### An Example of Statistical Modeling for Count Data Analysis in Secondary Education

Yoshinari Inaba

#### Abstract

In this paper we report on introductory lessons to the Poisson distribution and on statistical modeling in regards to probability distributions in secondary school in Japan. “Statistical modeling” is the use of data analysis and modeled data to describe, explain and predict real-world phenomena. In statistical modeling, we often see some examples which treat probability distributions as a separate data model. When students analyze some given data, we think that it is important they understand the statistics models to be used more deeply. We also think that the ability to determine “what kind of model applies to what kind of data” is also important from a viewpoint of “statistical literacy.” We therefore prepared some lessons about the Poisson distribution for high school students with modeling in mind. After that we instructed some task-based lessons as an example of count data analysis. In statistical analysis of count data, there are various cases. Some will fit the normal distribution, and some will fit the binomial distribution. However it is well known that the case with small integral-value observed data tend to fit the Poisson distribution. By the way, we cannot usually find the Poisson distribution in mathematics textbooks in secondary schools in Japan, but we can find it in many overseas textbooks. By knowing some properties of the Poisson distribution, students can get a typical model in the analysis of various observational data, especially count data. As a result, students were actually verifying the example with which the observed data fit the Poisson distribution. In the viewpoint of statistical modeling, we think that students get the technique of analyzing an actual phenomenon through a model by recognizing some typical statistics models.

#### Keywords

statistic education; mathematical modeling; Poisson distribution

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