Chapter 01 - Introduction

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Introductory chapter: what is statistics?

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<ul><li><p>PRELIMINARIES </p><p>The term we know today, statistics, is of Latin descent. It comes from the word status, which means </p><p>state or condition (hence the term status quo, which means the state in which). While the term only </p><p>became widely used during the 18th century, the practice had been around many centuries prior to </p><p>that. In fact, as early as the biblical times, people had been using statistics in order to help with the </p><p>administration of the state. For example civilized states would collect data on taxes, population </p><p>count, poultry and livestock, labor, resources, and agricultural products, as they realized that these </p><p>figures helped greatly in governance. </p><p>In no way did the discipline become obsolete. As a matter of fact, the use of statistics has become </p><p>more widespread in the government these days. Due to advancements in data collection techniques </p><p>and statistical programming tools, the amount and scope of data have greatly increased, thereby </p><p>allowing more and more avenues for its application. Now, countries regularly release data on gross </p><p>domestic product, consumer price index, inflation, unemployment rates, foreign exchange rates, </p><p>interest rates, and population counts. These data do not only monitor the performance of a certain </p><p>country, but they also help lawmakers and public officials make crucial policy changes or proposals. </p><p>The use of statistics is not limited to the government, though. Where data is needed and analyzed, </p><p>statistics would most likely be used. The following are some examples of applications of statistics: </p><p> Medicine. In order to develop new drugs, researchers use statistics to determine </p><p>effectiveness. Studies on the spread of certain diseases, together with studies for prevention, </p><p>diagnosis, and treatment, also use statistical analyses. </p><p> Economics. The field heavily relies on statistical methods, as economists analyze data in </p><p>order to understand the workings of both foreign and local economic climate. As such, </p><p>estimation of indicators such as inflation rate, interest rates, foreign exchange rates, and </p><p>gross domestic product. </p><p> Business. Other than market studies for launching new products and campaigns, businesses </p><p>also use statistics in order to ensure that their products are at par with certain standards. </p><p>Businesses also forecasts certain indicators, usually those related to production, that would </p><p>help them make decisions with regard to policies and actions for the firm. </p><p> Politics. As the election period draws near, politicians seek the help of survey and polls in </p><p>order to determine how they are faring compared to their competitors. This type of </p><p>information helps them formulate the tactics they would use in order to win the voters over. </p><p>The list of the uses of statistics would go on, and it would most probably keep on going. As long as </p><p>data is available, statistics would never run out of uses. As such, it is very important to possess some </p><p>knowledge in statistics. </p><p>STATISTICS 101 </p><p>Elementary Statistics </p><p>Chapter I: Introductory Concepts </p></li><li><p> Page | 2 </p><p>BASIC CONCEPTS </p><p>Whenever we hear the word statistics, several things immediately come to mind. It could be the vital </p><p>statistics of a beauty pageant contestant. It could be the season statistics of your favorite football </p><p>team. It could be the interviewer that comes knocking on your door to ask you questions. While </p><p>these are still connected to the discipline, statistics is not limited to any of these. What, then, is </p><p>statistics? </p><p>Definition. Statistics is the branch of science that deals with the collection, </p><p>organization, analysis, interpretation, and presentation of data. </p><p>From the definition above, statistics may sound like a highly technical courseas though it is </p><p>something that is not really applicable to our daily lives. This notion cannot be more incorrect, as we </p><p>apply and encounter statistics, even in the most dismal aspects of our lives. </p><p>Why is it important to study statistics? It is important because statistics give us the information that </p><p>we need. The information gathered would then enable people to make intelligent decisions. How is </p><p>this information obtained? The information is obtained through a process called statistical inquiry. </p><p>The process would help us answer problems and understand things a lot better. More specifically, it </p><p>would help us gain better understanding about a particular group of elements that is of interest to us. </p><p>That particular group of elements is called the population. </p><p>Definition. The population is the collection of all elements in a statistical inquiry. </p><p>Definition. The sample is a subset of the population. </p><p>The population is a big group which may contain individuals, objects, animals, or geographic areas, to </p><p>name a few. The following are some examples of populations: </p><p> Collection of all school-aged children in Metro Manila </p><p> Collection of Statistics 101 students currently enrolled </p><p> Set of fluorescent bulbs manufactured in a month </p><p>While we would like to use information culled directly from the population, this is not always </p><p>possible, since it costs a lot of money and time. Thus, we resort to using a subset of the population </p><p>which is the sample. Some examples of samples for each of the population specified above are as </p><p>follows: </p><p> 1325 school-aged children in Metro Manila </p><p> 80 Statistics 101 students currently enrolled </p><p> 100 light bulbs manufactured in a month </p></li><li><p> Page | 3 </p><p>Definition. The variable is a characteristic or attribute of an element that can assume </p><p>different values for different elements. </p><p>Definition. The observation is a realized value of a variable. </p><p>Definition. The data is the collection of observations. </p><p>Using the data on hand, we can then compute for a summary measure that would describe either the </p><p>population or the sample. These summary measures describe a certain characteristic of the </p><p>population or the sample. These are the parameter and the statistic. The parameter is for the </p><p>population while the statistic is for the sample. </p></li><li><p> Page | 4 </p><p>FIELDS OF STATISTICS </p><p>Statistics has two major fieldsapplied statistics and mathematical or theoretical statistics. Applied </p><p>statistics is concerned with the procedures and techniques used to collect, organize, analyze, </p><p>interpret, and present data. This allows us to properly select and implement the tools needed in </p><p>order to obtain solutions to the research problem. Mathematical or theoretical statistics, on the </p><p>other hand, deals with the development of the theoretical foundations of the methods used in </p><p>statistics. It is very important to also study theory because it is essential to understand the rationale </p><p>behind the methods. Studying these theories would allow us to develop new methods or modify </p><p>existing methods in order to keep up the new and more complex problems. </p><p>Applied statistics, likewise, has two major areas. These are descriptive statistics and inferential </p><p>statistics. </p><p>Descriptive statistics are techniques used in the collection, organization, presentation, analysis, and </p><p>interpretation of data. Conclusions drawn using descriptive statistics are only applicable to the data </p><p>on hand. No generalizations can be made to larger group. </p><p>On the flip side, inferential statistics are techniques used in analyzing data that would allow us to </p><p>generalize to a larger group. Here, conclusions are made with a degree of uncertainty because the </p><p>information we have is partial. As such, these conclusions are subject to some error. </p></li><li><p> Page | 5 </p><p>THE STATISTICAL INQUIRY </p><p>As mentioned earlier, it is through the statistical inquiry that we obtain information. Once the </p><p>process is done, we expect to have gained a better understanding of some things or characteristics </p><p>we are interested in. </p><p>A statistical inquiry is a planned research that provides information in order to answer a research </p><p>problem. Whenever we perform an inquiry, our goals fall under one or more of the following general </p><p>objectives: </p><p> Describe characteristics using a certain measure </p><p> Compare characteristics between two groups </p><p> Justify an assertion </p><p> Determine relationships between two variables </p><p> Identify groups of related variables </p><p> Reveal natural groupings with respect t values of a certain variable </p><p> Determine effects of one variable on another </p><p> Clarify patterns with the help of graphs </p><p> Predict values of a variable of interest using other variables </p><p> Forecast values of a variable through time </p><p>Because statistics is a branch of science, it is expected that a statistical inquiry would follow steps</p><p>very much like the scientific method or other problem-solving tools. </p><p>1. Identify the problem. </p><p>2. Plan the study. </p><p>3. Collect the data. </p><p>4. Explore the data. </p><p>5. Analyze the data and interpret results. </p><p>6. Present the results. </p><p>Indentifying the problem is the heart of a statistical inquiry. This problem can be in the form of either </p><p>a question or a statement. While many think that cooking up a problem would be very easy, that is </p><p>not the actual case, since more than anything, it needs much thought. It is the most important to </p><p>think of the problem thoroughly because the research problem would be the basis for all the actions </p><p>in a statistical inquiry. If the problem is formulated haphazardly, we might end up getting detailed </p><p>answers to irrelevant problems or lackluster answers to overambitious problems. Thus, it is </p><p>important to read up on as much literature as possible in order to properly formulate a research </p><p>problem. </p></li><li><p> Page | 6 </p><p>Once the problem has been identified, the next step would be to create a plan to answer the </p><p>problem. During this stage, it is imperative to consider all the outputs in the problem identification </p><p>stage. The concrete outcome for this stage would be the research design, a detailed discussion of </p><p>methods and strategies for data collection and analysis. The research design should include a list of </p><p>variables, the design for the instrument for measurement, the plan for data collection, the design for </p><p>sampling or experiment, and the tools that will be used for the analysis. Sticking to this plan to letter </p><p>would help ensure the quality of the data that is obtained. </p><p>After data has been collected, it is ready to be explored. Data is explored in order to check </p><p>assumptions, find peculiarities, and identify characteristics or features. Analysis and interpretation of </p><p>data would follow after exploring the data. Again, it is important to follow the planned method of </p><p>analysis. It is during this stage that we examine results and confirm whether objectives had been met </p><p>and whether the research problem had been answered. Finally, findings are presented in order to </p><p>add to the body of knowledge. Results and findings should be presented as clear as possible, using </p><p>the tools that are appropriate. </p></li></ul>