Chapter 01 - Introduction

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Introductory chapter: what is statistics?

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  • PRELIMINARIES

    The term we know today, statistics, is of Latin descent. It comes from the word status, which means

    state or condition (hence the term status quo, which means the state in which). While the term only

    became widely used during the 18th century, the practice had been around many centuries prior to

    that. In fact, as early as the biblical times, people had been using statistics in order to help with the

    administration of the state. For example civilized states would collect data on taxes, population

    count, poultry and livestock, labor, resources, and agricultural products, as they realized that these

    figures helped greatly in governance.

    In no way did the discipline become obsolete. As a matter of fact, the use of statistics has become

    more widespread in the government these days. Due to advancements in data collection techniques

    and statistical programming tools, the amount and scope of data have greatly increased, thereby

    allowing more and more avenues for its application. Now, countries regularly release data on gross

    domestic product, consumer price index, inflation, unemployment rates, foreign exchange rates,

    interest rates, and population counts. These data do not only monitor the performance of a certain

    country, but they also help lawmakers and public officials make crucial policy changes or proposals.

    The use of statistics is not limited to the government, though. Where data is needed and analyzed,

    statistics would most likely be used. The following are some examples of applications of statistics:

    Medicine. In order to develop new drugs, researchers use statistics to determine

    effectiveness. Studies on the spread of certain diseases, together with studies for prevention,

    diagnosis, and treatment, also use statistical analyses.

    Economics. The field heavily relies on statistical methods, as economists analyze data in

    order to understand the workings of both foreign and local economic climate. As such,

    estimation of indicators such as inflation rate, interest rates, foreign exchange rates, and

    gross domestic product.

    Business. Other than market studies for launching new products and campaigns, businesses

    also use statistics in order to ensure that their products are at par with certain standards.

    Businesses also forecasts certain indicators, usually those related to production, that would

    help them make decisions with regard to policies and actions for the firm.

    Politics. As the election period draws near, politicians seek the help of survey and polls in

    order to determine how they are faring compared to their competitors. This type of

    information helps them formulate the tactics they would use in order to win the voters over.

    The list of the uses of statistics would go on, and it would most probably keep on going. As long as

    data is available, statistics would never run out of uses. As such, it is very important to possess some

    knowledge in statistics.

    STATISTICS 101

    Elementary Statistics

    Chapter I: Introductory Concepts

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    BASIC CONCEPTS

    Whenever we hear the word statistics, several things immediately come to mind. It could be the vital

    statistics of a beauty pageant contestant. It could be the season statistics of your favorite football

    team. It could be the interviewer that comes knocking on your door to ask you questions. While

    these are still connected to the discipline, statistics is not limited to any of these. What, then, is

    statistics?

    Definition. Statistics is the branch of science that deals with the collection,

    organization, analysis, interpretation, and presentation of data.

    From the definition above, statistics may sound like a highly technical courseas though it is

    something that is not really applicable to our daily lives. This notion cannot be more incorrect, as we

    apply and encounter statistics, even in the most dismal aspects of our lives.

    Why is it important to study statistics? It is important because statistics give us the information that

    we need. The information gathered would then enable people to make intelligent decisions. How is

    this information obtained? The information is obtained through a process called statistical inquiry.

    The process would help us answer problems and understand things a lot better. More specifically, it

    would help us gain better understanding about a particular group of elements that is of interest to us.

    That particular group of elements is called the population.

    Definition. The population is the collection of all elements in a statistical inquiry.

    Definition. The sample is a subset of the population.

    The population is a big group which may contain individuals, objects, animals, or geographic areas, to

    name a few. The following are some examples of populations:

    Collection of all school-aged children in Metro Manila

    Collection of Statistics 101 students currently enrolled

    Set of fluorescent bulbs manufactured in a month

    While we would like to use information culled directly from the population, this is not always

    possible, since it costs a lot of money and time. Thus, we resort to using a subset of the population

    which is the sample. Some examples of samples for each of the population specified above are as

    follows:

    1325 school-aged children in Metro Manila

    80 Statistics 101 students currently enrolled

    100 light bulbs manufactured in a month

  • Page | 3

    Definition. The variable is a characteristic or attribute of an element that can assume

    different values for different elements.

    Definition. The observation is a realized value of a variable.

    Definition. The data is the collection of observations.

    Using the data on hand, we can then compute for a summary measure that would describe either the

    population or the sample. These summary measures describe a certain characteristic of the

    population or the sample. These are the parameter and the statistic. The parameter is for the

    population while the statistic is for the sample.

  • Page | 4

    FIELDS OF STATISTICS

    Statistics has two major fieldsapplied statistics and mathematical or theoretical statistics. Applied

    statistics is concerned with the procedures and techniques used to collect, organize, analyze,

    interpret, and present data. This allows us to properly select and implement the tools needed in

    order to obtain solutions to the research problem. Mathematical or theoretical statistics, on the

    other hand, deals with the development of the theoretical foundations of the methods used in

    statistics. It is very important to also study theory because it is essential to understand the rationale

    behind the methods. Studying these theories would allow us to develop new methods or modify

    existing methods in order to keep up the new and more complex problems.

    Applied statistics, likewise, has two major areas. These are descriptive statistics and inferential

    statistics.

    Descriptive statistics are techniques used in the collection, organization, presentation, analysis, and

    interpretation of data. Conclusions drawn using descriptive statistics are only applicable to the data

    on hand. No generalizations can be made to larger group.

    On the flip side, inferential statistics are techniques used in analyzing data that would allow us to

    generalize to a larger group. Here, conclusions are made with a degree of uncertainty because the

    information we have is partial. As such, these conclusions are subject to some error.

  • Page | 5

    THE STATISTICAL INQUIRY

    As mentioned earlier, it is through the statistical inquiry that we obtain information. Once the

    process is done, we expect to have gained a better understanding of some things or characteristics

    we are interested in.

    A statistical inquiry is a planned research that provides information in order to answer a research

    problem. Whenever we perform an inquiry, our goals fall under one or more of the following general

    objectives:

    Describe characteristics using a certain measure

    Compare characteristics between two groups

    Justify an assertion

    Determine relationships between two variables

    Identify groups of related variables

    Reveal natural groupings with respect t values of a certain variable

    Determine effects of one variable on another

    Clarify patterns with the help of graphs

    Predict values of a variable of interest using other variables

    Forecast values of a variable through time

    Because statistics is a branch of science, it is expected that a statistical inquiry would follow steps

    very much like the scientific method or other problem-solving tools.

    1. Identify the problem.

    2. Plan the study.

    3. Collect the data.

    4. Explore the data.

    5. Analyze the data and interpret results.

    6. Present the results.

    Indentifying the problem is the heart of a statistical inquiry. This problem can be in the form of either

    a question or a statement. While many think that cooking up a problem would be very easy, that is

    not the actual case, since more than anything, it needs much thought. It is the most important to

    think of the problem thoroughly because the research problem would be the basis for all the actions

    in a statistical inquiry. If the problem is formulated haphazardly, we might end up getting detailed

    answers to irrelevant problems or lackluster answers to overambitious problems. Thus, it is

    important to read up on as much literature as possible in order to properly formulate a research

    problem.

  • Page | 6

    Once the problem has been identified, the next step would be to create a plan to answer the

    problem. During this stage, it is imperative to consider all the outputs in the problem identification

    stage. The concrete outcome for this stage would be the research design, a detailed discussion of

    methods and strategies for data collection and analysis. The research design should include a list of

    variables, the design for the instrument for measurement, the plan for data collection, the design for

    sampling or experiment, and the tools that will be used for the analysis. Sticking to this plan to letter

    would help ensure the quality of the data that is obtained.

    After data has been collected, it is ready to be explored. Data is explored in order to check

    assumptions, find peculiarities, and identify characteristics or features. Analysis and interpretation of

    data would follow after exploring the data. Again, it is important to follow the planned method of

    analysis. It is during this stage that we examine results and confirm whether objectives had been met

    and whether the research problem had been answered. Finally, findings are presented in order to

    add to the body of knowledge. Results and findings should be presented as clear as possible, using

    the tools that are appropriate.