This is the fourth in a series of statistical articles for mathematics teachers. In this article, the authors discuss topics in General Mathematics in Unit 2 Topic 1 (Univariate data analysis and the statistical investigation process) and topics in Essential Mathematics, Unit 2 Topic 1 (Representing and comparing data).

The negative hypergeometric distribution is often not formally studied in secondary or collegiate statistics in contexts other than drawing cards without replacement. We present a different context with the potential of engaging students in simulating and exploring data.

This article describes four semesters of introductory statistics courses that incorporate service learning and gardening into the curriculum with applications of the binomial distribution, least squares regression and hypothesis testing. The activities span multiple semesters and are iterative in nature.

The sample mean is sometimes depicted as a fulcrum placed under the Dot plot. We provide an alternative geometric visualization of the sample mean using the empirical cumulative distribution function or the cumulative histogram data.

Students often are confused about the differences between bar graphs and histograms. The authors discuss some reasons behind this confusion and offer suggestions that help clarify thinking.

While looking for an inexpensive technology package to help students in statistics classes, the author found StatKey, a free Web-based app. Not only is StatKey useful for students' year-end projects, but it is also valuable for helping students learn fundamental content such as the central limit theorem. Using StatKey, students can engage in…

This article explores an example in finances in order to motivate the random variable learning to the very beginners in statistics. In addition, it offers a relationship between standard deviation and range in a very specific situation.

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…

This article proposes the use of the coefficient of determination as a statistic for hypothesis testing in multiple linear regression based on distributions acquired by beta sampling. (Contains 3 figures.)

The statistical output of interest to most elementary statistics students is the p-value, outputted in computer programs like SPSS, Minitab and SAS. Statistical decisions are sometimes made using these values without understanding the meaning or how these values are calculated. Most elementary statistics textbooks calculates p-values for z-tests…

In this article, I introduce a novel applet ("module") for exploring probability distributions, their samples, and various related statistical concepts. The module is primarily designed to be used by the instructor in the introductory course, but it can be used far beyond it as well. It is a free, cross-platform, stand-alone interactive…

Although many parametric statistical tests are considered to be robust, as recently shown in Methodologist's Corner, it still pays to be circumspect about the assumptions underlying statistical tests. In this paper I show that robustness mainly refers to "[alpha]", the type-I error. If the underlying distribution of data is ignored there…

There is considerable research on the difficulties students have in conceptualising individual concepts of probability and statistics (see for example, Bryant & Nunes, 2012; Jones, 2005). The unit of work developed for the action research project described in this article is specifically designed to address some of these in order to help…

The need to encourage "what if" questions for statistical thinking in a classroom environment is stressed in this article. (Contains 1 figure and 3 tables.)

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This seventh installment of "Explorations in Statistics" explores regression, a technique that estimates the nature of the relationship between two things for which we may only surmise a mechanistic or predictive…