Statistics

 Statistics is the study of the
collection, organization,
analysis, interpretation and
presentation of data. It deals
with all aspects of data
including the planning of data
collection in terms of the design
of surveys and experiments.

 The History of statistics can be said to start
around 1749 although, over time, there have
been changes to the interpretation of the
word statistics. In early times, the meaning
was restricted to information about states.
This was later extended to include all
collections of information of all types, and
later still it was extended to include the
analysis and interpretation of such data. In
modern terms, "statistics" means both sets of
collected information, as in national
accounts and temperature records, and
analytical work which requires statistical
inference.

 Statistical activities are often associated with
models expressed using probabilities, and
require probability theory for them to be put
on a firm theoretical basis. A number of
statistical concepts have had an important
impact on a wide range of sciences. These
include the design of experiments and
approaches to statistical inference such
as Bayesian inference, each of which can be
considered to have their own sequence in the
development of the ideas underlying modern
statistics.

 Actuarial science is the discipline that applies
mathematical and statistical methods to
assess risk in
the insurance and finance industries.
 Astrostatistics is the discipline that applies
statistical analysis to the understanding of
astronomical data.
 Biostatistics is a branch of biology that
studies biological phenomena and
observations by means of statistical analysis,
and includes medical statistics.

 Business analytics is a rapidly developing
business process that applies statistical
methods to data sets (often very large) to
develop new insights and understanding of
business performance & opportunities
 Chemometrics is the science of relating
measurements made on a chemical system or
process to the state of the system via
application of mathematical or statistical
methods.

 Demography is the statistical study of
all populations. It can be a very general science
that can be applied to any kind of dynamic
population, that is, one that changes over time or
space.
 Econometrics is a branch of economics that
applies statistical methods to the empirical study
of economic theories and relationships.
 Environmental statistics is the application of
statistical methods to environmental science.
Weather, climate, air and water quality are
included, as are studies of plant and animal
populations.

 Epidemiology is the study of factors affecting
the health and illness of populations, and
serves as the foundation and logic of
interventions made in the interest of public
health and preventive medicine.
 Geo statistics is a branch of geography that
deals with the analysis of data from
disciplines such as petroleum
geology, hydrogeology, hydrology, meteorolo
gy, oceanography, geochemistry , geography.

 Operations research (or Operational
Research) is an interdisciplinary branch of
applied mathematics and formal science that
uses methods such as mathematical modeling,
statistics, and algorithms to arrive at optimal
or near optimal solutions to complex
problems.
 Population ecology is a sub-field
of ecology that deals with the dynamics of
species populations and how these
populations interact with the environment.

 Psychometric is the theory and technique of
educational and psychological measurement
of knowledge, abilities, attitudes, and
personality traits.
 Quality control reviews the factors involved
in manufacturing and production; it can make
use of statistical sampling of product items to
aid decisions in process control or in
accepting deliveries.

 Quantitative psychology is the science of
statistically explaining and changing mental
processes and behaviors in humans.
 Reliability Engineering is the study of the ability
of a system or component to perform its required
functions under stated conditions for a specified
period of time
 Statistical finance, an area of econophysics, is an
empirical attempt to shift finance from
its normative roots to a positivist framework
using exemplars from statistical physics with an
emphasis on emergent or collective properties of
financial markets.

 Statistical mechanics is the application
of probability theory, which includes
mathematical tools for dealing with large
populations, to the field of mechanics, which
is concerned with the motion of particles or
objects when subjected to a force.
 Statistical physics is one of the fundamental
theories of physics, and uses methods
of probability theory in solving physical
problems.

 Statistical thermodynamics is the study of the
microscopic behaviors of thermodynamic
systems using probability theory and
provides a molecular level interpretation of
thermodynamic quantities such
as work, heat, free energy, and entropy.
 In education, statistics can be used to assess
students’ performance and correlatefactors
affecting teaching and learning processes to
improve quality of education.

 In Psychology, statistics is used to determine
attudinal patterns, the causes and effects of
misbehavior.
 In business and economics, statistics is used
to analyze a wide range of data like sales,
outputs, price indices, revenues, costs,
inventories, accounts, and the like.
 Meteorologists use statistics to find patterns
in the weather and make predictions about
what future weather will be like.

 Descriptive Statistics is concerned with the
methods of collecting, organizing, and
presenting data appropriately and creatively
to describe or assess group characteristics.
 Inferential Statistics is concerned with
inferring or drawing conclusions about the
population based from pre-selected elements
of that population.

 Constants refer to the fundamental quantities
that do not change in value. Fixed costs and
acceleration due to gravity are examples of
such.
 Variables, on the other hand, are quantities
that may take anyone of a specified set of
values. These set of values can be classified
as:
a.) Qualitative (categorical)
b.) Quantitative (numerical)
Variables

 Qualitative Variables are nonmeasurable
characteristics that cannot assume a
numerical value but can be classified into
two or more categories. Gender is a
qualitative dichotomous variable since an
individual may take one of the two values
“male” or “female”. In an opinion poll, the
response of individuals toward an issue
whether to go “for” or “against” it or
“undecided” is an example of qualitative
trichotomous variable.

Smoking habits of an individual in different
situations may be classified as “Always/Very
Often,” “Often,” “Seldom,” “Very Seldom,” or
“Never.” This set of qualitative values is called
multinomous variable. Those data that are
obtained about a qualitative variable is called
qualitative data.
 Quantitative Variables are those quantities that
can be counted with your bare hands, can be
measured with the use of some measuring
devices, or can be calculated with the use of a
mathematical formula.

Those data involving quantitative variables
are called quantitative data. Quantitative
Variables are classified as discrete and
continuous. Discrete Variables consist of
variates (actual values) usually obtained by
counting. Hence, they are represented by
counting numbers or whole numbers.
Continuous Variables are obtained by
measurements, usually with units such as
height in meters, weight in kgs, and time in
minutes.

 Variables also refer to any
observable characteristics or
attributes of a group of objects,
individuals or events. Those
variables having cause-and-effect
relationships are called
independent/endogenous variables
and dependent/exogenous variables.

 The process of using statistics always begins
with a question. We may ask: “Who will
probably become the next president?” or
“How long will a Brand X battery last?” or
“Which softdrinks are popular among
teenagers in our town?” When questions like
these have been asked the next step is to
collect information about the subject. The
kind of information we get from statistics is
called data and the people who collect,
organize, and analyze the data are called
researchers.

 Data usually refers to facts concerning things
such as status in life or people, defectiveness
of objects or effect of an event to the society.
 Information is a set of data that have been
processed and presented in a form suitable
for human interpretation, usually with a
purpose of revealing trends or patterns about
the population.

 There are two sources of obtaining data.
One is called the primary source from which
a first-hand information is obtained usually
by means of personal interview and actual
observation. On the other hand, the
secondary source of information is taken
from other’s works, news reports, readings,
and those that are kept by the National
Statistics Office, Securities and Exchange
Commission, Social Security System, and
other government and private agencies.

 Data are said to be an asset of a company if
they are accurate , updating , and available
when needed. Hence, any institution or
business organization must have a database
called Management Information System
where all information about their business
are made available in order to facilitate
verification of claims and to come up with
wise management decisions.

 In a statistical inquiry, a researcher should
prepare a list of questions, called
questionnaire which is intended to elicit
answers from respondents. A good
questionnaire should contain questions that
are arranged in a logical order and as much as
possible in a checklist type. Each question
should be provided with a list of possible
answers in order for the respondents to easily
complete the needed information.

 Data that will be obtained
either from discrete or
continuous variables shall be
classified depending on the
checklist found in a
questionnaire.

 These classifications, called scales of
measurement, are the ff:
1.) Nominal Scale --- classifies objects or
peoples’ responses so that all of those in a
single category are equal with respect to
some attributes and then each category is
coded numerically. Respondents can be
grouped according to marital status based
on four nominal scales, single-1, married-2,
seperated-3, or widow-4.

2.) Ordinal Scale --- classifies objects or
individual’s responses according to degree or
level, them each level is coded numerically.
Customers’ responses regarding their
satisfaction towards company’s services can
fall between an ordinal scale, Excellent-1,
Very Satisfactory-2, Satisfactory-3, Fair-4, or
Poor/Needs Improvement-5.

3.) Interval Scale --- refers to quantitative
measurements in which lower and upper
control limits are adapted to classify relative
order and differences of item numbers or
actual scores. Households’ socioeconomic
status are classified based from what income
level and age bracket they do belong.

4.) Ratio Scale --- takes into account the
interval size and ratio of two related
quantities, which are usually based on a
standard measurement. Weights, time, height,
rate of change in production, return on
investments, and economic order quantity are
measured with the use of a ratio scale.

1.) Direct or Interview Method --- is a person-to-
person interaction between an interviewer and
an interviewee. Tape recorded or written
interviews will help the researcher obtain exact
information from the interviewee.
Advantages: Precise and consistent answers can
be obtained by modifying or rephrasing the
questions especially to illiterate respondents or to
children under study.
Disadvantages: It is time, money, and effort
consuming and it will be applicable only for
small population, except when conducting a
census.

2.) Indirect or Questionnaire Method --- is an alternative
method for the interview method. Written responses
are obtained by distributing questionnaires (a list of
questions intended to elicit answers to a given
problem, must be given in a logical order and not too
personal) to the respondents through mail or hand-
carry.
Advantages: Lesser time, money, and efforts are
consumed.
Disadvantages: Many responses may not be
consistent due to the poor construction of the
questionnaire. The meaning of the questions may be
different from each respondent. Inconsistent
responses can no longer be modified, thus, it reduces
valid number of respondents.

3.) Registration Method --- is enforced by private
organizations or government agencies for
recording purposes.
Advantages: Organized data from an institution
can serve as ready references for future study or
for personal claims of people’s records.
Disadvantages: Problem arises only when an
agency doesn’t have a Management Information
System and if the system or process of
registration is not implemented well.

4.) Observation Method --- is a scientific method of
investigation that makes possible use of all
senses to measure or obtain outcomes/responses
from the object of study.
Advantages: Observation method is usually
applied to respondents that cannot be asked or
need not speak, especially when behaviors of
persons/culture of organization/performance
outcomes of employees/students are to be
considered.
Disadvantages: Subjectivity of information
sought cannot be avoided.

5.) Experimentation --- is used when the objective is
to determine the cause-and-effect of a certain
phenomenon under some controlled conditions.
Advantages: There is objectivity of information
since a scientific method of inquiry is used. An
equal number of respondents with relatively
similar characteristics are being examined to
obtain the different effects of something applied
to the experimental group.
Disadvantages: It’s too difficult to find
respondents with almost similar characteristics.
The whole method must be repeated if the
desired outcome is not reached.

 Data that are collected by these methods are
usually referred to as raw data. Responses out
from taped interviews, answered
questionnaires, furnished registration forms,
recorded observations, and results from an
experiment are considered raw data since they
are not yet organized and presented in a form
ready for interpretation. These data can only
be understood if appropriate forms of
presentation are adopted.

 In statistical usage, the word population is a finite and
infinite collection of objects, events, or individuals with
specified class or characteristics under consideration,
such as students in a certain university, legitimate taxi
drivers in Metro Manila, cellular phones user, etc. When
investigation of the entire population is difficult due to
material constraints like time, money, and efforts, a
sample or group of samples is drawn to represent the
population under study. A sample therefore is a finite or
limited collection of objects, events, or individuals
selected from a population. This sample is expected to
possess characteristics identical to those of the
population, otherwise, the validity and reliability of
information regarding the population will be in
question. A capital letter “N” is used to denote
population size whereas small letter “n” denotes sample

 The symbols that denote some statistical tools
to avoid confusion in their usage. The Greek
letters µ (read as miu), σ (sigma), σ² (sigma
squared), and ρ (rho) are used for parameters,
that is any numerical value describing a
characteristic of a population. While any of
those Arabic letters x, s, s² and r is used to
denote statistic, that is, any numerical value
describing a characteristic of a sample.

SYMBOLS for PARAMETER
 Population size……………………………… N
 Population mean……………………………..... µ
 Population standard deviation……………..... σ
 Population variance…………………………...σ²
 Population coefficient of correlation………. ρ

SYMBOLS for STATISTIC
 Sample size…………………………………… n
 Sample mean…………………………………. x
 Sample standard deviation………………… s
 Sample variance……………………………… s²
 Sample coefficient of correlation…………... r

 Questions such as “Who will probably become the
next president?” or “What was the employment rate
in the last five years?” or “Which cellular phone
brands are popular among teenagers in our town?”
require gathering of information from a number of
respondents in a population. In some cases,
complete enumeration or the so-called census taking
is a vital tool if the information gathered would be
used for administrative purposes and if it is of local
or national concern. Data from complete
enumeration or census are used as benchmarks or
reference points for current statistics and are used
as sampling frame for most current sample surveys.

 A complete enumeration survey is huge
undertaking which requires a large investment of
money and employment. It will consume a lot of
time and effort. This is the reason why the
National Census is held only once every decade.
The Census 2000 was recently conducted with the
help of the National Statistics Coordination
Board for data processing. The primary
disadvantage of complete enumeration survey is
that data might not be that accurate anymore
since this would undergo a lot of processes from
a different hands of enumerators in their own
locality to manual tallying and computerized
encoding of data.

 In most practical situations, sample surveys are allowed
since the entire population of a study is unavailable to
the researcher. Also, sample surveys are preferred due
to material constraints like money, time and efforts.
Sampling may usually produce an accurate result
because for the same resources we can afford to hire the
services of highly qualified selected personnel to gather
data from the sample. A sample is a portion or sub-
aggregate of the population that should represent the
common qualities or characteristics of the population.
With a limited length of time and resources, we can
obtain considerable amount of information from each
of the small number of respondents and validly infer
conclusions about the entire population using the
following random sampling designs.

 Random Sampling is the most commonly used
sampling technique in which each member in the
population is given an equal chance of being
selected in the sample. While non-random
sampling is a method of collecting a small portion
of the population by which not all the members
in the population are given the chance to be
included in the sample. Certain elements in the
population are deliberately left out from the
selection for varied reasons. Random sampling is
usually called fair sampling while non-random
sampling is a bias sampling.

1.) Equiprobability --- means that each member
of the population has an equal chance of
being selected and included in the sample.
For instance, there are 10,000 tickets, one
ticket assigned to each faculty or employee of
a company, to be raffled for a prize of Php.
10,000. The probability of each member of
this population to be drawn and get the Php.
10,000 prize is 1/10,000 or 0.0001 or 0.01%.

2.) Independence --- means that the chance
of one member being drawn does not
affect the chance of the other member.
In conducting a study on the product
preference of customers, the choice of
one member of the family cannot be
assumed as the choice of the entire
family members.

1.) Restricted Random Sampling --- involves certain
restrictions intended to improve the validity of the
sampling. This design is applicable only when the
population being investigated requires
homogeneity. A study on the effectiveness of a new
drug can be tested to two groups of animals, the
controlled and experimental groups. Those animals
that belong to the experimental group will be
treated with a new drug. The selection of a sample
of paired animals should be with restrictions
according to their degree of illnesses so that
significant difference between the two groups will
be accepted.

2.) Unrestricted Random Sampling
--- is considered the best
random sampling design
because there were no
restrictions imposed and every
member in the population has
an equal chance of being
included the sample.

A. Random Sampling Techniques
1.) Lottery or Fishbowl Sampling --- This is
done by simply writing the names or
numbers of all the members of the
population in small rolled pieces of paper
which are later placed in a container. The
researcher shakes the container thoroughly
then draws n out of N pieces of papers as
desired for a sample. This is usually done in
a lottery.

2.) Sampling with the use of Table of Random
Numbers --- If the population is large, a more
practical procedure is the use of Table of Random
Numbers which contains rows and columns of
digits randomly ordered by a computer. A sample
of size n can be generated by beginning at an
arbitrary point in Table of Random Numbers,
closing you eyes and haphazardly pointing at an
entry in the Table. Then proceed in any
direction, vertically, horizontally, or diagonally
until n distinct numbers could represent the
numerically coded elements in the population.

3.) Systematic Sampling --- This method of
sampling is done by taking every kth element
in the population. It applies to a group of
individuals arranged in a waiting line or in a
methodical manner. For instance, the
objective is to get the opinion of employees
regarding employee-management relations, a
sample of size n will be selected from a list
of employees arranged alphabetically or
according to age, experience, position or
academic rank.

4.) Stratified Random Sampling --- When the
population can be partitioned into several
strata or subgroups, it may be wiser to
employ the stratified technique to ensure a
representative of each group in the sample.
Random samples will be selected from each
stratum. Selecting a sample with this
technique is quite difficult and costly since it
requires a complete listing, called frame, of
all elements in the population. There are two
kinds of stratified random sampling.

Statistics

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