Statistics and statistical methods pdf.

Statistic

1. STATISTICS
INTRODUCTORY CONCEPTS

2. STATISTICS AND STATISTICAL
METHODS
Statisticsisabodyofknowledgethatdealswiththe
collection,presentation,analysisandinterpretationof
numericalandcategoricaldata.
Statisticalmethodsreferstotheproceduresusedinthe
collection,presentation,analysisandinterpretationofdata.

3. WHY STUDY STATISTICS?
Thefieldofstatisticsisthescienceoflearningfromdata.
Statisticalknowledgehelpsyouusethepropermethodsto
collectthedata,employthecorrectanalyses,andeffectively
presenttheresults.Statisticsisacrucialprocessbehindhowwe
makediscoveriesinscience,makedecisionsbasedondata,and
makepredictions.Statisticsallowsyoutounderstandasubject
muchmoredeeply.

4. TWO AREAS OF STATISTICS
DescriptiveStatisticscomprisesstatisticalmethodsconcerned
withcollectinganddescribingasetofdatasoastoyield
meaningfulinformation.
InferentialStatisticscomprisesstatisticalmethodsconcerned
withtheanalysisofasubsetofdataleadingtopredictionsor
inferencesabouttheentiresetofdata.

5. POPULATION AND SAMPLE
Populationconsistsofthetotalityofobservationwhichweareconcerned
about.
Sampleisasubsetofagivenpopulation.
Parameterreferstoanynumericalvaluedescribingacharacteristicofa
population.
Statisticreferstoanynumericalvaluedescribingacharacteristicofa
sample.

6. EXAMPLE
Situation:TherearetwelvemajorsuppliersofCalamansifruitacross
Region8.Theyweresurveyed,anddataontheamountoftheirmonthly
Calamansifruitsupplyforthepastsevenyearsweregatheredfromeach
supplier.Thefollowingwerepartoftheresultsofthesurvey:
a.Theaveragemonthlysupplyofthetwelvemajorsuppliersforthepast
sevenyearsis24.90thousandmetrictons.
b.Thetop1supplierisSupplierCwhoseaveragemonthlysupplyforthe
pastsevenyearsis6.80thousandmetrictons.
c.TherewillbeanincreaseofCalamansifruitsupplybythemajor
suppliersinthecomingyears.

7. EXAMPLE
Whatcomprisesthepopulation?
MonthlyamountofCalamansifruitsupplyforthepastsevenyears
ofeachofthetwelvemajorsuppliers
Giveasamplementionedinthegivensituation.
MonthlyamountofCalamansifruitsupplyforthepastsevenyears
ofSupplierC
Giveanexampleofparameter.
Averagemonthlysupplyofthetwelvesuppliersforthepastseven
years(24.90thousandmetrictons)

8. EXAMPLE
Giveanexampleofstatistic.
AveragemonthlysupplyofSupplierCforthepasttwelveyears
(6.80thousandmetrictons)

9. VARIABLE AND CONSTANT
Variableisacharacteristicofobjectsorindividualsthatcantakeon
differentvaluesfordifferentmembersofthegroupunderstudy.
Example:IQ,heightandweightofall10-yearoldfemalechildren
inaparticularbarangay
Constantisacharacteristicthatassumesthesamevalueforall
membersofthegroup.
Example:Age,sexandhomeaddressofall10-yearoldfemale
childreninaparticularbarangay

10. TYPES OF VARIABLES
QuantitativeVariableisavariablethattakesonlynumericalvalues.
Example:I.Q.,height,weight,incomeandage
QualitativeVariableisavariablethattakesonlynon-numerical
values,andnumbersareusedonlyascategories
Example:Gender,sex,religion,yearlevel,educationalattainment
andoccupation

11. TYPES OF VARIABLE ACCORDING TO
LEVEL OF MEASUREMENT
Nominal–numbersareusedmerelyaslabelsofthecategoriesof
thevariable
Ex.sex,religion,andoccupation
Ordinal–havethesamecharacteristicwithanominalvariableand
inaddition,thenumberscanbemeaningfullyranked
Ex.economicstatus,yearlevel,andsalarygrade
Interval–havethesamecharacteristicwithanordinalvariableand
inaddition,thecategoriesintheintervalscalearedefinedinterms

12. TYPES OF VARIABLE ACCORDING TO
LEVEL OF MEASUREMENT
ofa“standardunitofmeasurement”sothatequalityofdifferences
betweensuccessivecategoriesofthescaleisdefined
Ex.temperatureinDegreeCelsiusandIQscore
Ratio–havethesamecharacteristicwithanintervalvariableandin
addition,ithasatruezeropoint
Ratioandintervalvariablearewhatyoucallscalevariableswhile
ordinalandnominalvariablearecategoricalvariables.
Ex.age,height,andnumberofsiblings

13. FREQUENCY DISTRIBUTION
Itisatabulararrangementofdataindicatingthedifferentclasses
orcategoriesandthecorrespondingfrequencies.
Therearethreebasictypesoffrequencydistributions.Thethree
typesarecategorical,ungroupedandgroupedfrequency
distributions.

14. CATEGORICAL FREQUENCY
DISTRIBUTION
Thecategoricalfrequencydistributionisusedfordatathatcanbe
placedinspecificcategories,suchasnominal-orordinal-leveldata.
Forexample,datasuchaspoliticalaffiliation,religiousaffiliation,or
majorfieldofstudy.

15. EXAMPLE
Twenty-fivearmyinducteesweregivenabloodtesttodetermine
theirbloodtype.Thedatasetisasfollows:
RAW DATA OF BLOOD TYPE
A B B AB O
O O B AB B
B B O A O
A O O O AB
AB A O B A

16. EXAMPLE
Blood Type Tally Total %
A 5 25 20%
B 7 25 28%
O 9 25 36%
AB 4 25 16%

17. UNGROUPED FREQUENCY
DISTRIBUTION
Anungroupedfrequencydistributionisusedfornumerical
dataandwhentherange(thedifferencebetweenthehighest
andthesmallestvalues)issmall.

18. EXAMPLE
Considerthefollowingtable,whichliststhenumberoflaptopcomputersowned
byfamiliesineachof40homesinasubdivision.

19. EXAMPLE
Considerthefollowingtable,whichliststhenumberoflaptopcomputersowned
byfamiliesineachof40homesinasubdivision.
No. of Laptops Tally Total %
0 5 40 12.5
1 12 40 30
2 14 40 35
3 3 40 7.5
4 2 40 5
5 3 40 7.5
6 0 40 0
7 1 40 2.5

20. EXAMPLE
Considerthefollowingtable,whichliststhenumberoflaptopcomputersowned
byfamiliesineachof40homesinasubdivision.
No. of Laptops Frequency Percentage
0 5 12.5
1 12 30
2 14 35
3 3 7.5
4 2 5
5 3 7.5
6 0 0
7 1 2.5
N=30 100

21. GROUPED FREQUENCY
DISTRIBUTION
Whentherangeofthedataislarge,thedatamustbegroupedintoclassesthat
aremorethanoneunitinwidth.
Toconstructafrequencydistribution,followtheserules:
1.Thereshouldbebetween5and20classes.
2.Theclasswidthshouldbeanoddnumber.Thisensuresthatthemidpointof
eachclasshasthesameplacevalueasthedata.
3.Theclassesmustbemutuallyexclusive.Mutuallyexclusiveclasseshave
nonoverlappingclasslimitssothatdatacannotbeplacedintotwoclasses.
4.Theclassesmustbecontinuous.Thereshouldbenogapsinafrequency
distribution.

22. GROUPED FREQUENCY
DISTRIBUTION
Whentherangeofthedataislarge,thedatamustbegroupedintoclassesthat
aremorethanoneunitinwidth.
Toconstructafrequencydistribution,followtheserules:
5.Theclassesmustbeexhaustive.Thereshouldbeenoughclassesto
accommodateallthedata.
6.Theclassesmustbeequalinwidth.Thisavoidsadistortedviewofthedata.

23. GROUPED FREQUENCY
DISTRIBUTION
CONSTRUCTINGGROUPEDFREQUENCYDISTRIBUTION
1.Findtherange.
�??????���=ℎ??????�ℎ����??????���−�������??????���
2.Decideonthenumberofclassintervalsorclasses,wedenoteitby�.
➢�=�
➢5-20classes
3.Determinetheclasssizeorclasswidthoftheinterval,wedenoteitbyc.
(roundedtothenearestoddwholenumber)
4.DeterminethelowerlimitLLandtheupperlimitandtheupperlimitULofthelowest
classinterval.Thelowestclassintervalshouldcontainthelowestvalueinthedataset.

24. GROUPED FREQUENCY
DISTRIBUTION
CONSTRUCTINGGROUPEDFREQUENCYDISTRIBUTION
ThevalueoftheULisdeterminedusingtheequation.
????????????=????????????+(??????−1)
5.Determinetheupperclassintervalsbyconsecutivelyaddingtheclasssize??????to
thevaluesofLLandULofthelowestclassintervaluntilwegettheclassinterval
withthehighestvalueinthedataset.
6.Tallythedata,findthefrequencies.

25. GROUPED FREQUENCY
DISTRIBUTION
CONSTRUCTINGGROUPEDFREQUENCYDISTRIBUTION
▪Theclassboundariesareusedtoseparatetheclassessotatthereareno
gapsinthefrequencydistribution.
RuleofThumb:Classlimitsshouldhavethesamedecimalplacevalueasthe
data,buttheclassboundarieshaveoneadditionalplacevalueandendina5.
▪Theclassmidpointisfoundbyaddingtheupperandlowerboundaries(or
limits)anddividingby2.
▪Thecumulativefrequenciesareusedtodeterminethenumberofcasesfailing
below(for<cf)orabove(for>cf)aparticularvalueinadistribution.

26. GROUPED FREQUENCY
DISTRIBUTION
CONSTRUCTINGGROUPEDFREQUENCYDISTRIBUTION
▪Therelativefrequency(rf)ofaclassintervalistheproportionofobservations
fallingwithintheclassandmaybepresentedinpercent.Thus,
&#3627408479;&#3627408467;=
&#3627408467;
&#3627408475;
×100

27. EXAMPLE
DistributionofscoresoffortystudentsinaMathematicsclass.
RAW SCORES
76 92 87 78
87 88 85 92
67 85 93 91
85 79 92 82
99 95 79 85
81 96 75 88
82 86 83 87
79 92 80 74
86 93 98 71
81 86 80 94

28. EXAMPLE
SOLUTION:
Step1:????????????&#3627408475;&#3627408468;&#3627408466;=????????????&#3627408468;ℎ&#3627408466;&#3627408480;&#3627408481;&#3627408483;??????&#3627408473;&#3627408482;&#3627408466;−??????&#3627408476;&#3627408484;&#3627408466;&#3627408480;&#3627408481;&#3627408483;??????&#3627408473;&#3627408482;&#3627408466;=99−67=32.
Step2:&#3627408472;=&#3627408475;=40≈7
Step3:??????=
32
7
≈5
Step4:????????????=65+5−1=65+4=69
Step5:????????????=70+5−1=74
????????????=75+5−1=79
????????????=80+5−1=84

29. EXAMPLE
SOLUTION:
????????????=85+5−1=89
????????????=90+5−1=94
????????????=95+5−1=99

30. EXAMPLE
SOLUTION:
Step6:
Class Interval ?????? ?????? ???????????? <???????????? >????????????
95-99 4 97 10 40 4
90-94 8 92 20 36 12
85-89 12 87 30 28 24
80-84 7 82 17.5 16 31
75-79 6 77 15 9 37
70-74 2 72 5 3 39
65-69 1 67 2.5 1 40

31. HISTOGRAM, FREQUENCY
POLYGONS AND OGIVES
Thehistogramisagraphthatdisplaysthedatabyusingcontiguousvertical
barsofvariousheightstorepresentthefrequenciesoftheclasses.(class
boundariesalong&#3627408485;-axis)
Thefrequencypolygonisagraphthatdisplaysthedatabyusinglinesthat
connectpointsplottedforthefrequencies,atthemidpointsoftheclasses.(class
midpointsalong&#3627408485;-axis)
Theogive(cumulativefrequencygraph)isagraphthatshowsthecumulative
frequenciesfortheclasses.(withconnectedpointsandclassboundariesalong&#3627408485;-
axis)

32. HISTOGRAM, FREQUENCY
POLYGONS AND OGIVES

33. HISTOGRAM, FREQUENCY
POLYGONS AND OGIVES

34. HISTOGRAM, FREQUENCY
POLYGONS AND OGIVES

35. RELATIVE FREQUENCY GRAPHS
Class Interval ?????? ???????????? <???????????? >???????????? ??????????????????
95-99 4 10% 40 4 10%
90-94 8 20% 36 12 30%
85-89 12 30% 28 24 60%
80-84 7 17.5% 16 31 77.5%
75-79 6 15% 9 37 92.5%
70-74 2 5% 3 39 97.5%
65-69 1 2.5% 1 40 100%