The Four Components of Statistics and Probability:
Gathering data, whether in or out of a classroom, occurs on a daily basis. We are always observing and processing information as we go about the routine of our day. At this level data is like a pile of clothing that has just come from a dryer. When we sort the clothing we can see some order; in the same sense we see order in data when it can be displayed.
Displaying information occurs when we wish to communicate our data or when we want to make decisions about them. These displays can take several forms such as circle graphs, line graphs, bar charts, stem and leaf charts, or box and whisker plots. Displaying data is both an art and a science. For those who wish to explore this topic further, one of the best collections of the elegance of data display can be found in Edward Tufte’s masterful work The Visual Display of Quantitative Information.
Interpreting data can begin by determining measures of central tendency, outliers, symmetry, and range of a data set. Generally we call such measures “the shape of the data”, and determining these measures gives people a good sense for the overall meaning of the data. Many times students experience the first two components in the classroom, but do not explore further. When the last two components enter the curriculum in a structured fashion, students can gain facility in higher ordered thinking skills and become skilled consumers of information. They are then active instead of passive.
Inference is the highest cognitive level of working with data, and generally occurs when we wish to use data to make decisions based on past information as well as make predictions of future trends and events. Taking random samples of an event such as rolling dice allows us to look at past events. When we ask what is likely to happen in the future, we enter the realm of inference. Much of AP Statistics at the high school level deals with inference. doing statistics and probability activities with “hands-on” experiences at the elementary levels lays the groundwork for future success in high school and college level statistics and probability courses
The four components above are from the preface to the new book my partner, Brad Fulton, and I are working on to supplement our Simply Great series. The book will feature activities based on concrete statistical experiences; students are then guided into the abstract probability of the situation.
– Mr. L