basic statistics power point presentation 13 march

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    STATISTICSSTATISTICS

    StatisticsStatisticsis a field of study concern with:is a field of study concern with:

    Framing of questions to be answered by collecting dataFraming of questions to be answered by collecting data

    Designing of all relevant data is to be collectedDesigning of all relevant data is to be collected Summarization of data (Frequency Distribution)Summarization of data (Frequency Distribution) Analysis of dataAnalysis of data Draw conclusion, drawing of conclusion of dataDraw conclusion, drawing of conclusion of data resentation of conclusion!resentation of conclusion!

    ORORStatisticsStatistics is the science of ma"ing effective use ofis the science of ma"ing effective use ofnumerical data relating to grou#s of individuals ornumerical data relating to grou#s of individuals ore$#eriments! %t deals with all as#ects of this, includinge$#eriments! %t deals with all as#ects of this, includingnot only the collection, analysis and inter#retation ofnot only the collection, analysis and inter#retation ofsuch data, but also the #lanning of the collection ofsuch data, but also the #lanning of the collection ofdata, in terms of the design of surveys anddata, in terms of the design of surveys and

    e$#eriments!e$#eriments!

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    DISCRIPTIVE STATISTICSDISCRIPTIVE STATISTICS

    Descriptive StatisticsDescriptive Statisticsdeals withdeals withcollection of data ,its #resentation in variouscollection of data ,its #resentation in variousforms, such asforms, such as tables, gra#hs and diagramstables, gra#hs and diagramsand finding averages and other measuresand finding averages and other measures

    which would describe the data! &he #ur#osewhich would describe the data! &he #ur#oseof descri#tive statistics is to #resent theof descri#tive statistics is to #resent the

    information in such a way as can readily hel# theinformation in such a way as can readily hel# thedecision ma"ers!decision ma"ers!

    '$am#le:'$am#le:AA BIOSTATISTICIANBIOSTATISTICIANma"e use of descri#tive statistics inma"e use of descri#tive statistics in

    #resenting their annual re#orts!#resenting their annual re#orts!

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    INFERENTIAL STATISTICSINFERENTIAL STATISTICS

    Inferential StatisticsInferential Statistics is the branch ofis the branch of

    statistics which deals with #rocedure ofstatistics which deals with #rocedure ofdrawing inferences about the #o#ulationdrawing inferences about the #o#ulationon the basis of information obtain fromon the basis of information obtain fromsam#le!sam#le!

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    POPULATION & SAMPLEPOPULATION & SAMPLE

    Population:Po

    pulation:

    A statistical #o#ulation is defined as the aggregate orA statistical #o#ulation is defined as the aggregate ortotality of all individual members or obects* whethertotality of all individual members or obects* whether

    finite or infinite, relevant to some characteristics offinite or infinite, relevant to some characteristics ofinterest!interest!

    Sample:Sam

    ple:

    %t is a small #art of #o#ulation which re#resents the%t is a small #art of #o#ulation which re#resents thecharacteristics of o#ulation!characteristics of o#ulation!

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    VARIABLE & CONSTANTVARIABLE & CONSTANT

    Variable:Variable:

    A measurable quantity which can vary from one individual orA measurable quantity which can vary from one individual orobect to another is called a obect to another is called a Variable.Variable.

    Example:Example: heights and weights of individuals, no ofheights and weights of individuals, no ofchildren in a family!children in a family!

    ConstantConstant::

    A quantity which can assume only one value is called aA quantity which can assume only one value is called a++!"#a!#!"#a!#!!

    Example":Example": - .!/0/12,e - 3!4/535, etc! - .!/0/12,e - 3!4/535, etc!

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    DISCRETE & CONTINUOUSDISCRETE & CONTINUOUS

    VARIABLESVARIABLESDiscrete Variable:Discrete Variable:

    A variable which can assume only some s#ecific values withinA variable which can assume only some s#ecific values withina given range is called a a given range is called a Di"$re#e VariableDi"$re#e Variable!!

    Example:Example:no of children in a family can beno of children in a family can be6,/,3,7but cannot be 3!1 or .!50!6,/,3,7but cannot be 3!1 or .!50!

    Continuous Variable:Continuous Variable:

    A variable which can assume any value within a given range isA variable which can assume any value within a given range iscalled a called a C!#i!%%" Variable.C!#i!%%" Variable.

    Example:Example: heights and weights of individualsheights and weights of individuals ..

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    UANTITATIVEUANTITATIVE& UALITATIVE& UALITATIVEVARIABLESVARIABLES

    Quantitative Variable:Quantitative Variable:

    A variable is called is called aA variable is called is called a '%a!#i#a#i(e Variable'%a!#i#a#i(e Variablewhen a characteristic can be e$#ressed numericallywhen a characteristic can be e$#ressed numerically

    such assuch as a)e* +ei),#* ! - "#%e!#"* e#$.a)e* +ei),#* ! - "#%e!#"* e#$.

    Qualitative Variable:Qualitative Variable:

    %f the characteristic is non8numerical such as education,%f the characteristic is non8numerical such as education,

    se$, eye8color, quality, satisfaction etc! the variable isse$, eye8color, quality, satisfaction etc! the variable isreferred to as areferred to as a '%ali#a#i(e Variable.'%ali#a#i(e Variable.

    A qualitative characteristic is also called anA qualitative characteristic is also called an 'A##rib%#e.'A##rib%#e.

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    PRIMAR/ & SECONDAR/ DATAPRIMAR/ & SECONDAR/ DATA

    Primary Data:Primary Data:

    Data that have been originally collected(raw data) and haveData that have been originally collected(raw data) and havenot undergone any sort of statistical treatment, are callednot undergone any sort of statistical treatment, are called

    Primar0 Da#a.Primar0 Da#a.

    Secondary Data:Secondary Data:

    Secondary data are a sequence of observations that haveSecondary data are a sequence of observations that have

    undergone any sort of treatment by statistical methods atundergone any sort of treatment by statistical methods atleast once, i!e! the data have been collected, classified,least once, i!e! the data have been collected, classified,tabulated or #resented in some form for a certain #ur#ose ,tabulated or #resented in some form for a certain #ur#ose ,are called are called Se$!ar0 Da#a.Se$!ar0 Da#a.

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    TABULATIONTABULATION

    A table is a systematic arrangement of dataA table is a systematic arrangement of data

    into vertical columns and horizontal rows!into vertical columns and horizontal rows!&he #rocess of arranging data into rows and&he #rocess of arranging data into rows and

    columns is called columns is called Tab%la#i!Tab%la#i!9!9!

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    FREUENC/ DISTRIBUTIONFREUENC/ DISTRIBUTION

    A Frequency Distribution is a tabularA Frequency Distribution is a tabular

    arrangement of the data which shows thearrangement of the data which shows thedistribution of observations among differentdistribution of observations among different

    classes!classes!

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    ExampleExample

    &he birth weights("g) of .6&he birth weights("g) of .6

    children were recorded as follows:children were recorded as follows:

    3!6,3!/,3!.,.!6,.!/,3!4,3!5,0!6,3!.,3!6,3!/,3!.,.!6,.!/,3!4,3!5,0!6,3!.,

    .!1,0!3, .!4,.!3,3!4,.!/,.!6,3!2,3!5,.!1,0!3, .!4,.!3,3!4,.!/,.!6,3!2,3!5,

    3!2,.!1,0!/,.!1,.!1,.!4,3!1,3!4,.!5,3!2,.!1,0!/,.!1,.!1,.!4,3!1,3!4,.!5,

    .!2,3!5,3!3!.!2,3!5,3!3!

    +onstruct Frequency Distribution+onstruct Frequency Distribution n - .6n - .6

    ;ange - o of classes

    h - 3!3 @ -h - 3!3 @ - 6!06!0

    Classes Tally Mark Freuency

    3!6 8 3!. %%%% 1

    3!0 = 3!4 %%%% 0

    3!5 = .!/ llll llll /6

    .!3 = .!1 %%%% 0

    [email protected] = .!2 %%%% 0

    0!6 = 0!. %%% .

    &otal .6

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    C1ARTS OR DIA2RAMC1ARTS OR DIA2RAM

    Bi"e gra#hs, charts or diagram give visualBi"e gra#hs, charts or diagram give visualre#resentations of magnitudes, trends andre#resentations of magnitudes, trends and#atterns in the data! Diagrams also show#atterns in the data! Diagrams also show

    com#arisons between two or more sets of data!com#arisons between two or more sets of data!M"# $mm!l0 $,ar#" %"e i! S#a#i"#i$":M"# $mm!l0 $,ar#" %"e i! S#a#i"#i$":

    C Sim#le ar +hartSim#le ar +hartC

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    Simple Bar C,ar#Simple Bar C,ar#

    ExampleExample

    Country Population!million"

    +hina /655

    %ndia 5/@

    %ndonesia /41

    Ea#an /3.

    a"istan /[email protected]

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    M%l#iple Bar C,ar#M%l#iple Bar C,ar#

    ExampleExample

    Division Male Female

    ;awal#indi 3. 3/

    ahawal#ur 30 3.

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    Pie C,ar#Pie C,ar#

    ExampleExampleAll [email protected] Districts of unabAll [email protected] Districts of unab

    have re#orted inhave re#orted in>ovember, 3662>ovember, 3662

    Facilities Percenta#e

    ;e#orted 54

    >on;e#orted

    /.

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    Mea"%re" - Ce!#ral Te!e!$0Mea"%re" - Ce!#ral Te!e!$0

    rrA(era)eA(era)e

    A value which is used in this way to re#resentA value which is used in this way to re#resent

    the distribution is called anthe distribution is called an 'A(era)e.'A(era)e.Since theSince theaverages tend to lie in the centre of a distributionaverages tend to lie in the centre of a distributionthey are calledthey are called 'Mea"%re" - Ce!#ral Te!e!$0.'Mea"%re" - Ce!#ral Te!e!$0.

    &hey are also called measures of location&hey are also called measures of locationbecause they locate the centre of a distribution!because they locate the centre of a distribution!

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    T0pe" - A(era)e"T0pe" - A(era)e"

    &he most commonly used averages are:&he most commonly used averages are:

    (i)(i)&he Arithmetic

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    Ari#,me#i$ Mea!Ari#,me#i$ Mea!

    &he &he Ari#,me#i$ Mea!Ari#,me#i$ Mea! ororsim#ly mean is definedsim#ly mean is definedas a value obtained byas a value obtained bydividing the sum of all thedividing the sum of all the

    observations by theirobservations by theirnumber, that isnumber, that is

    Example:Example:

    &he weights ("g) of 2&he weights ("g) of 2students are given below:students are given below:

    01,.3,.4,[email protected],.2,[email protected],0/,05,[email protected]!01,.3,.4,[email protected],.2,[email protected],0/,05,[email protected]!

    +alculate the

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    Meia!Meia!

    &he &he Meia!Meia!9 of a set of values9 of a set of valuesarranged in ascending orarranged in ascending ordescending order of magnitudedescending order of magnitudeis defined as the middle valueis defined as the middle valueif the number of values is oddif the number of values is oddand the mean of the twoand the mean of the twomiddle values if the number ofmiddle values if the number ofvalues is even! &he medianvalues is even! &he mediandivides a distribution into twodivides a distribution into twohalves and the number ofhalves and the number of

    values greater than the medianvalues greater than the medianis equal to the number ofis equal to the number ofvalues smaller than thevalues smaller than themedian!median!

    Example:Example:a)a) 0,1,@,0,1,@,55,/6,//,/3,/6,//,/3

    Ghen the number of values isGhen the number of values is, the median is the middle, the median is the middle

    value that is 5!value that is 5!

    b)b) Ghen the number of values isGhen the number of values ise(e!e(e!, the median is the mean, the median is the meanof the two middle values i!e!of the two middle values i!e!

    Meia! 3Meia! 3 4567845678 33 99

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    MeMe

    &he&he'Me'Me is defined asis defined asa value which occursa value which occurs

    most frequently in a set ofmost frequently in a set ofdata, that is it indicatesdata, that is it indicatesthe most common result!the most common result!

    Example"Example"::

    &he observations are&he observations are

    (i) /,3,.,0,.,1(i) /,3,.,0,.,1&he mode is .&he mode is .

    (ii) 3,0,0,@,@,4(ii) 3,0,0,@,@,4

    &he mode is 0 and @&he mode is 0 and @

    (iii) 3,0,@,5,/6(iii) 3,0,@,5,/6

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    Varia!$e a! S#a!ar De(ia#i!Varia!$e a! S#a!ar De(ia#i!

    Variance:Variance:

    &he &he Varia!$eVaria!$e of aof aset of observations isset of observations is

    defined as the meandefined as the meanof the squares ofof the squares ofdeviations of all thedeviations of all theobservations fromobservations fromtheir mean!their mean!

    Formula:Formula:

    Standard Deviation:Standard Deviation:

    &he #ositive square&he #ositive squareroot of the variance isroot of the variance is

    calledcalled 'S#a!ar'S#a!arDe(ia#i!.De(ia#i!.

    Formula:Formula:

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    VITAL STATISTICSVITAL STATISTICS

    &here are some factors which cause changes inthe size and com#osition of human #o#ulation,e!g!, births add and deaths ta"e away some

    member of the #o#ulation! Such factors arecalled Vi#al E(e!#", and they include births,deaths, migrations (which change the size of the#o#ulation), sic"ness, etc! (which affect the

    #o#ulation com#osition)! &he collection,#resentation and analysis of vital eventsconstitute Vi#al S#a#i"#i$"9!

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    Per$e!#a)ePer$e!#a)e

    A #ercentage is sim#ly another way ofA #ercentage is sim#ly another way ofe$#ressing a fraction! %n #ercentage, the basee$#ressing a fraction! %n #ercentage, the base(denominator) is always /66! ercentage(denominator) is always /66! ercentage

    means #er /66!means #er /66! &o turn a fraction into a #ercentage it should be&o turn a fraction into a #ercentage it should be

    multi#lied by /66! For e$am#le:multi#lied by /66! For e$am#le:

    /1/1 -- /1 $ /66/1 $ /66 - 36H- 36H

    /./. -- /. $ /66 - ..!.H/. $ /66 - ..!.H

    // -- / $ /66/ $ /66 - /66H- /66H

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    Ra#e" a! Ra#i"Ra#e" a! Ra#i"

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    Ra#e

    A rate is a ty#e of ratio which in vital statistics may be defined as aA rate is a ty#e of ratio which in vital statistics may be defined as anumerical #ro#ortion of the number of vital events to the #o#ulationnumerical #ro#ortion of the number of vital events to the #o#ulationin which the events too" #lace! %n other words,in which the events too" #lace! %n other words,

    Rates $ aRates $ aa %ba %b

    where IaJ stands for the no of times the given vital event occurs, andwhere IaJ stands for the no of times the given vital event occurs, and

    IIbJ is the number of times, the event which does not occur!bJ is the number of times, the event which does not occur!

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    Cr%e Dea#, Ra#eCr%e Dea#, Ra#e

    &he crude death rate may be defined as a ratio of total&he crude death rate may be defined as a ratio of totalregister deaths of sum s#ecified year to the total midyearregister deaths of sum s#ecified year to the total midyear#o#ulation in the same year, multi#lied by thousands!#o#ulation in the same year, multi#lied by thousands!

    C&D&R $C&D&R $ DD ' ()))' ()))

    PP

    where IDJ denotes the total no of death from all causeswhere IDJ denotes the total no of death from all causes

    during a calendar year, andduring a calendar year, andIIJ denotes the midyear total #o#ulation during the sameJ denotes the midyear total #o#ulation during the sameyear!year!

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    ExampleExample

    +!;!D of the local o#ulation is+!;!D of the local o#ulation is

    +!D!; - @4 1666 -+!D!; - @4 1666 - /.!0/.!0

    *+, +RO-P.,*RS /OC*/POP-/*T0O1 1O OF D,*T2S01 /OC*/POP-/*T0O1

    682 066 /@

    /68/2 /166 @

    36812 3066 [email protected] 466 3/

    &otal 1666 @4

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    I!-a!# Mr#ali#0 Ra#eI!-a!# Mr#ali#0 Ra#e

    %t is defined as a ratio of registered deaths of infants during a%t is defined as a ratio of registered deaths of infants during as#ecified year to the total live births registered in the sames#ecified year to the total live births registered in the sameyear!year!

    0&M&R $0&M&R $ d)d) ' ()))' ()))

    33

    where do9 denotes the no of deaths under one year of agewhere do9 denotes the no of deaths under one year of ageregistered during a given year in a locality, andregistered during a given year in a locality, and

    9 denotes the no of life births registered during the same9 denotes the no of life births registered during the sameyear in the locality!year in the locality!

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    Ma#er!al Mr#ali#0 Ra#e 4MMR8Ma#er!al Mr#ali#0 Ra#e 4MMR8

    MMRMMRis the number of deaths assigned to causesis the number of deaths assigned to causesrelated to #regnancy (maternal deaths) during arelated to #regnancy (maternal deaths) during agiven year #er /666 live births re#orted during thegiven year #er /666 live births re#orted during the

    same year in a given area (country, region, orsame year in a given area (country, region, ordistrict)!district)!

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    Cr%e Bir#, Ra#eCr%e Bir#, Ra#e

    %t is a ratio of total registered live births during a%t is a ratio of total registered live births during acalendar year to the total midyear #o#ulation duringcalendar year to the total midyear #o#ulation duringthe same year and multi#lied by /666! it is com#utedthe same year and multi#lied by /666! it is com#utedby the formulaby the formula

    C&3&R $C&3&R $ 33 ' ()))' ()))

    PP

    where 9 denotes the total no of live births registeredwhere 9 denotes the total no of live births registeredduring a given year, andduring a given year, and

    9 denotes the midyear total #o#ulation during the9 denotes the midyear total #o#ulation during thesame year!same year!

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    +ontinue+ontinue

    0ncidence Rate:0ncidence Rate:

    A rate calculated as the number of incidence cases over a defineA rate calculated as the number of incidence cases over a definestudy #eriod divided by the #o#ulation at ris" at mid #oint of thatstudy #eriod divided by the #o#ulation at ris" at mid #oint of that#eriod!#eriod!

    Incidence RateIncidence Rate $$ 1o o4 ne8 cases durin# a speci4ied time1o o4 ne8 cases durin# a speci4ied timeTotal mid period population at riskTotal mid period population at risk

    Prevalence Rate:Prevalence Rate:

    &he #ro#ortion of a #o#ulation that has a defined disease or&he #ro#ortion of a #o#ulation that has a defined disease orcondition at a #articular #oint in time!condition at a #articular #oint in time!

    Point Prevalence RatePoint Prevalence Rate $$ 1o o4 e'istin# cases at a speci4ied point in time1o o4 e'istin# cases at a speci4ied point in time

    Total mid year populationTotal mid year population

    Period Prevalence RatePeriod Prevalence Rate $$ 1o o4 e'istin# cases at a speci4ied period in time1o o4 e'istin# cases at a speci4ied period in time

    Total mid year populationTotal mid year population

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    Ra#iRa#i

    &he ratio of one number, a9 to another number c9 is defined bya divided by c9! %t thus indicates the relative size of twomembers!

    Ratio $ a

    c

    IaJ denotes the number of times the given "ind of event occurs,and

    IcJ denotes the number of times and another event occurs!

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    Impr#a!# #0pe - Ra#i" i!Impr#a!# #0pe - Ra#i" i!

    Vi#al S#a#i"#i$"Vi#al S#a#i"#i$"

    /)/) Se$ ;atioSe$ ;atio3)3) +hild8 woman ;atio+hild8 woman ;atio

    .).) irth8death ratioKital inde$irth8death ratioKital inde$

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    Sex Ra#iSex Ra#i

    &he ratio between males and females in a human&he ratio between males and females in a human#o#ulation, is called a #o#ulation, is called a Sex Ra#iSex Ra#i! %t is com#uted by! %t is com#uted by

    dividing the number ofdividing the number ofmale"male"

    in a #o#ulation by the numberin a #o#ulation by the numberofof -emale"-emale" in the same #o#ulation and the result isin the same #o#ulation and the result ise$#ressed in H!e$#ressed in H!

    %t is com#uted by the formula:%t is com#uted by the formula:

    Se' Ratio $Se' Ratio $ 1o o4 Males1o o4 Males ' ())' ())

    1o o4 Females1o o4 Females

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    C,il;

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    Bir#,;Dea#, Ra#iBir#,;Dea#, Ra#i

    OROR

    Vi#al I!exVi#al I!ex

    &he ratio between the total number of births and the total&he ratio between the total number of births and the totalnumber of deaths of a #o#ulation during a #articular year isnumber of deaths of a #o#ulation during a #articular year iscalled called Bir#,;Dea#, Ra#iBir#,;Dea#, Ra#i or Kital %nde$!or Kital %nde$!

    %t is com#uted by the formula:%t is com#uted by the formula:

    Vital 0nde' $ Total 1o o4 3irt5s ' ())

    Total 1o o4 Deat5s

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    I!i$a#r"I!i$a#r"

    %ndicators are items which can be measured to%ndicators are items which can be measured toindicate9 how your #rogramme is doing!indicate9 how your #rogramme is doing!Lou will learn to calculate the following indicators:Lou will learn to calculate the following indicators:

    Antenatal coverageAntenatal coverage Average number of visits #er new caseAverage number of visits #er new case

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    I!i$a#r" $!#=I!i$a#r" $!#=

    To calculate the antenatal coverage, use the formulaTo calculate the antenatal coverage, use the formula

    No. of new antenatal attendeesNo. of new antenatal attendees x 100x 100

    No. of estimated birthsNo. of estimated births

    This tells you the % of pregnant women who received antenatal care.This tells you the % of pregnant women who received antenatal care.

    Example:Example: 241 estimated births last year. 110 new antenatal241 estimated births last year. 110 new antenatal

    registrations.registrations.

    AnswerAnswer 110110 ! 100 " 4#% of pregnant women received! 100 " 4#% of pregnant women received

    241241 antenatal careantenatal care

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    I!i$a#r" $!#=I!i$a#r" $!#=

    &o calculate the average number of visits by #atients,&o calculate the average number of visits by #atients,use the formulause the formula

    1o& o4 total visits !ne8 % old"1o& o4 total visits !ne8 % old" ' ()) ' ())

    1o& o4 ne8 cases1o& o4 ne8 cases

    &his tells you how many times a #atient comes to a&his tells you how many times a #atient comes to ahealth facility for one e#isode of illness!health facility for one e#isode of illness!

    ExampleExample: //6 new cases, 366 old cases!: //6 new cases, 366 old cases!

    Answer:Answer: 110 + 200110 + 200 x 100 x 100

    110110

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    I!i$a#r" $!#=I!i$a#r" $!#=

    &o calculate the measles incidence rate, use&o calculate the measles incidence rate, usethe formulathe formula

    1o& measles cases1o& measles cases ' ()) ' ()) PopulationPopulation

    &his tells you how many #eo#le, out of each&his tells you how many #eo#le, out of each/666 had measles!/666 had measles!