Applied Maths Presentation 2010

8/8/2019 Applied Maths Presentation 2010

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WHAT CRITICS ASK WHAT CRITICS ASK

IF THERES TOO MUCHIF THERES TOO MUCH

TECHNOLOGY IN THE CLASTECHNOLOGY IN THE CLAS


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BIG DREAMSBIG DREAMS

BILL GATES, Founder of Microsoft tookBILL GATES, Founder of Microsoft took

time out to visit some schools and this istime out to visit some schools and this iswhat he said:what he said:

I need to see what youre doing with theI need to see what youre doing with thecomputers and how we can make itcomputers and how we can make itbetter in the classroombetter in the classroom ((March 3, 1998March 3, 1998))


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ContCont BIG DREAMBIG DREAM

President Clinton says in a speech thatPresident Clinton says in a speech that

he wants to seehe wants to seethe day when computers are as much athe day when computers are as much a

part of a classroom as blackboardspart of a classroom as blackboards( Jan, 1998)( Jan, 1998)


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SOME QUESTIONS TOBE ASKEDSOME QUESTIONS TOBE ASKED

COMPUTERS BETTER FOR STUDENTS ?COMPUTERS BETTER FOR STUDENTS ?

FOR WHOM ?FOR WHOM ?

BETTER FOR SCHOOLS, DISTRICT,POLITICIANS ?BETTER FOR SCHOOLS, DISTRICT,POLITICIANS ?

OR BETTER FOR TECHNOLOGY COMPANIES ?OR BETTER FOR TECHNOLOGY COMPANIES ?


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Statement of the problemStatement of the problem

Modern education in statistics must involveModern education in statistics must involve practicalspracticals,,

ComputerComputer based data analysisbased data analysis

The question arises;The question arises;how computational elements should be integrated into thehow computational elements should be integrated into thecanon of methodological education ?canon of methodological education ?

Should the students see and study high level programmingShould the students see and study high level programmingcode right at the beginning of his or her studies ?code right at the beginning of his or her studies ?


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StatementStatement contcont

which technology can be presented during class ?which technology can be presented during class ?

Which computational elements can reWhich computational elements can re--occur (at increasingoccur (at increasing

level of complexity) during the different courses.level of complexity) during the different courses.


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In this presentation, I will address theseIn this presentation, I will address thesequestions and discuss where equestions and discuss where e techniquestechniqueshave their limits in statistics education;have their limits in statistics education;


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INTRODUCTIONINTRODUCTIONSINCE THE ENTERING OF MODERN COMPUTING EQUIPTMENT INTOSINCE THE ENTERING OF MODERN COMPUTING EQUIPTMENT INTOSCHOOLS/INSTITUTIONS there has been increased efforts toSCHOOLS/INSTITUTIONS there has been increased efforts touse computers not only for research and numericaluse computers not only for research and numerical

computations but also for education of students.computations but also for education of students.While traditional textbooks on statistics are usuallyWhile traditional textbooks on statistics are usuallyrestricted to small examples;restricted to small examples;

Computers offer great opportunities to enrich the teachingComputers offer great opportunities to enrich the teachingof statistics by means of explaining animations or onof statistics by means of explaining animations or on thethe--flyflycomputations of large realcomputations of large real--world datasets.world datasets.


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IntroductionIntroduction contcont

Technology does not only hold opportunities and advantages,Technology does not only hold opportunities and advantages,there may also be hazards and risk (Johnthere may also be hazards and risk (John TukerTuker 1989)1989)

The outline of thoughts about the integrations of electronicThe outline of thoughts about the integrations of electronicand computational elements into statistics along the coursesand computational elements into statistics along the courses

taught at Universities and polytechnic institutions in Ghana,taught at Universities and polytechnic institutions in Ghana,for business and economics.for business and economics.

Students from the bachelor, where statistics is taught in aStudents from the bachelor, where statistics is taught in a

twotwo--term lecture three hours a week, the students whoterm lecture three hours a week, the students whochoose statistics as one main subject are required to take achoose statistics as one main subject are required to take acourse on Multivariate Data Analysis (MDA)course on Multivariate Data Analysis (MDA)


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ToTo analyseanalyse highhigh dimensional data by means of clusterdimensional data by means of cluster--principal component and factor Analysis.principal component and factor Analysis.

Non and semi parametric Modeling focuses on nonparametricNon and semi parametric Modeling focuses on nonparametricdensity estimation and regression. Students compute datadensity estimation and regression. Students compute dataanalysis using SPSS and real world data.analysis using SPSS and real world data.

Supplementary to the computer based statistics coursesSupplementary to the computer based statistics coursesareare XploReXploRe.. NumericsNumerics Introductory Course focusing on theIntroductory Course focusing on thepractical work withpractical work with XploReXploRe..


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TRADITIONAL AND MODERNTRADITIONAL AND MODERNTEACHING MATERIALTEACHING MATERIAL

The main components of MM*stat that was developed toThe main components of MM*stat that was developed tosupport the universities and polytechnic teaching of statssupport the universities and polytechnic teaching of statsare lecture units, additional information and interactive (non)are lecture units, additional information and interactive (non)examples.examples.

The structure called MD* Booklet has also been used forThe structure called MD* Booklet has also been used forNumerical Methods in stats and finance.Numerical Methods in stats and finance.course(course(http://www.quantlet.com/mdstat/products/htmlhttp://www.quantlet.com/mdstat/products/html))

These provide important formulas, graphicsThese provide important formulas, graphics--fully explained,fully explained,enhanced and interactive.enhanced and interactive.


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ExamplesExamples

The interactive examples are one of the main features ofThe interactive examples are one of the main features ofMM*stat by using a combination of embedded javaMM*stat by using a combination of embedded java--basedbasedXploReXploRe QuantletQuantlet client :client :

CHECK THE OUTPUT FROM THE SOFTWARECHECK THE OUTPUT FROM THE SOFTWARE


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X ploReX ploRe java client java client


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Graphical user interfaceGraphical user interface


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1Additional informationFully Explained examples

2Enhanced examplesInteractive examples

3Model shapeBehaviour

SEQUENCE OF LECTURES


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Remote or locally installedRemote or locally installed XploReXploRe QuantletQuantlet server, theserver, thestudent can compute distribution functions, histogram andstudent can compute distribution functions, histogram andtest results.test results.

Compared with classical textbooks where effects ofCompared with classical textbooks where effects ofparameters changes can only be presented as sequence ofparameters changes can only be presented as sequence of

graphics or tables, the user can experience the results ofgraphics or tables, the user can experience the results ofdifferent settings indifferent settings in realtimerealtime..

Students can recall definitions of used terms in the glossaryStudents can recall definitions of used terms in the glossary

which is linked in MM*Stat.which is linked in MM*Stat.Student can complete multiple choice questions by selectingStudent can complete multiple choice questions by selectingradio buttons, the results are given instantly.radio buttons, the results are given instantly.


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X ploReX ploRe,, X ploreX plore QuantletQuantlet serverserver

Besides SPSS which is used for computational statisticsBesides SPSS which is used for computational statisticscourses the software packagecourses the software package XploReXploRe is also used foris also used foreducating students.educating students.

Developed byDeveloped by MD*tech (MD*tech (http://www.mdtech.dehttp://www.mdtech.de))

FullFull--featured statistical programming languagefeatured statistical programming language

Uses matrixUses matrix oriented approach with coriented approach with c--style syntax.style syntax.Can handle diverse statistical problems conveniently.Can handle diverse statistical problems conveniently.


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LIMITS OF ELIMITS OF E--LEMENTS INLEMENTS INSTATISTICS EDUCATIONSTATISTICS EDUCATION

Electronics and computational elements in education can beElectronics and computational elements in education can belimited from variety of different reasonslimited from variety of different reasons

technical implementation or the educational approach.technical implementation or the educational approach.

MM*Stat relies on a complex framework, cascading styleMM*Stat relies on a complex framework, cascading stylesheets, java andsheets, java and javaScript javaScript. These were implemented in. These were implemented indifferent ways for each browser, so extensive work had todifferent ways for each browser, so extensive work had tobe invested.be invested.


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ContCont

From educational point of view each use of electronics mediaFrom educational point of view each use of electronics mediashould be questioned carefully. Analysis byshould be questioned carefully. Analysis by BrandesBrandes, U., U.(2004) showed no significant improvements in the results of(2004) showed no significant improvements in the results ofthose students who used MM*Stat in comparison to thosethose students who used MM*Stat in comparison to thosewho use classical textbooks.who use classical textbooks.

The educational limits also lie in the way the information isThe educational limits also lie in the way the information ispresented.presented.

The classical way of using a textbook or boards also offerThe classical way of using a textbook or boards also offerthe opportunity to include on the fly notes from the teacherthe opportunity to include on the fly notes from the teacher

or the studentor the student


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ContCont 22

Electronic teaching solutions either do not offer thisElectronic teaching solutions either do not offer thiscapabilities at all or required significant technical resources.capabilities at all or required significant technical resources.


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END OF PRESENTATIONEND OF PRESENTATION


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THANK YOUTHANK YOU


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DEMOGRAPHYDEMOGRAPHY -- is the mathematical and statisticalis the mathematical and statisticalstudy of the size (# of persons in a population),study of the size (# of persons in a population),

composition (measurable characteristics) and spatialcomposition (measurable characteristics) and spatialdistribution (arrangement of the population in space in adistribution (arrangement of the population in space in agiven time) of human populations, and of changes over timegiven time) of human populations, and of changes over timein these aspects, through the operation of the fivein these aspects, through the operation of the fiveprocesses of:processes of:-- FertilityFertility-- no. of children being bornno. of children being born MortalityMortality -- deathsdeaths MarriageMarriage -- age of getting marriedage of getting married MigrationMigration-- in and out migrationin and out migration Social mobilitySocial mobility


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USES OFUSES OF

DEMOGRAPHIC DATADEMOGRAPHIC DATA


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To determine the number and distribution of To determine the number and distribution of population in a certain area for planning,population in a certain area for planning,priority setting, and for purposes of fundpriority setting, and for purposes of fund

allocation.allocation.

To determine the growth (or decline) andTo determine the growth (or decline) anddispersal of population in the past.dispersal of population in the past.


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To establish a causal relationshipTo establish a causal relationshipbetween population trends and variousbetween population trends and variousaspects of social organization.aspects of social organization.

To predict future developments andTo predict future developments and

their possible consequences.their possible consequences.


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SOURCES OF DEMOGRAPHIC DATSOURCES OF DEMOGRAPHIC DAT

CensusCensus -- may be defined as the total processmay be defined as the total process

of collecting, compiling and establishingof collecting, compiling and establishingdemographic, economic and social datademographic, economic and social datapertaining, at a specified time or times, to allpertaining, at a specified time or times, to all

persons in a country or delimited territory.persons in a country or delimited territory.


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Essential Features of aEssential Features of a

Population Census:Population Census:Individual enumerationIndividual enumeration-- each individual iseach individual isenumerated separately and theenumerated separately and thecharacteristics of each person arecharacteristics of each person arerecorded separately.recorded separately.

Universality within a defined territoryUniversality within a defined territory-- allallpeople are includedpeople are included


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SimultaneitySimultaneity a population is enumerateda population is enumeratedusing one reference date with respect tousing one reference date with respect toa well defined point in timea well defined point in time

PeriodicityPeriodicity -- censuses are taken at regularcensuses are taken at regularintervals. Previously, every 5 years.intervals. Previously, every 5 years.Currently, every 10 years.Currently, every 10 years.


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Types of Census Allocation:Types of Census Allocation:

De jure method De jure method -- ind ividu als are ind ividu als are assigned to the place o f the ir u su alassigned to the place o f the ir u su alre side nce , without re fere nce to re side nce , without re fere nce to where the y were actu allywhere the y were actu ally

e numer ated dur ingthe ce nsu s.e numer ated dur ingthe ce nsu s.


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De facto method De facto method -- ind ivid uals are allo cated ind ivid uals are allo cated to the are as in wh ich the y are ph ysicallyto the are as in wh ich the y are ph ysically

pre se nt at the ce nsus d ate , witho ut pre se nt at the ce nsus d ate , witho ut refe re nce to whe re the y usually live .refe re nce to whe re the y usually live .


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Usual Information ObtainedUsual Information Obtainedin a Census:in a Census:

Geographic informationGeographic information-- location at time of censuslocation at time of censusHousehold or family informationHousehold or family information-- household/ family sizehousehold/ family sizePersonal characteristicsPersonal characteristics -- sex, age, marital statussex, age, marital statusEconomic characteristicsEconomic characteristics-- occupationoccupationCultural characteristicsCultural characteristics -- language/s spokenlanguage/s spokenEducational characteristicsEducational characteristics -- literacy, educationalliteracy, educationalattainmentattainmentFertility dataFertility data -- number of children ever bornnumber of children ever born


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SOURCES OF DEMOGRAPHIC DATA.contn.SOURCES OF DEMOGRAPHIC DATA.contn.

2.2. Sample SurveysSample Surveys -- studies done on a subset of astudies done on a subset of apopulation.population.

3.3. Registration SystemRegistration System -- deals with continuous recordingdeals with continuous recordingof vital events. Compulsory of births, deaths andof vital events. Compulsory of births, deaths andmarriagesmarriages

4.4. ContinuingPopulation RegistersContinuingPopulation Registers -- continuouscontinuousrecording of information about the population.recording of information about the population.


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SOURCES OF DEMOGRAPHIC DATA.contn.SOURCES OF DEMOGRAPHIC DATA.contn.

Other Record SystemsOther Record Systems

Voters RegistrationVoters Registration School EnrollmentSchool Enrollment

Income Tax ReturnsIncome Tax Returns

Social Security SystemsSocial Security Systems


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IMPORTANCE OF STUDYING THE AGE AIMPORTANCE OF STUDYING THE AGE ASEX COMPOSITION OF A POPULATIONSEX COMPOSITION OF A POPULATION

Almost any measurements that can be taken ofAlmost any measurements that can be taken ofhuman beings will show substantial variation byhuman beings will show substantial variation byage and sexage and sex

Ex. Illness and death characteristics areEx. Illness and death characteristics areaffected by age and sex.affected by age and sex.


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The age and sex structure of a population is theThe age and sex structure of a population is thebasic demographic determinant of a nationsbasic demographic determinant of a nationsmanpower supply. It influences requirements formanpower supply. It influences requirements forvarious essential goods and services.various essential goods and services.

A populations age and sex structure is both aA populations age and sex structure is both a

cause and an effect. It determines the rate ofcause and an effect. It determines the rate ofpopulation growth.population growth.


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1. THE SEX COMPOSITION OF A POPULATION1. THE SEX COMPOSITION OF A POPULATION

Tools for describing the sex compositionTools for describing the sex compositionNo. of malesNo. of males

a.1.a.1. Sex RatioSex Ratio== ------------------------------------------------------ x 100x 100No. of femalesNo. of females

> The resulting figure represents the number of> The resulting figure represents the number ofmales for every 100 females in the population.males for every 100 females in the population.

a.2.a.2. Sex StructureSex Structure = sex ratio for each group (life cycle)= sex ratio for each group (life cycle)Ex. sex ratio for preEx. sex ratio for pre--schoolers, sex ratio for schoolschoolers, sex ratio for school

children, etc.children, etc.


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Some generalizations of the SexSome generalizations of the Sex

Composition of aPopulation:Composition of aPopulation:b.1b.1 Sex ratio at birth is generally 105. There are moreSex ratio at birth is generally 105. There are more

males than females in the younger age group.males than females in the younger age group.

b.2b.2 The sex ratio tends to decrease with age, eventuallyThe sex ratio tends to decrease with age, eventually

falling below 100. This is because agefalling below 100. This is because age-- specificspecificmortality rates are usually higher among malesmortality rates are usually higher among malesthan females.than females.


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b.3b.3 Sex ratio is higher in rural areas than inSex ratio is higher in rural areas than inurban areas. There are less femalesurban areas. There are less females andandmore males in the rural areas.more males in the rural areas.

b.4b.4 Frontier communities and colonies haveFrontier communities and colonies havehigher sex ratioshigher sex ratios


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2. THE AGE COMPOSITION OF A POPULATI2. THE AGE COMPOSITION OF A POPULATI

Tools for Describing the Age CompositionTools for Describing the Age Composition

a.1a.1 Median Age of thePopulationMedian Age of the

Population -- dividesdividesthe population into 2 equal parts. It isthe population into 2 equal parts. It is

the age below which 50% of thethe age below which 50% of the

population fall and above which the restpopulation fall and above which the restof the other 50% of the population fall.of the other 50% of the population fall.


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a.2a.2 Dependency RatioDependency Ratio-- represents the number ofrepresents the number ofdependents that need to be supported by everydependents that need to be supported by every100 population in the working age group.100 population in the working age group.

Popn aged 0Popn aged 0--14 +Popn aged 65+14 +Popn aged 65+Dependency Ratio =Dependency Ratio = ------------------------------------------------------------------------------------------ x10x100

Popn. aged 15Popn. aged 15--6464

The dependency ratio provides an index of the ageThe dependency ratio provides an index of the age--inducedinducedeconomic drain on manpower resources.economic drain on manpower resources.


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b. Factors Affecting the Age Compositionb. Factors Affecting the Age Composition

b.1 Fertilityb.1 Fertility-- a higher fertility leads to aa higher fertility leads to ayounger populationyounger population

b.2 Urbanb.2 Urban-- rural differencesrural differencesIn general, an urban population tendsIn general, an urban population tends

to have an olderto have an older age composition than aage composition than arural population as a result of the fertilityrural population as a result of the fertilityfactor.factor.


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b.3Peace and Order Situation (War)b.3

Peace and Order Situation (War)Immediate postImmediate post--war periods bring about a babywar periods bring about a babyboom and a resultant younger populationboom and a resultant younger population

b.4 Cultural practices, example, age at marriage.b.4 Cultural practices, example, age at marriage.Women in rural areas get married early (at 20Women in rural areas get married early (at 20

years old women are already considered oldyears old women are already considered oldmaid).maid).


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POPULATION PYRAMIDPOPULATION PYRAMID --graphical representation of thegraphical representation of theage and sex composition of aage and sex composition of apopulation.population.


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1.1. Data NeededData Needed

>> Population distribution by age and sexPopulation distribution by age and sex2.2. Compute the percentage falling underCompute the percentage falling under

each ageeach age -- sex group, using the totalsex group, using the totalpopulation as the denominator.population as the denominator.

Steps in Constructing aSteps in Constructing a

Population PyramidPopulation Pyramid


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Construct the population pyramid usingConstruct the population pyramid using

the percentages computed. The followingthe percentages computed. The followinggeneral rules are followed:general rules are followed:

a. Each group is represented by aa. Each group is represented by ahorizontal bar, with the first bar athorizontal bar, with the first bar at

the base of the pyramid representingthe base of the pyramid representingthe youngest age groupthe youngest age group


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b.b. The bars for males are traditionallyThe bars for males are traditionallypresented on the left side of the centralpresented on the left side of the centralvertical axis while the bars for females arevertical axis while the bars for females arepresentedpresented on the right side.on the right side.

c. The length of each bar corresponds to thec. The length of each bar corresponds to the% of the population falling in the specific% of the population falling in the specific ageageand sex group being plotted.and sex group being plotted.

N b d P Di ib i f h P l i


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MALEMALE FEMALEFEMALE

Age group (yrs)Age group (yrs) No.No. %% No.No. %%

00 4455 99

1010 14141515 19192020 24242525 29293030 3434

3535 39394040 44444545 49495050 54545555 59596060 64646565 6969

7070 74747575 797980 +80 +

96,98096,98099,76899,76894,03994,03982,97982,97972,58772,58758,66158,66150,73250,732

43,30743,30734,96234,96226,66426,66422,36022,36017,61317,61313,61213,61210,08410,084

7,8497,8495,9295,9294,5824,582

6.66.66.86.86.46.45.65.64.94.94.04.03.43.4

2.92.92.42.41.81.81.51.51.21.20.90.90.70.7

0.50.50.40.40.30.3

91,27191,27193,89393,89388,96288,96278,92678,92669,24169,24156,41156,41149,52349,523

42,85242,85235,77335,77328,29628,29624,37324,37319,89519,89515,82015,82013,22613,226

9,9599,9597,4897,4896,6056,605

6.26.26.46.46.06.05.45.44.74.73.83.83.43.4

2.92.92.42.41.91.91.71.71.31.31.11.10.90.9

0.70.70.50.50.40.4

ALL AGESALL AGES 742,708742,708 50.350.3 732,515732,515 49.749.7

TOTALPOPULATION = 742,708 + 732,515TOTALPOPULATION = 742,708 + 732,515

= 1,475,223= 1,475,223

N umber and Percent Distribution of the Populationby Age and Sex, Batangas, 1990

P l ti Di t ib ti b A d S


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M ales Age Females

80 +

75 - 79

70 - 74

65 - 69

60 - 64

55 - 59

50 - 54

45 -49

40 - 44

35 - 39

30 - 34

25 - 29

20 - 24

15 - 19

10 - 14

5 - 9

0 - 4

8 6 4 2 0 P ercent 0 2 4 6 8

Population Distribution by Age and SexBatangas, 1990

*Assuming that the old est pers on is 100 years old.


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Since population pyramids represent the age andSince population pyramids represent the age and

sex distribution of a population, thissex distribution of a population, thisrepresentation may take on various shapes,representation may take on various shapes,some of which do not resemble a pyramid at all.some of which do not resemble a pyramid at all.

Several types of population pyramids and theirSeveral types of population pyramids and theirunique features are represented by theunique features are represented by thefollowing figuresfollowing figures


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T ype 1 pyramid has a broad base andgently sloping sides. T his pyramid istypical of countries with high rates of birth and death. T he population can alsobe characterized as having a low median

age and high dependency ratio.


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Type 2, compared to Type 1,has a broader base and its

sides bow in much moresharply as they slant from the0-4 age group to the top. T hissecond type of pyramid istypical of countries that arebeginning to grow rapidlybecause of marked reductionin infant and child mortality,but are not yet reducing their

fertility. As a consequence of a rapidly increasingpopulation, the median age isdecreasing.


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T he third type of pyramid does

not resemble a pyramid at all,but an old-fashioned beehive.T his age-sex structure istypical of countries with levelsof birth and death rates found

in the Western Europeancountries. Because of the lowbirth rates, the median age ishighest and its dependencyratio is lowest compared withother age-sex structures. T hedependents are mostlyelderlies.


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T he fourth type of pyramid,a bell-shaped one, is atransitional type of pyramid.T his represents apopulation which, after more than 100 years of declining birth and deathrates, has reversed thetrend in fertility whilemaintaining the death rateat low levels.


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T he last type of populationpyramid represents a

population which isexperiencing a marked andrapid decline in fertility. If thisdecline continues, however,

the absolute loss in numberswill soon become apparent.T he population representedby this pyramid has usually alow death rate and asmentioned above, hasreduced its birth rate veryrapidly


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CONSEQUENCES/ EFFECTS OF AGECONSEQUENCES/ EFFECTS OF AGE AND SEX STRUCTURE AND SEX STRUCTURE

1. ConsumptionPatterns1. ConsumptionPatterns -- If the population has aIf the population has a

large proportion of children, there is a need forlarge proportion of children, there is a need forgreater spending on food and education. On thegreater spending on food and education. On theother hand, a large proportion of old personsother hand, a large proportion of old persons

necessitate greater spending for medical carenecessitate greater spending for medical careand social services.and social services.


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CONSEQUENCES/ EFFECTS OF AGE AND SEX STRUCTUREcontn.CONSEQUENCES/ EFFECTS OF AGE AND SEX STRUCTUREcontn.

2. Death rate is affected by age structure. A2. Death rate is affected by age structure. Ayounger population has a lower Crude Death Rate.younger population has a lower Crude Death Rate.

3. Migration rates. Young adults tend to be more3. Migration rates. Young adults tend to be moremobile than middle aged and elderly personsmobile than middle aged and elderly persons

4. Variations in age and sex structure affect the4. Variations in age and sex structure affect the

probabilities of marriage for men and womenprobabilities of marriage for men and women5. Power structure. An older population is usually5. Power structure. An older population is usually

more conservative.more conservative.


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OTHER IMPORTANT POPULATIONOTHER IMPORTANT POPULATION

CHARACTERISTICSCHARACTERISTICS1.1. Marital statusMarital status -- affects fertility and mortalityaffects fertility and mortalityrates. The greater the population of marriedrates. The greater the population of married

women, the higher the Crude Birth Rate.women, the higher the Crude Birth Rate.2.2. Religious compositionReligious composition

3.3. Lingual compositionLingual composition4.4. Economic compositionEconomic composition

5.5. Educational compositionEducational composition


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POPULATION ESTIMATIONPOPULATION ESTIMATION

Tools in Describing Change inPopulation SizeTools in Describing Change inPopulation Size

a. Natural Increasea. Natural Increase

= number of births= number of births --number of deathsnumber of deaths

b. Rate of Natural Increaseb. Rate of Natural Increase

= CBR= CBR -- CDRCDR


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c. Relative Increase inPopulation Size (RI)c. Relative Increase inPopulation Size (RI)

= Measures the % increase or decrease in= Measures the % increase or decrease inpopulation count relative to an earlier countpopulation count relative to an earlier count

PtPt PoPo

RI =RI = ------------------------------ x 100x 100

PoPo

Where:Where: Pt = population at present time, tPt = population at present time, t

Po = population at earlier time, oPo = population at earlier time, o


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d. Absolute increase in population per year (b)d. Absolute increase in population per year (b)

PtPt PoPo

b =b = ------------------------------ x 100x 100

tt

Where:Where:

t = no. of years betweent = no. of years between tim e otim e o andand tim e ttim e t


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e.e. Annual rate of growth (r)Annual rate of growth (r)= formula for= formula for rr

depends on the assumption takendepends on the assumption takenregarding the nature of the rate ofregarding the nature of the rate ofgrowth of the population per year.growth of the population per year.

This rate of growth takes on the assumptionThis rate of growth takes on the assumptionthat the population is changing at athat the population is changing at a

constant rate per year.constant rate per year.


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Types of EstimatesTypes of Estimatesand Projectionsand Projections

1. According to detail desired2. According to time reference3. According to Method of Estimation


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1. According to Detail Desired1. According to Detail Desired

a. Total population vs. populationa. Total population vs. populationsubgroupssubgroups

b. Population by selected characteristicsb. Population by selected characteristics(age and sex)(age and sex)

Examples: Estimate nos. of infantsExamples: Estimate nos. of infantsEstimate nos. of mothersEstimate nos. of mothers


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2. According to Time Reference2. According to Time Reference

a. Intercensal Estimatesa. Intercensal Estimates -- refersrefersto ato a date intermediate to twodate intermediate to twocensuses and take the results ofcensuses and take the results ofthese censuses into account.these censuses into account.


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b.b. Postcensal EstimatesPostcensal Estimates -- refers to a past orrefers to a past orcurrent date following a census and takescurrent date following a census and takesthat census and possibly earlier censusesthat census and possibly earlier censusesinto account, but not later censuses.into account, but not later censuses.

c.c. ProjectionsProjections -- refers to dates following the lastrefers to dates following the lastcensus for which no current reports arecensus for which no current reports areavailable.available.

The distinction between these two types are notThe distinction between these two types are notquite clearquite clear--cut.cut.


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3 . According to Method of Estimation3 . According to Method of Estimation

a.a. Component Method (InflowComponent Method (Inflow Outflow Method)Outflow Method)consists of adding natural increase and netconsists of adding natural increase and netmigration for the period since the last census tomigration for the period since the last census tothe latest count or the latest previous estimatethe latest count or the latest previous estimate

best implemented where continuous populationbest implemented where continuous populationregisters are maintainedregisters are maintained

Pt = Po + (BPt = Po + (B--D) + (ID) + (I--O)O)


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b.b. Mathematical MethodsMathematical Methods

1. Arithmetic Method1. Arithmetic Methodassumes an equal amount of increaseassumes an equal amount of increase

every yearevery year2. Geometric Method2. Geometric Method

assumes that the population increases orassumes that the population increases ordecreases at a constant rate, over eachdecreases at a constant rate, over eachunit of timeunit of time


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3. Exponential Method3. Exponential Methodassumes a constant rate of increaseassumes a constant rate of increaseor decrease, with the populationor decrease, with the populationsizesize changing continuously atchanging continuously atevery infinitesimal amount of timeevery infinitesimal amount of time

assumes population growing by theassumes population growing by theseconds.seconds.


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RATIORATIO-- is a relative number expressing the magnitude of oneis a relative number expressing the magnitude of oneoccurrence or condition in relation to another.occurrence or condition in relation to another.

Ex.1. Sex Ratio= N umber of Ma les x 1 00

Number of F ema les

2. Dependency Ratio= No. of p ers ons age d 0-14 + 65 y rs & over x 1 00

No. of p ers ons age d 15-64


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RATERATE-- refers to the occurrence of events over a given intervalrefers to the occurrence of events over a given intervalof time relative to the size of the population at risk of theof time relative to the size of the population at risk of theevent during the same time interval.event during the same time interval.

Ex.

Crude Birth Rate (CBR)= No. of l ive births in a yr . x F Average Pop ulati on


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It is necessary that theIt is necessary that the

numerator of the rate should benumerator of the rate should bedefined according to:defined according to:

1.1. the character of the event in question;the character of the event in question;2.2. the geographical area to which the event belongs;the geographical area to which the event belongs;

3.3. the time period within which it occurred.the time period within which it occurred.


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Events should be tabulated by:Events should be tabulated by:1.1. date of occurrence than by date of registrationdate of occurrence than by date of registration

2.2. by place of residence rather than by place of occurrenceby place of residence rather than by place of occurrence


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Important factors to consider inImportant factors to consider in

interpreting rate and ratio:interpreting rate and ratio:1. The source of the numbers that entered into the numerator and1. The source of the numbers that entered into the numerator and

denominator, how were they obtained?denominator, how were they obtained?

2. Do they represent an accurate count of the event under study?2. Do they represent an accurate count of the event under study?

3. What is the time period involved? A week? Month? Year?3. What is the time period involved? A week? Month? Year?


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4. Does the rate obtained after analysis measure what it is4. Does the rate obtained after analysis measure what it issupposed to measure?supposed to measure?

5. Is the magnitude of the rate reasonable in relation to what5. Is the magnitude of the rate reasonable in relation to whatone may expect the rate to be?one may expect the rate to be?


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Mortality RatesMortality Rates-- measures the probability of dyingmeasures the probability of dying

Different kinds of M ortality rates:

1. C rude Death Rate (CDR)= Total deaths, all causes x FAverage Population

- measure the decrease of thepopulation due to death, the force of mortality or the probability of dying


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Disadvantage:Disadvantage:

not a very useful method of comparing population groupsnot a very useful method of comparing population groupsthat are radically different in composition and may givethat are radically different in composition and may givemisleading conclusions.misleading conclusions.


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2. Cause2. Cause--ofof--death rate (CSDR)death rate (CSDR)== No. of deaths from a particular causeNo. of deaths from a particular cause x Fx F

AveragePopulationAveragePopulation

most causes of death rates arecomputed on total population, except

IM R and some age-specific rates.


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3. Specific Death Rate:3. Specific Death Rate:

- necessary to study in detail the mortalityconditions in a community

a)Age-specific-death rate

= Deaths, a ll causes in particu lar age gr p x F Average pop ulation of same age gr oup


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b) Age-and-sex specific death rate

= D eaths in partic . age & se x gr oup x F Average popn of same age & se x gr p.

c) Age-sex & cause-specific death rate

= D eaths f r om partic . cause in se x & age gr oup x F

Ave . pop n of same age & se x gr p


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4 . Proportionate Mortality rate4 . Proportionate Mortality rate-- this rate may be cause, age, sex, occupation etc.this rate may be cause, age, sex, occupation etc.

- used for describing the relative importance of different fatal diseases in the population,of different ages, sex, occupation, etc.

- can be calculated for specific age groupuseful for determining the order of importance of cause of death in differentage groups.

denominator: total death all causesdenominator: total death all causes


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Swaroops Index:

- the higher this rate the better is the hea lth status of the pop ulation

- this is a good indicat or in com paring the hea lth status of d iff erent countries, since it is ver y sim ple an d most of the informati on nee de d are a vai lab le .

tota l deaths 50 yrs old & ab ove

tota l death, a ll causes SI - X 100


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5 . Infant Mortality Rate (IMR)5 . Infant Mortality Rate (IMR)

==No. of deaths below 1 yrNo. of deaths below 1 yr x Fx FNo. of livebirthsNo. of livebirths

- one of the m ost sensiti ve in dices of the hea lth c ondition of the genera l

pop ulati on


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6 . Neonatal6 . Neonatal--Mortality Rate (NMR)Mortality Rate (NMR)

== No. of deaths below 28 daysNo. of deaths below 28 days x Fx F

Total livebirthsTotal livebirths

- deaths in this period are m ost lydue t o p renata l causes an d aremore diff icu lt to re duce than thepo st -ne onata l death rate


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7. Post7. Post--Neonatal Mortality Rate (PNMR)Neonatal Mortality Rate (PNMR)

== Infant deaths 28 days to


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9 . Perinatal Mortality Rate9 . Perinatal Mortality Rate== Fetal deaths, 28 wks & over gestation + infant deaths < 7 daysFetal deaths, 28 wks & over gestation + infant deaths < 7 days x Fx F

Total livebirthsTotal livebirths

= Deaths among women directly due topregnancy, labor & puerperium x FTotal livebirths

10 . Maternal Mortality Rate


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measure the risk of dying from causes associated with childbirthmeasure the risk of dying from causes associated with childbirth

ideal denominator in the number of women but since this number isideal denominator in the number of women but since this number isunknown, the number of livebirths has been adopted for practicalunknown, the number of livebirths has been adopted for practicalreasons.reasons.

caution must be exercised in comparing this rate from differentcaution must be exercised in comparing this rate from differentplaces.places.


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11. Case Fatality Rate11. Case Fatality Rate== No. of deaths from a particular diseaseNo. of deaths from a particular disease x Fx F

No. of cases of same diseaseNo. of cases of same disease

- mod if ied by the c ompleteness of both re po rte d cases an d d eaths .


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-- refers to diseases or sicknessrefers to diseases or sickness

Morbidity RatesMorbidity Rates


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Two genera l types of Mo rbidity R ates:

1. I nci dence Rate = N o. of N ew Cases of Dse. over a prd. of time x F

Population at risk- this is a broad term & the figures in the

numerator is usually obtained fromnotification during an interval of time,

usually a year and hence are usually

underenumerated


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2. Prevalence Ratio2. Prevalence Ratio

== No. of existing old & new cases at a point in timeNo. of existing old & new cases at a point in time x Fx FTotalPopulationTotalPopulation

- this is a static c ount of the number of

individua ls su ff ering f r om a particu lar diseasein a particu lar instant of time


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Fertility RatesFertility RatesMost commonly used of fertility rates are:Most commonly used of fertility rates are:

= No. of l ivebirths in a year x F Average Pop ulation

1. Crude Birth Rate (C BR)

this rate gives the number of livebirths re lative to the tota l pop ulationdata is a lwa ys a vai lab le wide ly use d


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2. General Fertility Rate (GFR)2. General Fertility Rate (GFR)

== No. of livebirths in 1 yearNo. of livebirths in 1 year x Fx F

No. of Women 15No. of Women 15--44 yrs44 yrs

- more appropriate measure of fertility


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PART 2

Relationships of Death Rates andProbability of Death, andDifferential in Mortality BetweenPopulations

Death Rate andProbability of Death Calculation :

Deriving probability of dying (nqx) from observed mortalityrate (nMx), using the actuarial method

Let n Dxt = D = Deaths in age group (x, x+n) in year t

n Pxt = P = Mid-point population in age

group (x, x+n) in year t


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n Mxt = M = Mortality rate in age group

(x, x+n) in year t

n Mxt = n Dxt / nPxt

Also assume that n Dxt are constant over

the years Deaths are linearly distributed

throughout the year

ect on


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Definition of Migration, Types of Migration,

and Estimation of Net Migration

Definitions

MoverA person who changes residence

MigrantA person who moves from one political area to

another- Non-migrantNon-movers and local movers


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Definitions cont

MigrationGeographic or spatialmobility involving a relatively permanentchange in usual residence betweenclearly defined political or statistical

units; has dimensions of time and space


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Definitions cont

In-migrantA person who moves in a political area within thesame country

ImmigrantAn international migrant who enters the areafrom a place outside the country

Out-migrantA person who moves out of a political areawithin the same country

EmigrantAn international migrant departing to anothercountry by crossing the international boundary


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Definition cont

Net Migration - In-migrants -Out-migrants

Net Immigration - Immigrants Emigrants

Note: Net migration for an area often includes bothinternational and internal migration

Gross MigrationIn-migrants + Out-migrants = Migrationturnover


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Definitions cont

Migration streamA group of migrants having a commonorigin and destination in a given migration period

Migration counterstreamIn opposite direction of stream

Estimating Net Migration


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Estimating Net MigrationResidual Method

Let I= Number of in-migrants

O = Number of out-migrants

P0 =Population at time 0

Pt = Population at time t

B = Number of birthsD = Number of deaths

DB)P(POI ot! DB)P(POI ot! DB)P(POI ot!


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Estimating Net Migration Residual Method cont

Estimates net migration as difference in population counts at

two time points and net vital events in-between, i.e.,subtracts an estimate of natural increase during the periodfrom the net change in population during the period.

Also known as the bookkeeping method or balancing equation

DB)P(POI ot!


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Estimating Net Migration Residual Method cont

Because the census counts and vital statistics are subject tounknown and usually differing degrees of error, the residualestimate of net migration may be in substantial error.

The relative error in net (in-) migration may be considerablewhen the amount of migration is small

The residual method can be used to estimate net migrationfor sex, race etc. .



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Estimating Net MigrationCohort-Component Method

Involves the calculation of estimates by age groups on thebasis of separate allowances for the components ofpopulation change.

Estimates net migrants as the difference between actualpopulation at time tand the population at time 0survived

to time t(must do age-specific and then add)



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Estimating Net MigrationCohort-Component Method cont

Survival rates are used instead of death rates because thecompilation of death statistics is often laborious, even whenbasic statistics on death are available

Let = Population in age group aat time 0

=Population in age (group) a+t at time t

s = Life table survival ratio =

O

aP

t

taP

a

ta

L

L

Three Ways of Estimating Net


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Three Ways of Estimating NetMigration

Forward estimate oa

t

ta1sPPM !

o

asP

Age

a + t

t

taP

O ta

C


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Cont

Reverse estimate

o

asP

Age

a + t

t

taP

O ta

o

a

t

2P-

s

PM

t a

!

No te that M2 > M1

C


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Cont

Average estimate

2M 21

3

M M !

F d E i i


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Forward Estimation

All migrants come at the end of the time

interval (or, none of the migrants die for theperiod between time 0and t)

R E i i


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Reverse Estimation

All migrants come at the beginning of the

time interval (or, all migrants are subjectedto populations mortality for the entireperiod between time 0and t)

A E i i


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Average Estimation

All migrants come at the middle of the time

interval (or, all migrants are subjected topopulations mortality for the half of theperiod between time 0and t)

C l l ti th E ti t


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Calculating the Estimates

When calculating the estimates, it is important to

remember that the survival rates for children bornduring the period are of a different form from thosefor the older ages, i.e., for the case of five yearsbetween population counts:

C h t C t M th d


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Cohort-Component Method

Does not require accurate vital statistics but does require a lifetable.

This method yields estimates of net migration by age and sex withoutnearly as much labour as is involved in the use of deaths by age

Unlike the residual method, none of the variants of the cohort-component method measure net migration exactly even when thereare no errors in the underlying population and vital statistics

C t


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Cont

The average estimate implies a more meaningful assumptionregarding the timing of net migration than does either theforward or reverse method

E ti ti g N t Mig ti


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The amount of difference between the migration estimatesfrom the forward and reverse methods depends on theamount of net migration and on the level of the survival rate

S


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Summary

Migration is an important element in the growth of thepopulation and the labour force of an area.

International and internal are the two broad types ofmigration.

Many indicators have been developed to measuremigration under its multiple facets

ect onIndicators and Wa s of


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Indicators and Ways of

Studying Migration

Crude In Migration Rate


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Crude In-Migration Rate

Crude In-Migration RateNumber of in-migrants

per 1,000 populationI * 1000P

Crude Out Migration Rate


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Crude Out-Migration Rate

Crude Out-Migration RateNumber of out-migrantsper 1,000 population

O * 1000P

Crude Net Migration Rate


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Crude Net Migration Rate

Crude Net Migration RateDifference between

the number of in-migrants and the number ofout-migrants per 1,000 population.

( I O ) * 1000

P

Specific Rates


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Specific Rates

Let Ma = Number of in-migrants (or out-migrants) in agegroup a

Pa = Midyear population in age group

Ms = Number of in-migrants (or out-migrants) of sex s

Ps = Midyear population of sex s

Age Specific Migration Rates


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Age-Specific Migration Rates

Age-Specific Migration RatesNumber ofmigrants of age group a per 1,000 population ofage group a

Ma * 1000

Pa

Sex Specific Migration Rates


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Sex-Specific Migration Rates

Sex-Specific Migration RatesNumber of

migrants of sex sper 1,000 population of sexs

Ms * 1000

Ps

Ratios


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Ratios

Various types of ratios can be computed to indicate therelative magnitude of in-migration, out-migration, netmigration, and gross migration to or from a country:

Let I = Number of in-migrants

O = Number of out-migrants

I+O = Gross migration

I-O = Net migration

Ratios cont


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Ratios cont.

Ratio of out-migration to in-migration = magnitude of out-migration compared to in-migration

O

..

I

Ratios cont


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Ratios cont

Ratio of net migration to in-migration

I O. Where I > O

I

Ratios cont


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Ratios cont

Ratio of net (out-) migration to out-migration

O I

..

O where O > I

Ratios cont


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Ratios cont

Ratio of in-migration to gross migration = magnitude of in-migration to the overall migration movement.

I

..

I + O

Ratios cont


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Ratios con t

Ratio of out-migration to gross migration = magnitude of out-migration to the overall migration movement

O

..

I + O

Ratios cont


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Ratios con t

Ratio of net migration to gross migration = migrationeffectiveness (magnitude of the effective addition [or loss]through migration to the overall gross movement)

I O

..

I + O

Partial Migration Rate


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LetIij= Number of in-migrants to area ifrom area j

Oij = Number of out-migrants from area i to area j

Iij = Oji (by definition)

Also letPi = Midyear population in area i

P j = Midyear population in area j



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Partial Migration RateNumber of migrants to an area froma particular origin, or from an area to a particulardestination, per 1,000 of the population at either origin ordestination.

Summary


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Summary

Migration is an important element in the growth of thepopulation and the labour force of an area.

International and internal migration are the two broadtypes of migration.

The measurement and analysis of migration areimportant in the preparation of population estimates andprojections

LIFE TABLE


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LIFE TA BLE

The life table is another and effective way of expressing thedeath rates experienced by a population during a chosenperiod of time.


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Thank YouThank YouandandGod Bless!God Bless!

Applied Maths Presentation 2010

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Transcript of Applied Maths Presentation 2010