtain the result or a prediction is surprisingly relatively small. Math models can also help in improving one's understanding of how individual systems in the world work since some of the variables in the model can be readily changed and the change in behavior observed. Predictions of a real-world phenomenon are also possible with the use of a model since mathematical data may be incorporated into the model to give the future values predicted
Weaknesses of the Mathematics Model
Generally, a model is a simplified form of the real situation or problem. This implies that not all aspects of the issue at hand are put into consideration. So many properties of the case are unaccounted for in the model making it relatively unreliable. The mathematics model only works under ideal conditions, and thus a lot of underlying assumptions are made. In cases where the conditions change the model may be dimmed inefficient to use. Lastly, if the person who forms the model is unaware of what they are trying to accomplish, the output that results from the model may be incorrect.
In this paper, we also check and analyze the relationship between divorced and married men and women in the United States. A mathematical model aimed at observing the relationship between the married men and women for two different years is built with the assumption that the marriages, in this case, involve only a woman and a man. The following results are obtained from the data by the use of a correlation coefficient statistic that shows the relationships. The correlation between the divorced women and divorced men in 2008 is 0.233 which is a value greater than one indicates a positive but weak linear relationship between divorced women and men in 2008 as seen in the graph.
Figure SEQ Figure_ \* ARABIC 1 graph of divorced men and women in 2008 in the US (Cohen 620)
In 2014, the value hikes to 0.5729 which implies that there is now a robust positive relationship between the divorced women and men compared to 2008. This shows that the number of women in 2008 who were involved in a divorce was more than men, but after the six years, the value of men in divorces has increased.
In the marriage numbers, the correlation coefficient for the year 2008 from the data is 0.9603 which indicates a stable almost perfect positive linear relationship between the women in marriage and men in marriage. This value is a sign that for every woman at a wedding in 2008, there was a man in marriage as can be seen in the graph
Figure SEQ Figure_ \* ARABIC 2 Graph of women and men in marriage in 2008 (Cohen 626)
The curve belonging to women is almost exact to that of men in marriage.
In 2014, the value changes to 0.9167 implying that the relationship weakens at a slow rate, and hence we conclude a decrease in the number of men in marriages in 2014 compared to the year 2008.
From the data, in the comparison between both the married men and the married women, we observe the presence of a positive linear relationship between the two sets of data provided. A linear relationship can also be termed as a relationship of direct proportionality, i.e. a percentage increase or decrease in one variable results in the same percentage increase or decrease in the other variable.
The relationship exhibited can also be referred to as a positive relationship. A positive linear relationship is one in which if one variable increase; then it leads to a rise in the other variable, not a decrease. In the data, an increase in divorced women is observed to increase the number of divorced men though not exactly (weak linear relationship). A similar situation of a direct relationship has been found in the cases of the married men versus married women
The linear relationship between the data sets is an appealing and straightforward method to use. It is straightforward to use and understand how it works even when dealing with massive data. An individual with little mathematical knowledge can comprehend the concept and use the relationship to analyze the data given. The linear relationship works well even in cases where the data doesn't follow an exact line.
The above linear relationship from the data may be appealing but still has some inconsistencies. First, over the years there has been an increase in the population in the United States. This would make it hard to know the proportional change since an increase in for instance the divorced men would have resulted from population increase but not an equivalent increase in the number of divorces happening.
From the data, we can also conclude that the relationship only models the two variables, e.g. divorced men against divorced women. This implies that it assumes the other factors that may be considered in shaping the data at our hands. It also understands all other external factors that may affect the number of marriages and divorces in the country. These may include the poverty level, education (some learned individuals would most likely prefer freedom and independence to pursue their ambitions uninterrupted), the invention of artificial birth methods which would positively prompt divorces, government-related factors.
The mathematical model also assumes that the relationship is linear which may also be incorrect since the divorce rates and marriages are different at different ages. Usually, the divorce rate is high during the youth and the early adulthood periods and then sharply reduces during the late years. This means that the mathematical model does not give enough information on these variations and changes. In our case our linear relationship only a result of modeling the numbers only without considering the other factors.
Mathematical modeling plays a crucial part in the interpretation of the real world situations and this case the divorce and marriage numbers. The linear relationship obtained is seen to be present between the data sets such that an increase in one variable leads to a rise in the other. It is concluded that it is dull but prone to many weaknesses and loopholes since it ignores so.
Cohen, Philip N. "Recession and divorce in the United States, 2008-2011." Population research and policy review 33.5 (2014): 615-628.
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