1.1 Introducing Statistics: What Can We Learn from Data?

Depending on how we use data, the study of statistics is divided into two main areas: descriptive and inferential. In descriptive statistics, we describe a situation by collecting, organizing, summarizing, and presenting the data. In inferential statistics, we try to make an inference from our collected data to populations by generalizing, estimating, testing, and making predictions. We will preserve the inferential statistics for the future and will focus on the descriptive branch of statistics here.

Suppose the statistics class just had a test. The teacher checked and recorded the test scores of students. The test scores represent numbers that, in statistical terms, are called data, and the whole set of numbers of the students is called a data set. But these numbers are meaningless if we don’t know what measures and who those numbers are measured on. Since we know that these are the test scores for the students enrolled in statistics class, these numbers may convey important information about class performance, test difficulty, students’ abilities, content knowledge, and even testing environment if placed in context. 

The statisticians will call the students as elements, and the score of each student as an observation. Soon These observations were part of the teacher’s assessment, and she needs to use these data to analyze the content she taught. Imagine if she had over 30 students, it would be hard for her to look at a data set. It would be much more helpful if she organized the data into tables, drawn graphs, or calculated the average. 

Large data is hard to read and to draw conclusions from it. By constructing tables, drawing graphs, or calculating summary measures such as averages, make up the descriptive portion of statistics. The next few sections will show how to construct tables, graphs, and calculate summary measures.  

The two branches of statistics are strongly connected, and the knowledge gained in the first few units is going to help you when you are introduced to many inference procedures.