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Relative frequency in the study of statistics

Getting familiar with the relative frequency

In terms of statistics, when talking of the relative frequency one should mean a certain number of times that an occurrence happened within an experiment, research, some kind of study, etc. As a rule, the relative frequency is presented in the graphical manner, often in the form of a histogram. A histogram serves to represent different data that deals with numbers. It is the most comfortable way to represent the results of a statistical research, like relative frequency because it gives an opportunity to show numerical data in such a way that it can be further analyzed, compared and better understood. The term relative frequency, which is sometimes also called as empirical probability (or an experimental probability, since it often has to do with scientific experiments) is meant to describe the number of different outcomes, where that or another event appears to the overall number of certain trials within a real experiment. In other words, the relative frequency serves to estimate actual possibilities from a particular experience and scientific observation.

As it was already said the term relative frequency describes the specific number of outcomes where that or another occurrence appears to the overall amount of trials. It is important to remember that the relative frequency is not really meant to be used within a theoretical sample space. Quite the opposite, the relative frequency has to be used within practice, like real and actually done experiment. If to speak in more general terms, the relative frequency helps deal with estimating of the probabilities within certain observation or scientific experiment.

The study of statistics says that the relative frequency is a kind of an estimate, which is applied to the probability. It is sometimes also called an estimator. When talking of an estimator, one should mean a particular rule that is used in order to estimate certain quantity that is grounded on the basis of data, which is being observed at the moment. When dealing with elementary cases, where the number of outcomes represents result demonstrating whether that or another event appeared or not, it is completely appropriate to model the statistical situation by means of using the binomial distribution. The term binomial distribution is usually used in the area of statistics (and sometimes in the theory of probability) and demonstrates the discrete probability distribution of the overall amount of successful trials in particular sequence of scientific experiments, where the researchers deal exceptionally with successes and failures of the experiment.

Advantages and disadvantages of using the relative frequency

Even though dealing with a great number of statistical problems and experiments requires using the methodology of the relative frequency, it is still not perfect and has its advantages and disadvantages. As for the advantages of using of the relative frequency, they are quite beneficial to the researcher who deals with experiments, where the usage of assumptions is not appropriate. For example, you can do an experiment about the male population, where you want to estimate certain probability, considering that all the men satisfy a couple of certain conditions. These conditions may be the following: they are all more that thirty years old and they prefer playing football rather than basketball. Eventually, in order to figure out what the direct estimate in this case is, you will have to calculate the overall number of men who satisfy all the conditions that you have provided. Thus, you will be able to find the empirical probability of the mixed condition, which includes all the provided conditions. At the same time, you can figure out the alternative estimate. In this case, you will have to multiply the proportion of men who are more than thirty years old with the proportion of the men who prefer playing football rather than basketball. However, in this case, you will have to deal with the assumption. This assumption can be that all the provided conditions are independent one fro another statistically.

As for the disadvantages of the usage of the relative frequency, they appear in most of cases when you deal with estimating probabilities, which demonstrate numerical data that is very close to zero (it can also be very close to the one). Here, you will have to use very big sample sizes, as long as the estimating the probabilities like these require those in order to get an appropriate standard of accuracy in terms of the relative frequency. A good way to deal with such kinds of statistical problems would be to use statistical models, which would, of course, depend on the given background. Statistical models can be helpful in providing better accuracy, in comparison to the relative frequency. Generally speaking, a statistical model represents a set of various assumptions in regard to the development of the data that is being observed. It provides a representation of the generating process of the numerical data, sometimes in quite an idealized form. Usually such models can be specified by means of mathematical equations, and in this case a statistical model can serve as a formal demonstration of a theory.

For example, take into consideration estimating of the probability providing data that the highest of the daily-minimum temperatures in March in any year that you choose is more than one degree Celsius. In order to deal with this statistical problem, you can turn to the data characterizing the highest daily-minimums of March temperatures within the several past years. Here, an alternative grounded on a statistical model will be to choose a family of distributions of probability and apply it to the set of the data that contains the values of the several past years. This kind of probability distribution will give you an appropriate alternative estimate of the needed probability. The usage of the statistical method can be helpful when dealing with an estimate of the probability in such cases, when the recorder values are higher than one degree Celsius.

What you should know about the study of statistics

Taking into consideration that you probably have to deal with the relative frequency within the study of statistics, it would be quite useful to get familiar with some basic information about this kind of study. Thus, you will understand the relative frequency better and also, it will be easier to realize why, where and how to use the relative frequency.

Therefore, first of all you need to understand the definition of the term. Statistics is used to describe the study of the organizing, interpretation, analyzing, collecting, presenting data, which is often numerical. The study of statistics can be applied to a wide range of problems, including but not limited to the problems of societal, industrial, scientific and other character. When applying the study of statistics to the problems of such character, we should also keep in mind the process of a statistical model, as well as the statistical population. As for the population, there is a wide range of topics that can be covered in this area, beginning with the number of all people living in that or another country and finishing with the number of components making up a chemical compound. Statistics is a unique study that has to do with all possible aspects of different data. It can help with the collection of the data, including planning this data in the light of various scientific experiments and design of surveys.

As a rule, statisticians deal with standard statistical procedures, which serves to provide the relationship and dependence between two particular sets of statistical data, which can be either numerical data or synthetic data. As a result of a statistical experiment, there has to be a hypothesis, which describes that or another relationship between the two sets of data that were used within the statistical experiment. This hypothesis should be presented as an alternative to another hypothesis, which is considered to be the idealized one and is called as the null hypothesis. The null hypothesis, in its term, has to be disproved or rejected within the statistical experiment. As a matter of fact, the purpose of a statistical experiment has to be to disprove or reject the idealized hypothesis and suggest your own vision in the form of a new hypothesis.

The areas of using the study of statistics

Apart from the fact, that statistics is used with the purpose of collecting, analyzing, interpreting, explaining and presenting various data, it is also considered to be a branch of mathematics. As a matter of fact, there are statisticians who argue that the statistics is even more like an independent mathematical science, rather than a branch of mathematics. In any case, below are listed areas where the usage of statistics is the most actual and helpful:

  • Mathematical statistics. This is the method of applying the study of mathematics to the study of statistics. As a rule, it is used when dealing with data that refers to the indicators describing situation in a country in that or another field (for example, the economy, the population, the military area and so on).
  • Descriptive statistics is commonly used specifically to deal with the data concerning the population. In this case, population can cover a wide range of topics, which are not limited by the populations of different countries. This can be also the topic covering components of a chemical compound or all the people living on a continent.
  • Inferential statistics is usually used, when it comes to dealing with researches concerning the entire population. In this case, the statistics may be used in the form of providing answers in regard to that or another data (which is also called as hypothesis testing), providing an estimate of numerical data and its characteristics (in other words, the estimation), providing the description of the data associations (also known as the correlation) and finally, researching the relationships in the data by means of using different kinds of analysis.
  • Data collection. One of the main purposes that statistics is used for is data collecting. By means of it, statisticians can predict or forecast the implementing of that or another data within statistical models. In this case, the statisticians tend to use survey samples that serve as guides to the overall population.
  • Experimental and observational studies. Apart from the data collecting, statistics is also used with the purpose of investigating the causality, specifically to make up a conclusion concerning the influence of the changes in the values. There are two main kinds of statistical studies, such as the studies of observation and the studies of experiments. Both kinds deal with the observation, although their methods of observation are different.

Even though statistics (particularly dealing with the relative frequency ) is one of the most difficult disciplines that students deal with, it plays a significant role in a number of other studies. In addition, the relative frequency helps understand the relationships between different data in global context, as well as in small issues.

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