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| UNIT 1. INTRODUCTION TO STATISTICS READING/SPEAKING Text 1. Basic ideas of Statistics 1 The word statistics has two different but related meanings. In the most common usage, statistics means "a collection of numerical data." For example, we could look at the statistics that show the populations of the cities in a state or that describe the performance of a baseball team. 2 The word statistics also refers to the branch of mathematics that deals with the analysis of statistical data. There are two branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is the process of obtaining meaningful information from sets of numbers that are often too large to deal with directly. A large pile of numbers that have not been summarized is called raw data. Even though the raw data contains a lot of information, it is not very mean ingful because people have a limited capacity to absorb the informa tion. In order to convey meaning, it is usually necessary to summarize the data. You are already familiar with some concepts from descriptive statistics, such as the use of the average (also known as the mean) to indicate the typical value in a group of numbers. 3 Statistical interference refers to the process of obtaining infor mation about a larger group from the study of a smaller group. The complete group that we are interested in is called the population. For example, we might be interested in the entire population of the United States, or in the population of a particular city. In statistics, the word population does not have to refer to people; for example, the popula tion we are interested in might consist of all fish in a lake, or it might consist of all ice cream cartons produced at an ice cream factory. 4 The group of items selected from the population is known as the sample. Examples include the following: • population: all voters in the United States sample: the 1,000 people in a poll that attempts to predict the result of the election 5 The characteristics of the objects in the sample are known, whereas the characteristics of the objects in the population are usually un known. We would like to use the information we have obtained from the sample to make inferences about the nature of the population. If the sample happens to be representative of the population, then we will be correct in making those predictions. However, if the sample has been chosen so that it is unrepresentative (for example, it includes entirely people of one political party although the population is evenly split between the two parties), then you will be quite wrong when you attempt to use the sample to indicate the nature of the population. How can you tell if the sample is representative or not? There is no way to know for sure, since the characteristics of the population are unknown. However, the use of statistical inference makes it possible to make statements about the probability that the characteristics calcu lated from the sample are close to the characteristics of the population, provided that the sample has been selected randomly. 6 You might be tempted to think, "Wouldn't it be better to investigate the entire population? That way we would not have to worry about the danger of choosing an unrepresentative sample." This plan would definitely provide greater accuracy, but at a heavy price. The main reason for investigating samples, instead of populations, is that it is much less expensive. If you have limited resources, then there are better things to do with your resources than checking the entire population, especially since a sample will often provide an accurate enough result for most purposes. 7 There are also other reasons why it is necessary to check samples instead of populations. In some cases the process of investigating the item destroys it. For example, if you are tasting the ice cream coming off the assembly line, then testing the entire population of items would leave you without any items left. It is also possible that data collected from a sample will be measured more accurately than data from a population because the smaller size of the sample makes it possible to be more careful in training interviewers, entering data, and processing answers. 8 In order to understand inferential statistics it is necessary to un derstand several concepts in probability. Probability and inferential statistics are very closely related because they ask the opposite types of questions. In probability, we know how a process works and we want to predict what the outcomes of that process will be. In statistics, we don't know about the nature of the population, but we can observe the outcomes of the sample selected from the population. We will try to use this information to make predictions about the population. EXERCISES 1. Read the following words paying attention to the proper pronunciation of the underlined vowels, consonants, and the word stress. word, group, accuracy, numerical, branch, data, example, directly, raw, inferences, entirely, worry, variable, of 2. Answer the following questions.
3 Decide whether the following statements are true or false according to the text.
4 Complete the following sentences using your own ideas.
5. Find English equivalents in Text 1.
6. Match terms on the left with their corresponding definitions on the right.
7. Find partners among the following words to make up a collocation.
8. Translate the following sentences using terms and collocations from the text and the previous tasks.
9 Fill in the gaps using words given below. empirical experiments advanced applications inference mathematical aspects subject meaningful Statistics is the study of how to acquire __1__ information by analyzing data, such as a list of numbers. Sometimes this data comes from planned __2__ in controlled environments where it is possible to vary the factors that we are concerned with. When it is not possible to do experiments, then we must rely on __3__ data from observations of the uncontrolled "real" world. You're probably wondering whether statistics is a hard __4__. The answer to that question is "yes and no." Many of the important ideas in statistics can be understood even by someone with only a slight __5__ background. However, there are also parts of statistics that are hard. Many require the use of __6__ mathematical methods such as calculus. To understand statistics it is necessary to understand probabil ity. Probability, the study of chance phenomena, is also an interesting subject in its own right. There are many fun __7__ of probability since it includes the study of dice, cards, and related games. There are also many important practical __8__ of probability, and the important concepts of statistical __9__ are based on the ideas of probability. 10. Choose the correct letter.
11 Choose the correct preposition.
12 Choose the proper form of the word to complete the sentence to predict 1 The outcomes of their work were just so _______________________. 2 The __________________ value of this new method of analysis has still to be proven. 3 __________________, after the initial media interest, the refugees now seem to have been forgotten. 4 Although her job is boring and monotonous, she likes the sense of _________________ and security that it gives her. an inference 1 I ______________________ from the number of cups that he was expecting visitors. 2 The lawyer applied ________________ proof method to prove his client’s innocence. 3 These conclusions have been drawn ______________________. analysis 1 Let's ____________________ the problem and see what went wrong. 2 He's working as a political ______________________, but he's an engineer by profession. 3 You need a great deal of ______________________ skills to understand Statistics. 4 All demographic data must be examined ___________________________. 13. Look at the following pair of words, spot the difference and do the task. TO AFFECT ≠ TO EFFECT
14 Here are thirty verbs/verb phrases which are used to express changes. Which words could be used to describe the change or movement in each graph? Write the phrases in the column below the appropriate graph.
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