In your study of statistics, you will utilize the power of mathematics and probability to analyze and interpret your data. You might use probability to decide to buy a lottery ticket or not. A stockbroker uses probability to determine the rate of return on a client’s investments. Doctors use probability to determine the chance of a medical test incorrectly diagnosing the presence of a disease. To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities. Predictions take the form of probabilities.
The theory of probability began with the study of games of chance such as poker. The fraction is equal to 0.498 which is very close to 0.5, the expected probability. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern of outcomes when there are many repetitions. The expected theoretical probability of heads in any one toss is or 0.5. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. It deals with the chance (the likelihood) of an event occurring. Probability is a mathematical tool used to study randomness. Statistical inference uses probability to determine how confident we can be that our conclusions are correct. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life. The calculations can be done using a calculator or a computer. Keep in mind, the goal of statistics is not to perform numerous calculations using the formulas, but to interpret data to gain an understanding. You will encounter what will seem to be a lot of mathematical formulas to make calculations.
The formal methods are called inferential statistics.Įffective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination. After you have studied probability and probability distributions, you will use formal methods for drawing useful conclusions from data while filtering out the noise. Two ways to summarize data are by graphing and by using numbers (for example, finding an average). Organizing, summarizing, and presenting data is called descriptive statistics.
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You will first learn how to organize and summarize data. This is reflected in the data analysis process which we will expand on in the next section. The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives. You will also learn how data are gathered and how “good” data can be distinguished from “bad.” The Study of Statistics You will soon understand that statistics and probability work together. Included in this chapter are the basic ideas and words of probability and statistics. The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics. Think about buying a house or managing a budget. Since you will undoubtedly be given statistical information at some point in your life, you need to know some techniques for analyzing the information thoughtfully. With this information, you may make a decision about the correctness of a statement, claim, or “fact.” Statistical methods can help you make the “best educated guess.”
Typically, when you read a newspaper article or watch a television news program, you are given sample information. There are statistics about crime, sports, education, politics, and real estate. You are probably asking yourself the question, “When and where will I use statistics?” If you read any newspaper, watch television, or use the Internet, you will see statistical information.
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