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Basic Concepts of Statistics

Prof. dr. Liliana Duguleanldugul@unitbv.ro

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Discipline Definition

Statistics is the science of data. Itinvolves:

collecting, classifying,

summarizing,

organizing,

analyzing and

interpreting the numerical information.

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Applications of Statistics

Descriptive Statistics uses numerical and graphicalmethods:

to look for patterns in a data set,

to summarize the information revealed in a data set,

to present the information in a convenient form.

Inferential Statistics uses sample data:

to make estimates, decisions, predictions, or othergeneralizations about a larger set of data.

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Basic Concepts of Statistics

The population (collectivity) = thephenomenon to be studied (events, people,objects, tranzactions)

The experimental unit (statistic unit) = theintegrant element of the population (simpleor complex)

A variable (characteristic) = is a property ofan individual experimental unit

The value (measurement)

The frequency (the number of units with the

same value of characteristic)

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Fundamental Elements of Statistics

A sample = a subset of the units of a population

Astatistical inference = an estimate or prediction

or some other generalization about a population

based on information contained in a sample A measure of reliability = a statement (usually

quantified) about the degree of uncertainty

associated with a statistical inference.

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Types of Data

Quantitative data are measurements that

are recorded on a naturally occurring

numerical scale.

Qualitative data can only be classified into

categories.

The statistical methods for describing,

reporting and analyzing the data, depend on

the data type (quantitative or qualitative).

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Describing Qualitative Data

Aclass is one of the categories into which qualitative datacan be classified.

Theclass frequency is the number of observations in the

data set falling into a particular class. Theclass relativefrequency (class percentage) is the class frequency dividedby the total number of observations in the data set (*100).

Summary of Graphical Descriptive Methods for qualitativedata: Bar graph,

Pie chart,

Pareto diagrams: a column graph with the categories of thequalitative variable (the columns) arranged by height in descendingorder from left to right.

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Bar graphFunction Asistent Lecturer Assistant

professor

Professor total

fi 82 82 49 57 270

The distribution of academic staff in a survey, at Transilvania

University, in 2009

82 82

49

57

0

10

20

30

40

50

60

70

80

90

Assistant Lecturer Ass. Professor Professor

functions

number

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Pie chartFunction Asistent Lecturer Assistant

professorProfessor total

fi 30.4% 30.4% 18.1% 21.1% 100%

The structure of the academic staff survey, at Transilvania

University, in 2009

Assistant

31%

Ass. Professor

18%

Lecturer

30%

Professor

21%

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Pareto diagram

The Pareto diagram of the academic staff distribution in a survey, atTransilvania University, in 2009

30% 30%

21%

18%

0%

5%

10%

15%

20%

25%

30%

35%

Assistant Lecturer Professor Ass. Professor

functions

number

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

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The 40 Best Paid Executives

fifi*

Bachelors 820%

Law 410%

Masters 410%

MBA 2050%

None 2

5%

PhD 25%

Total 40 100%

fi fi* fi*c

MBA20 50% 50%

Bachelors

8 20% 70%

Law4 10% 80%

Masters4 10% 90%

None2 5% 95%

PhD2 5% 100%

Total

40 100%

Source: Forbes, May 8, 2006

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The 40 Best Paid Executives

The Pareto diagram for degrees of 40 CEOs, in 2005

50%

20%

10% 10%5% 5%

0%

10%

20%

30%

40%

50%

60%

MBA Bachelors Law Masters None PhD

degrees

frequency(%)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Source: Forbes, May 8, 2006

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The Pareto Principle

Vilfredo Pareto (1843 1923) Born in Paris, University of Turin: engineering

and mathematics

Univ. of Lausanne in Switzerland (1896) - Cours

deconomie politique proved that the distribution of income and

wealth in society is not random

The pattern appears throughout history in all

societies: approximately 80% of the totalwealth in a society lies with only 20% of thefamilies.

vital few and the trivial many - the Pareto

principle in economics

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Graphical Methods for

Describing Quantitative Data

Dot plots

Stem-and-leaf displays

Histograms

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the use of a diagram

A diagram can be used for the purposes:

to summarize large sets of data (structure), or

to focus attention on some aspectof the data, or

to display a trendin the data over time.

A good diagram enables the viewer to grasp in a single

glance the relevant features of the data, features thatwouldn't be obvious from the raw numbers themselves.

The power that diagrams have to give us an instant

impression of the data can also be abused. Diagramscan be constructed to give the impression that the datahave a feature that they don't really have, or somecommon ways of pictorially representing (andmisrepresenting) data.

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Hong Kong's soaring population

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Example

Years Newspaper A(thou. pieces)

Newspaper B(thou. pieces)

1990 510 19111991 621 1829

1992 624 1636

1993 654 1555

1994 732 1490

S l i i

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Scales originesusing two Y Axis, one for each series

Number of copies evolution for newspaprs A and B,during 1990-1994

0

500

1000

1500

2000

2500

1990 1991 1992 1993 1994

years

n

r.ofpiecesB

(thou.)

500

550

600

650

700

750

n

r.ofpiecesA(

thou.)

B A

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Using two Y Axis (a)

Number of copies evolution for newspaprs A and B,during 1990-1994

0

500

1000

1500

2000

2500

1990 1991 1992 1993 1994

years

nr.ofpiecesB(thou.)

0

100

200

300

400

500

600

700

800

n

r.ofpiecesA

(thou.)

B A

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Using two Y Axis (b)

Number of copies evolution for newspaprs A and B,

during 1990-1994

1250

1350

1450

1550

1650

1750

1850

1950

1990 1991 1992 1993 1994

years

nr.ofpiecesB(thou.)

400

450

500

550

600

650

700

750

nr.ofpiecesA

(thou.)

B A

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Using two Y Axis (c)

Number of copies evolution for newspaprs A and B,

during 1990-1994

1450

1500

1550

1600

1650

1700

1750

1800

1850

1900

1950

1990 1991 1992 1993 1994

years

nr.ofpiecesB(thou.)

500

550

600

650

700

750

nr

.ofpiecesA

(thou.)

B A

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Correct graph

Number of copies evolution for newspaprs A and B,during 1990-1994

0

500

1000

1500

2000

2500

1990 1991 1992 1993 1994

years

nr.of

pieces

(tho

u.

)

A B

Comparative evolution of newspapers A si B, during 1990-1994

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Using plane images

Doubling the production

1996 1999

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The mobile phone revolution

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Using spatial images

2 errors: the dimensions and the inflation

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Tricky comparisons

Absolute values

Governmental expenditure evolution in U.S.A. during 1930-1984

(Wonnacott, ediia a4 -a. pag.64)

0

100

200

300

400

500

600

700

800

900

bilioane

$

1930193619421948195419601966197219781984

anii

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Correct graph Relative values (%)

Governmental expenditure evolution in U.S.A. (% din PNB) during 1930-1984(Wonnacott, ediia a4 -a. pag.64)

0

10

20

30

40

50

60

procentedinPN

B(%)

1930193619421948195419601966197219781984

anii

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An effective campaign?

In 1956, the U.S.A.state of Connecticut

began a severe

crackdown on

speeding drivers.

The following

graph shows the

annual number oftraffic fatalities

before and after the

crackdown.