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 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.

The ability to interpret graphs is highly important in modern society, but has proven to be a challenge for many people. In this paper, two teaching methods were used to remediate one specific misinterpretation: the area misinterpretation of box plots. First, we used refutational text to explicitly state and invalidate the area misinterpretation…

This thesis examined middle school students' current understanding of variability using a constructed response item assessment question. Variability is an essential concept in the teaching and learning of statistics. However, many students have difficulty with the concept of variability especially when constructing boxplots. Using a framework…

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…

This study examined a random stratified sample (n = 62) of teachers' work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological statistical knowledge when investigating a statistical task. We examined how teachers engaged…

In most school achievement research, the relationships between achievement and explanatory variables follow the Newton and Einstein concept/principle and the viewpoint of the macro-observer: Deterministic measures based on the mean value of a sufficiently large number of schools. What if the relationships between achievement and explanatory…

Statistical graphs are commonly used in scientific publications. Unfortunately, graphs in psychology journals rarely portray distributional information beyond central tendency, and few graphs portray inferential statistics. Moreover, those that do portray inferential information generally do not portray it in a way that is useful for interpreting…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The materials are centered on the fictional town of Happy Shores, a coastal community which is at risk for hurricanes. Actuaries at an insurance company figure out the risks and…

Provides an algorithm for determining the median and quartiles of discrete data sets. Describes the graphical equivalent of the numerical method. (JM)

Sophisticated simulations using computer graphics can lead to students deducing virtually all conditions of the Central Limit Theorem. Eight graphs illustrate the discussion. (MNS)

Describes a five-number summary which is a display of the minimum value, lower quartile, median, upper quartile, and maximum value. Indicates how to draw box plots as graphical representations of a five-number summary. (YP)

Presents an activity considering whether a difference exists in the age of Oscar winners. Describes how to draw a stem plot and a box plot as an example of implementing the recommendations of the NCTM Standards. Provides tables showing the name, movie titles, and ages of the Oscar winners since 1928. (YP)

Considers definitions of quantiles. Describes median and quartiles. Compares the usefulness of 3 different definitions of quartile using a computer program to simulate 500 quantiles on a sample of a fixed size. Five references are listed. (YP)