Math16 Notes

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LESSON 1: Definition, History and Methodology of

Statistics

Statistics – science of counting; any set or mass of

quantitative data; body of methodologies or techniques

used for the collection, presentation, analysis, and

interpretation of quantitative data.

Statistical Methodology

a) Descriptive Statistics is the treatment of data which is

designed to summarize or describe some of the

important features of the quantitative data without any

attempt to infer anything that goes beyond the data.

Essentially it summarizes the whole data by describing or

expressing what was observed in the data either

numerically or graphically.

b) Correlational Statistics is the statistical method which

uses measures or concepts that relate various kinds of

data. Furthermore if a relationship exists in any given

data, what kind of relationship is it and what is the

magnitude of the relationship?

c) Inferential Statistics is the treatment of data which

makes generalizations about a whole population out of

the results and patterns observed from experimenting

with a sample. What is used here is inductive reasoning.

Population – totality of the statistical units or

observations in which one is concerned

Sample – a part of the population that is relatively small

compared to the population itself but is representative

of the population in which you gather the observations

forming conclusions.

LESSON 2: Collection of Data

Types of Statistical Data

Statistical Data can be defined also as a group of

information that represent the qualitative or

quantitative attributes of a variable or set of variables,

which means it can be any set of information that

describes a given entity

Ungrouped data- data in its purest form as when it has

just been collected and no attempt has been made to

process it.

Group Data - data is arranged, organized and classified

into groups collectively known as classes then a certain

level of processing has been done to the data and

analysis could be readily done on the data

Sources for the Collection of Data

Primary data are defined as the first hand information

collected, compiled and published. Primary data are

mostly original data and have never undergone any type

of statistical treatment.

Some of the methodology on collecting primary data is

through the following:

Census is a study that obtains data from every member

of a population.

Sample Survey is a study that obtains data from a subset

of a population, in order to estimate population

characteristic or attributes.

Experiment is a controlled study in which the researcher

attempts to understand cause and affect relationships. A

particular example on how a researcher can control in a

sense his study although this is only one way is through

assigning each subject to groups and even how these

subjects are assigned to their corresponding groups is a

means of control and then determining what or which

treatments/process each group receives and would have

undergone.

Observational Study much like experiments, attempt to

understand cause and affect relationships but unlike

experiments the study is in no way being subject to

being controlled or limited to a controlled environment.

Secondary data are defined as the second hand

information which are originally collected by institution

or organization for their initial purpose and study and

once published and the information accessible, other

people or researchers used their finding and data for

their own study.

Population vs Sample in Data Collection

A study conducted with population whenever it could be

done is considered more accurate and precise than a

study done with samples. The accuracy and precision

gap could be bridge during the selection of the samples,

making sure that the samples are truly representative of

the population as much as possible.