Frequency distribtution curve

explains the formation of the frequency distribution curve

2. •Diagramming the Data
Picturecanspeak1000
words.Ratherthan
tellingaboutwhole
dramaofa20/20cricket
match,justthepicture
ontheright,isenough.
Statisticsalsogivesdata
intheformofdiagram
anditismoreelegantto
see.

3. •Diagrammatisationof Data
TypesofDiagram
Piediagram
Bargraph
FrequencyPolygon
Histogram
Cumulativefrequencycurve
Cumulativefrequencypercentagecurve

4. •Pie Diagram
Piediagramisintheformofcircle,
henceitisalsocalledascircle
diagram.Itcanbefragmentedinto
differentproportions,which
representsthedata.
InEnglish,thewordpiemeansatype
offoodmadewithmeat,vegetables
orfruitcoveredinpastryandbaked.

5. •Charting a Pie
Astudentgotthe
followingmarksinfive
subjects.Themaximum
marksineachsubjectis
100.
Letthedatabevisualized
inthepieform.
Totalangleinapie=360
0
Totalmarksforallsubjects=434/500
ForEnglish
For434marks=360
0
for60marks=60x360/434=49.7
0
≈50
0
LikeaboveTamil=66.6
0
≈67
0
Maths=82.9
0
≈83
0
Science=81.2
0
≈81
0
SocialScience=79.6
0
≈80
0

6. •Pie Chart
isualizedinthepieform.

7. •Assignment
DrawapiechartmanuallyhavingyourownXstandardmarks.

8. •Bar Graph

9. •Diagrammatisationof Data
TypesofDiagram
Piediagram
Bargraph
Frequencycurve
Histogram
Cumulativefrequencycurve
Cumulativefrequencypercentagecurve

10. •Bar Graph
InaBargraph,
thedatais
exhibitedthrough
rectangles.The
presentationcan
beeithervertical
orhorizontal.

11. •Charting a Bar Graph
Astudentgotthefollowing
marksinfivesubjects.The
maximummarksineachsubject
is100.
Letthedatabevisualizedinthe
formofbargraph.
InXaxis(Subjects)
1cm=1Subject
InYaxis(Marks)
1cm=20Marks

13. •Assignment
DrawaBarGraphmanuallyhavingyourownXstandardmarks.Draw
inapieceofgraphsheetandpasteitinyourassignment.

14. •Frequency Polygon
TypesofDiagram
Piediagram
Bargraph
FrequencyPolygon
Histogram
Cumulativefrequencycurve
Cumulativefrequencypercentagecurve

15. •Frequency Polygon
Thelinediagramof
frequencydistributionis
calledfrequencypolygon.
Thesuffixpolygonisdueto
thepresenceofmanyangles
inthecurve.Forexample,if
therearethreeanglesitis
triangle,fouranglesmeans
tetragonandsoon.

16. Add one above and below hypothetical class in the Frequency
Distribution Table. Since it is hypothetical, the frequency is zero.
Class f
90 -94 2
85 -89 2
80 -84 4
75 -79 8
70 -74 6
65 -69 11
60 -64 9
55 -59 7
50 -54 5
45 -49 0
40 -44 2
Class f
95 –99 0
90 -94 2
85 -89 2
80 -84 4
75 -79 8
70 -74 6
65 -69 11
60 -64 9
55 -59 7
50 -54 5
45 -49 0
40 -44 2
35 –39 0

17. Drawing Frequency Polygon.
InXaxis(Class)
1cm=1class
InYaxis(Frequency)
1cm=2frequency
Markthedotagainstfrequencyandits’
correspondingmid-pointoftheclass.
Drawalineconnectingallthedots.The
curveinordertotouchthexaxis,two
hypotheticalclassesweretaken.This
curveisknownasFrequencyPolygon
Class f
95 –99 0
90 -94 2
85 -89 2
80 -84 4
75 -79 8
70 -74 6
65 -69 11
60 -64 9
55 -59 7
50 -54 5
45 -49 0
40 -44 2
35 –39 0

19. •Assignment
Drawafrequencypolygonmanuallyhavingthedataofyour
frequencydistributiontabledrawnbefore.Drawfrequencypolygon
inapieceofgraphsheetandpasteitinyourassignment.

20. •Frequency Polygon
TypesofDiagram
Piediagram
Bargraph
FrequencyPolygon
Histogram
Cumulativefrequencycurve
Cumulativefrequencypercentagecurve

21. •Histogram
Thebargraphoffrequency
distributioniscalled
Histogram.

22. Frequency Distribution Table without Hypothetical Class
Class f
90 -94 2
85 -89 2
80 -84 4
75 -79 8
70 -74 6
65 -69 11
60 -64 9
55 -59 7
50 -54 5
45 -49 0
40 -44 2

23. Drawing a Histogram
InXaxis(Class)
1cm=1class
InYaxis(Frequency)
1cm=2frequency
Class f
90 -94 2
85 -89 2
80 -84 4
75 -79 8
70 -74 6
65 -69 11
60 -64 9
55 -59 7
50 -54 5
45 -49 0
40 -44 2

24. Drawing a Histogram
Thefirstclass40-44istakenasan
exampleforexplanation.Arectangleis
drawnbyhavingreallowerlimitofthe
class(39.5)totherealupperlimit
(44.5)asbreadthandthefrequency(2)
aslength.Likewisethesecond
rectangleisdrawnbyhaving44.5to
49.5asbreadthandfrequencyas
length(0).Thusarectangleforeach
classisdrawn.Thisseriesofrectangles
withrespecttofrequencydistribution
iscalledashistogram.

26. Drawing a Histogram
Thebaseofeachrectangleissame,
because
Baseαi(classinterval)
Thelengthoftheeachrectangleis
differentbecause
Lengthαf(frequency)
AreaofHistogramαN(Totalnumberof
scores)

27. •Assignment
Drawahistogrammanuallyhavingthedataofyourfrequency
distributiontabledrawnbefore.DrawHistograminapieceofgraph
sheetandpasteitinyourassignment.

28. •Frequency Polygon
TypesofDiagram
Piediagram
Bargraph
FrequencyPolygon
Histogram
Cumulativefrequencycurve
Cumulativefrequencypercentagecurve

29. •Cumulative Frequency Curve
Thecurvedrawnbyhaving
exactupperlimitofeach
classtoitscorresponding
cumulativefrequencyis
calledascumulative
frequencycurve.

30. Data
Class f cf
90 -94 2 56
85 -89 2 54
80 -84 4 52
75 -79 8 48
70 -74 6 40
65 -6911 34
60 -64 9 23
55 -59 7 14
50 -54 5 7
45 -49 0 2
40 -44 2 2
CumulativeFrequency
Thecumulativefrequencyis
thefrequencyofthatclass
plusthefrequenciesall
otherclassesarrangedin
ascendingorder.

31. Modified Data
Class f cf
90 -94 2 56
85 -89 2 54
80 -84 4 52
75 -79 8 48
70 -74 6 40
65 -6911 34
60 -64 9 23
55 -59 7 14
50 -54 5 7
45 -49 0 2
40 -44 2 2
35 –390 0
Inorderforthecurveto
touchthe‘x’axis,
hypotheticalclass35-39is
addedwhosefrequencyis
zero.
In‘x’axis
1cm=1class
In‘y’axis
1cm=10frequencies

32. •Cumulative Frequency Curve
Dotsaremarkedagainst
exactupperlimitofeach
classcorrespondingtoits
cumulativefrequency.The
curvethusobtainedby
joiningallthedotsiscalled
ascumulativefrequency
curve.

34. •Assignment
Drawacumulativefrequencycurvemanuallyhavingthedataofyour
frequencydistributiontable.Drawcumulativefrequencycurveina
pieceofgraphsheetandpasteitinyourassignment.

35. •Cumulative Frequency Percentage Curve
TypesofDiagram
Piediagram
Bargraph
FrequencyPolygon
Histogram
Cumulativefrequencycurve
Cumulativefrequencypercentagecurve

36. •Cumulative Frequency Percentage Curve
Thecurvedrawnbyhaving
exactupperlimitofeach
classtoitscorresponding
cumulative frequency
percentageiscalledas
cumulative frequency
percentagecurve.Thecurve
isalsoknownasogive.

37. Cumulative Frequency
Class f cf
90 -94 2 56
85 -89 2 54
80 -84 4 52
75 -79 8 48
70 -74 6 40
65 -6911 34
60 -64 9 23
55 -59 7 14
50 -54 5 7
45 -49 0 2
40 -44 2 2
CumulativeFrequency
Thecumulativefrequencyis
thefrequencyofthatclass
plusthefrequenciesall
otherlowerclasses
arrangedinascendingorder.

38. Cumulative Frequency Percentage
Classfcfcf%
90 -94256100
85 -8925496.42
80 -8445292.85
75 -7984885.71
70 -7464071.42
65 -69113460.71
60 -6492341.07
55 -5971425
50 -545712.5
45 -49023.5
40 -44223.5
Cf%
Totalfrequency=56
56istakenas100%
Percentageforcf2
=2/56x100=3.5
Percentageforcf7
=7/56x100=12.5

39. Data
Class f cf
90 -94 2 56
85 -89 2 54
80 -84 4 52
75 -79 8 48
70 -74 6 40
65 -6911 34
60 -64 9 23
55 -59 7 14
50 -54 5 7
45 -49 0 2
40 -44 2 2
35 –390 0
Inorderforthecurveto
touchthe‘x’axis,
hypotheticalclass35-39is
addedwhosefrequencyis
zero.
In‘x’axis
1cm=1class
In‘y’axis
1cm=20%

40. •Cumulative Frequency Percentage Curve
Dotsaremarkedagainst
exactupperlimitofeach
classcorrespondingtoits
cumulative frequency
percentage.Thecurvethus
obtainedbyjoiningallthe
dotsiscalledascumulative
frequencypercentagecurve.

42. •Percentile -Concept
Percentileisapointinthedatalinebelowwhichgivenpercentageof
scorelies.Letallthescoresbedividedinto100equalparts.Itis
calledaspercentilesandcanberepresentedasfollows;

43. •Percentile -Concept
The1
st
percentileisapointbelowwhich1%ofscoreliesandabovewhich
99%ofscorelies.ItisrepresentedasP
1.GoingfurtherP
20isapointbelow
which20%ofscoreliesandabovewhich80%ofscorelies.
WhataboutP
50?
P
50isapointbelowandabovewhich50%ofscorelies.Thispointis
otherwiseknownasMedian.

44. •Quartile -Concept
Thedatalinecanbedividedintofourquadrants.Eachquadrantis
termedasquartile.Q
1isfirstquartileandQ
2issecondquartileand
soon.Q
2isMedian.
Thiscanbediagrammaticallyrepresentedindatalineas

45. •Decile-Concept
Thedatalinecanbedividedinto10equalparts.Eachpointistermed
asaDecile.Q
1isfirstquartileandQ
2issecondquartileandsoon.Q
2
isMedian.
Thiscanbediagrammaticallyrepresentedindatalineas

46. •Percentile –Quartile -Decile

47. •Calculation of Median from ogive.
MedianorP
50orQ2orD5can
befoundfromogive.Mark50on
the‘y’axisandfromtherea
horizontallineisdrawntotouch
thecurveanditismarked.From
themarkedpointonthecurve,a
verticallineisdroppeddownto
touchthe‘x’axisandmarked.
Thismarkgivesthemedian
whichis64.5.
LikewiseP
25,P
75,P
90andP
10can
befoundout.

48. •Assignment
1.Drawacumulativefrequencypercentage
curvemanuallyhavingthedataofyour
frequencydistributiontable.Drawcumulative
frequencypercentagecurveinapieceof
graphsheetandpasteitinyourassignment.
2.CalculateMedian,QD,andKurtosisfrom
ogiveandusepiecesofgraphsheets
separatelyforfindingMedian,QDand
Kurtosis.
3.CalculateSkewnessmanuallyfromthe
valuesofmeanandstandarddeviationand
Medianfromogive.
QD=Q
3–Q
1/2
Ku = QD / P
90–P
10
Sk= 3(Mean -Median) / σ

49. •Musings
Withthis,ourclassforthissemestercomestoanend.Thisisan
opportunityprovidedbyyouuponme.Thanksforcomingalongwith
meinthisjourney.Ican’tsaythatsyllabusiscoveredbutithastobe
discoveredbyus.HavingsaidtotakeonWritingQuestions,
StandardizingaQuestionPaperandStatistics,Ihavedoneabit.

50. •Musings
Thesuccessoftheteachingliesinapplyingallthatyouhavelearntin
ALinunderstandingaboutmeasurement,assessmentand
evaluation,differenttypesofevaluation,writingGIO&SIOwith
respecttoBloom’staxonomy,writingquestions,preparingblueprint,
standardizingaquestionpaper,fairevaluationofthescripts,
understandwhatthedatasays,……

51. References
•Garrett, H. E. (1926). Statistics in psychology and education. Longman’s Green & Co
•Mathew, T.K., and Mollykutty, T.M. (2011). Science education -Theoretical bases of
teaching and pedagogic analysis -Physical Science and Natural Science.Rainbow Book
Publishers
•Mangal. S. K. (2014). Statistics in psychology and education. PHI Learning Private
Limited
•NCERT. (2013). Teaching of science.
•RadhaMohan. (2007). Teaching of physical science. (3
rd
ed.). PHI Learning
•Rathinasabapathy, P. (2001). கல்வியில்தேர்வு[Examination in Education]. (2
nd
ed.). ShanthaPublishers.
•Srinivasan, P. (2011). அறிவியல்கற்பிே்ேல்[Teaching of science]. DDE, Tamil
Univeristy
•Images from google