There are a number of different quantitative strategies that give individuals the ability to break down criminal justice trends in order to understand what is happening in the world today. Many focus on cumulative distribution figures, and these provide the theoretical basis for empirical distribution figures. When one considers the cumulative distribution function, one is looking at the probability that a random variable will be less than a given value, depending upon the details of the problem that one is trying to detail.

With this in mind, there are critical differences between just a cumulative distribution function and an empirical distribution function. As one might suspect, the empirical distribution function deals with actual swaths of data rather than simply dealing with a theoretical function. That is an important distinction that takes empirical distribution figures out of the realm of the theoretical into the realm of the actual. This is critical for analysis of criminal justice figures because, in the effort to understand the numbers, one is not simply trying to solve contrived problems, but rather, is looking to solve actual problems that involve real data and real consequences, too.

When statisticians talk about the term “sampling distribution,” they are discussing the probability distribution of any statistic in relation to a random sampling of data that one might be analyzing. There are many different factors that can influence the sampling distribution. For instance, the size of the sample, the underlying character of the population that is being assessed, and the way in which the sample was derived. Statisticians recognize that coming up with the sampling distribution is important because it allows for inferences to be made from the data. This is critical, especially when one I talking about the use of data for actual sociological purposes.

Because of the large number of assumptions that must be made when looking at the data, this tool becomes useful for providing context so that the data can be better understood. One of the most critical things to understand about the use of sampling distribution is that it allows for statisticians to pull various samples out of an overall population. There are a number of different samples of the size n that can be pulled from an overall population. The sampling distribution provides the capacity to understand the differences in a given statistic pulled from these samples. That might mean using sampling distribution to understand the differences in the mean of these samples. It might also mean using this distribution to understand the differences in median. Depending upon the goals and aims of the person using the statistic, this is a tool that can either be instructive or just helpful for contextual purposes.

There are many examples of the ways that these tools are used in reality for people who are breaking down statistics in the field of criminal justice. If one were conducting a study on the variability of victimization of crime, then one might use empirical distribution to come up with an understanding of how widespread distribution is in the area of inequality. One can gain a bigger picture of who is victimized and how wide-ranging victimization actually is. Criminal justice researchers will use the sampling distribution to be able to draw bigger trends to an entire population from a small sample of people who commit crimes. For instance, one might be able to extrapolate trends to an entire population of people from just looking at a smaller sample of individuals. One could conduct a study on victimization and contextualize the findings in such a way that is useful for the overall population at large.