Quantitative Data Activity

Abstract:: The activity involves a set of data dealing with the percentage difference between measure calories and labeled calories of particular items, in two categories, per item and per gram. Students are asked to make stem-and-leaf plots, dotplots, and histograms of the two variables. The students are then asked to describe the distributions of the two variables: “per gram” and “per item” and compare the resulting distributions. The students are asked to use the appropriate descriptive statistics to describe the respective distributions.

Star Library: Histogram Sorting

Abstract:: This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.).

Abstract:: The activity is designed to help students develop a better intuitive understanding of what is meant by variability in statistics. Emphasis is placed on the standard deviation as a measure of variability. As they learn about the standard deviation, many students focus on the variability of bar heights in a histogram when asked to compare the variability of two distributions. For these students, variability refers to the “variation” in bar heights. Other students may focus only on the range of values, or the number of bars in a histogram, and conclude that two distributions are identical in variability even when it is clearly not the case. This activity can help students discover that the standard deviation is a measure of the density of values about the mean of a distribution and to become more aware of how clusters, gaps, and extreme values affect the standard deviation.