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Statistical Tools for Environmental Quality Measurement - Chapter 2

Công cụ cơ bản và mô tả khái niệm dữ liệu Mục tiêu của thống kê là để đạt được thông tin từ dữ liệu. Bước đầu tiên là để hiển thị các dữ liệu trong một đồ thị để đôi mắt của chúng tôi có thể có trong các mô hình tổng thể và phát hiện những quan sát bất thường. Tiếp theo, chúng ta thường tóm tắt các khía cạnh cụ thể của dữ liệu, chẳng hạn như mức trung bình của một giá trị, bằng các biện pháp số. Như chúng ta nghiên cứu các đồ thị và. | C H A P T E R 2 Basic Tools and Concepts Description of Data The goal of statistics is to gain information from data. The first step is to display the data in a graph so that our eyes can take in the overall pattern and spot unusual observations. Next we often summarize specific aspects of the data such as the average of a value by numerical measures. As we study graphs and numerical summaries we keep firmly in mind where the data come from and what we hope to learn from them. Graphs and numbers are not ends in themselves but aids to understanding. Moore and McCabe 1993 Every study begins with a sample or a set of measurements which is representative in some sense of some population of possible measurements. For example if we are concerned with PCB contamination of surfaces in a building where a transformer fire has occurred our sample might be a set of 20 surface wipe samples chosen to represent the population of possible surface contamination measurements. Similarly if we are interested in the level of pesticide present in individual apples our sample might be a set of 50 apples chosen to be representative of all apples or perhaps all apples treated with pesticide . Our focus here is the set of statistical tools one can use to describe a sample and the use of these sample statistics to infer the characteristics of the underlying population of measurements. Central Tendency or Location The Arithmetic Mean Perhaps the first question one asks about a sample is what is a typical value for the sample. Usually this is answered by calculating a value that is in the middle of the sample measurements. Here we have a number of choices. We can calculate the arithmetic mean x whose value is given by - - xi x -N 2.1 where the Xi s are the individual sample measurements and N is the sample size. The Geometric Mean Alternatively we can calculate the geometric mean GMx given by GM x expX ln x N 2.2 2004 CRC Press LLC That is GM x is the antilogarithm of the mean of the .