Statistics

Introduction to Statistics

Some Statistical Terms

1.) Data is any quantitative or qualitative information.

a.) Quantitative data refers to numerical information

obtained from counting or measuring that which be

manipulated by any fundamental operation.

Examples:

age, I.Q. scores, height, weight, income

b.) Qualitative data refers to descriptive attributes

that cannot be subjected to mathematical

operations.

Examples:

gender, citizenship, educational attainment,

religion

2.) Population refers to the totality of all the

elements or persons for which one has an interest at

a particular time.

For example, the members of the faculty of a school,

the graduating class, the Visayan-speaking

employees of a company, the male students, etc. A

particular variable of a population can be associated

to the population.

A researcher may associate a population to the ages

of graduating students,, the I.Q. scores of the

employees, the income of single parent, and so on.

The usual notation for population is N.

3.) Sample is a part of population determined by

sampling procedures. It is usually denoted by n.

4.) Parameter is any statistical information or

attribute taken from a population. It is a true value or

actual statistics since its source is the population

itself.

5.) Statistic is any estimate of statistical attributes

taken from a sample.

6.) Variable is a specific factor, property, or

characteristic of a population or a sample which

differentiates a sample or group of samples from

another group.

For example, the score obtained from a coeducation

class may differ by gender. Hence, gender is

considered variable. In a catholic congregation,

religion cannot be considered a variable since every

member the population is Catholic.

a.) Discrete variable is a variable that can be

obtained by counting. Examples: the number of

cellphone users in a company, the number of

computers in the laboratory.

b.) Continues variable is a variable that can be

obtained by measuring objects or attributes.

Examples: the weight of students, the temperature

in a city over a period of time, the area of

classrooms.

Definition of Statistics

Statistics is a branch of Mathematics that deals

with the scientific collection, organization,

presentation, analysis, and interpretation of

numerical data in order to obtain useful and

meaningful information.

Collection of data refers to the process of

obtaining information.

Organization of data refers to the

ascertaining manner of presenting the data

into tables, graphs, or charts so that logical

and statistical conclusions can be drawn

from the collected measurements.

Analysis of data refers to the process of

extracting from the given data relevant

information from which numerical description

can be formulated.

Interpretation of data refers to the task of

drawing conclusions from the analyzed data.

Branches of Statistics

1.) Descriptive Statistics

The branch of statistics that focuses on

collecting, summarizing, and presenting a

set of data.

Examples:

a.) The average age of citizens who voted for

the winning candidate in the last presidential

election.

b.) The average length of all books about

statistics.

2.) Inferential Statistics

The branch of Statistics that analyzes

sample data to draw conclusions about a

population.

Examples:

a.) For instance, suppose a survey group wants to

know the prevailing sentiments among Filipino

people on a certain issue. Asking every Filipino to

answer a questionnaire would be impossible. It is

expensive, time-consuming, and impractical.

Instead, a small part of the entire population is

scientifically chosen. The data gathered from this

group is used to draw a general opinion of the entire

population.

b.) A survey that sampled 2001 full or part-time

workers ages 50 to 70, conducted by the American

Association of Retired Persons (AARP), discovered

that 70% those polled planned to work past the

traditional mid-60s retirement age. By using

inferential statistics, this statistics could be used to

draw conclusions about the population of all

workers ages 50 to 70.

History of Statistics

The processing of statistical information has a history

that extends back to the beginning of humanity.

* As early as 3800 B.C., there were records of

population in Babylonia and in China.

Babylonia

China

* In biblical times, the census was undertaken by

Moses in 1491 B.C. and by David in 1017 B.C..

* Indian literature dating back to the reign of the

northern Hindustan King Asoka (270-230 B.C.) also

described methods of taking census.

King Asoka of Northern Hindustan

Reign268–232 BCE

Coronation 268 BCE

Born304 BCE, Close to 7th Aug

BirthplacePataliputra, Patna

Died232 BCE (aged 72)

Place of death

Pataliputra, Patna

* The Athenians and other ancient Greeks conducted

the census in times of stress, counting the adult

male citizens in war time and the general populace

every time the food supply was endangered.

Athenians

Athenians

Ancient Greeks

* The Romans registered adult males and their

property for military and administrative purposes.

Romans

* The sixth king of Rome, Servinus Tullius (578-534

B.C.) was given credit for instituting the gathering of

population data.

Servinus Tullius

Reign c. 578 – 535 BC

PredecessorLucius Tarquinius Priscus

SuccessorLucius Tarquinius Superbus

Father Unknown

Mother Ocrisia

* Two thousand years ago, each male in the Roman

Empire had to return to the city of his birth to be

counted and taxed. Thus, the Bible gives an account

of the return of Joseph and Mary to Bethlehem for

such purpose, (The Holy Bible, Luke 2: 4-5).

Joseph and Mary in Bethlehem

* In the Middle Ages, registrations of land ownership

and manpower for wars were made.

* In the thirteenth century, tax lists of Paris included

the registration of those who were subjected to tax.

* In England, William the Conqueror required the

compilation of information on population and

resources. The compilation “The Domesday Book” is

the first landmark in British statistics. Later on, the

need to register births, deaths, baptisms, and

marriages was reinforced as the population grew

bigger.

Born: 1028, Château de

Falaise, Falaise, France

Died: September 9, 1087,

Rouen, France

Nickname: William the Bastard

Full Name: William I

Spouse: Matilda of Flanders

Children:

Henry I of England

William II of England

Doomsday Book

* It was Gottfried Achenwall who first introduced the

word statistiks in a preface to a statistical work. He

was a German philosopher, historian, economist,

jurist and statistician. He is counted among the

inventors of statistics.

Born: October

20, 1719,

Elblag Poland

Died: May 1,

1772

Gottingen,

Germany

Education: University of Leipzig

Gottfried Achenwall

* Girolamo Cardano, an Italian mathematician,

physician, and gambler, wrote Liber de Ludo Aleae

in which appeared the first known study of principles

of probability. He wrote more than 200 works on

medicine, mathematics, physics, philosophy,

religion, and music.

Born:

September 24, 1501 Pavia, Italy

Died: September 21, 1576 Rome, Italy

Parents: Fazio Cardano

Books: The Rules of Algebra The book of my life The rules of algebra

Education: University of Padua University of Pavia

Gerolamo Cardano

Liber de Ludo Aleae

* Another gambler, Chevalier de Mere, made a

proposal to Blaise Pascal in the famous Problem of

Points, a work which marked the beginning of the

mathematics of probability. Marquis de Laplace’s

Theorie Analytique des Probabilities of 1812

stabilized and supported the said theory.

He was a French

writer born in Poitou.

Although he was not a nobleman,

he

adopted the title Chevalier for the

character in his dialogues who

represented his own views.

Born: 1607, Poitou

Died: December 29, 1684

Chevalier de Méré

Chevalier de Méré

He was a French mathematician,

physicist, inventor, writer and

Christian philosopher. He was a

child prodigy who was educated by

his father, a tax collector in Rouen.

Born: June 19, 1623

Clermont-Ferrand, France

Died: August 19, 1662

Paris, France

Full name: Blaise Pascal

Parents: Antoinette Begon

Étienne Pascal

Blaise Pascal Siblings:

Jacqueline Pascal

Gilberte Pasca

* Modern theories of Statistics were attributed to

the great names like Abraham De Moivre (1667-

1754) who discovered the equation of the normal

curve.

He was a French mathematician

famous for de Moivre's formula,

which links complex numbers and

trigonometry, and for his work on

the normal distribution and

probability theory.

Born: May 26, 1667

Vitry-le-François, France

Died: November 27, 1754

London, United Kingdom

Education: Academy of Saumur

Books: The Doctrine of Chances,

Abraham de Moivre A Method of Calculating

the Probabilities of Events

in Play

* Karl Pearson who made an extensive study on

correlation among several variables.

He was an influential English

mathematician who has been

credited with establishing the

discipline of mathematical

statistics. In 1911 he founded the

world's first university statistics

department at University College

London.

Born: March 27, 1857

Islington, United Kingdom

Died: April 27, 1936

Capel, United Kingdom

Children: Egon Pearson

Karl Pearson Education: Ruprecht Karl University of

Heidelberg, University of Cambridge,

King's College, Cambridge

* Just right after the World War II, the need for a

basic understanding of statistics arose. Statistical

literacy became a necessity in today’s modern

world.

* Nowadays, the use of Statistics has extended to

such things as theater attendance, sports results,

car sales in a certain period of time, heights,

weights, birth rates, death rates, and other things

that can be expressed numerically.