Chapter 1 – Gathering and Exploring DataDefinition: statistics is the art and science of designing studies and analyzing the data that those studies produce. It is the science of learning from data. (It’s right in the title of the book.)There are four components to statistics (the field).1. Formulate a statistical question (e.g., is X a better drug than Y, in terms of number of hospital visits?)2. Collect data3. Analyze the data4. Interpret the resultsStatistics (and scientific inquiry) are about observation (2&3) and inference (4).Definition: a population is the total set of subjects in which we are interested (coin flips, people, etc.)Definition: a sample is a subset (any subset) of the population form which we have/plan to have data.All samples are not created equal (Chapter 4).Statistics comes in two flavors:Definition: descriptive statistics summarize the collected data, usually graphs or numbers (e.g., averages, frequencies, proportions)Example: 80% of elevator “door close” buttons are never wired up upon installation. The 80% describes the state of door close buttons, it is a descriptive statistic.Definition: inferential statistics refers to making decisions or predictions about a population, based on data obtained from a sample of that populationExample: You ride 100 elevators and the door close button works in 10 of them. What can you infer about the proportion of all door close buttons that work?Example: Flip a coin 1,000 times, and you get Heads 900 times. Is this a fair coin?Definition: A sample statistic is a numerical summary (mean, proportion, etc.) of a sample taken from the populationDefinition: a population parameter is a numerical summary of the populationBecause samples change from one to the next, sample statistics vary. Variation and randomness in statistics is a good thing and an important thing. We strive for random sampling, which has good properties (Chapter