ACMS 10140 – Spring 2011 Elements of Statistics

1. ACMS 10140 – Spring 2011 Elements of Statistics With a title like that, it seems appropriate that the course should start with an explanation of what STATISTICS is. Quoting from the textbook, p. 4, we get: Statisticsis the science of data. This involves collecting, classifying, summarizing, organizing, analyzing and interpreting numerical information. All that comes to mind after that definition is a bunch of questions: • Numerical information about what? • Who does (and how) the collecting? • What do all those verbs mean? (classifying, summarizing, organizing, analyzing and interpreting) We better start at the beginning:

2. The STATISTICS game. Any situation that requires “statistics” has four main ingredients. We look at them one at a time. • The initial ingredient occurs when you want to know something about something Here we encounter a first instance when English lacks precision when communicating ideas. We have used the word “something” twice, but …. with different meanings!

3. The first “something” is what you want to know, like in “What is the class average height?”, so the first “something” is … a single datum while the second “something” is all of you ! OK, the first “something” will be named later, just remember it’s a datum, the second “something” however is easy to name, it’s the totality of things about which you want to know the first “something” . We call this the POPULATION.

4. We have already learned a new word: POPULATION You will find out that often one of the troubles with the science of Statistics is that it uses everyday words, but with a very technical meaning. It is often a cause of error not to define precisely what is the population of interest. Let’s look at the three remaining components of a statistical situation. They are best represented with the diagram shown in the next slide.

5. The 4 components