Probability, Random Variables, Statistics, and Random Processes

8Descriptive Statistics

Statistics is a field that bridges probability theory to actual data from the real world. Statistics is concerned with the collecting, arranging, summarizing, and analyzing data and with drawing conclusions or inferences from data based on the results of such analysis. Modern statistics has an essential role in a diverse array of major applications, including manufacturing and quality control, climate change and weather forecasts, opinion polling and marketing forecasts, public health, safety and security, economic and stock market forecasts, testing the effectiveness of drugs and treatments, plant breeding and crop production, risk analysis and gambling, and human behavior in psychology, to name a few.

8.1 Overview of Statistics

The raw material of statistics is data, generally defined as numbers that result from making a measurement or from the process of counting, and data set refers to the set of all observations made for a given purpose. A characteristic is known as a quantitative variable when observations made convey information regarding amount, such as patients' age in a hospital. On the other hand, a characteristic is referred to as a qualitative variable when observations taken provide information on attribute, such as the ethnic designations of citizens of a county. Data can be gathered from one or more sources, such as records, surveys, experiments, and already published data.

In collecting data, the totality of observations in which we ...