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

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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.

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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.

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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.

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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.