Data are the result of sampling from a population.īecause it takes a lot of time and money to examine an entire population, sampling is a very practical technique. The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. To study the population, we select a sample. You can think of a population as a collection of persons, things, or objects under study. In statistics, we generally want to study a population. In your study of statistics, you will use the power of mathematics through probability calculations 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 vaccination causing the disease the vaccination is supposed to prevent. 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. 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. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. You will encounter what will seem to be too many mathematical formulas for interpreting data. Statistical inference uses probability to determine how confident we can be that our conclusions are correct.Įffective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination of the data. The formal methods are called inferential statistics. After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from “good” data. Two ways to summarize data are by graphing and by using numbers (for example, finding an average). Organizing and summarizing data is called descriptive statistics. In this course, you will learn how to organize and summarize data. With this example, you have begun your study of statistics. The questions above ask you to analyze and interpret your data. Where do your data appear to cluster? How might you interpret the clustering? Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not?
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