Information is all around us. It affects every aspect of our lives. To gather and work with numerical information using statistical concepts is the overall purpose of this unit. I am planning to use “An Introduction to Statistical Thinking” in technical math classes grades 9-12. The content is basic enough to be used with data from different disciplines. The structure is flexible and may be used as a whole or in part. There are three sections.
Section I: Data provides for the experience of gathering, organizing and analyzing classroom data attendance, grades and temperature. The primary objective of this section is to take a set of data and be able to see both how the values are centering by determining the mean, median and mode averages and how they are varying by determining the range and making a Box plot diagram.
In the first section we work with only the full set of values being considered. The full set of values is called the population. Since it is not always possible or practical to study an entire population, we must use samples. Samples are subsets of the population. Selecting samples is one of the most important tasks of statistics because from the samples chosen inferences are made about the entire population. The reliability of the inferences depends in large part on the reliability of the sample.
Not all samples are useful. If we want reliable information about a population, the sample we choose must be representative of the entire population. The sample we want is called a random sample which means that every member of the population has an equal chance at being picked. The primary objective of Section II: Random Sample is to introduce the idea of randomness and to solve random sample problems.
Section III: Probability has as its objective to use the traditional definition of probability in finding probabilities and comparing experimental and theoretical probabilities. No matter how much information we acquire, we almost never know everything there is to know about any given situation. However, since decisions must be made, we guess-sometimes using only intuition and sometimes partial information. The more information, the more reliable the guess. Probability helps us put a numerical measure on the uncertainty of an event, on the risk we’re taking.
I consider Section I to be the most important part because it allows students to not only begin at the beginning of statistical work by gathering data, but it allows them also to be the generators of it. I am looking forward to the discussions in class as we evaluate the four week records.