2 Methods of Data Presentation print.pdf

Biostatistics

1. Methods of Data Presentation
•Thedatacollectedinsurveyorotherempirical
inquiryarecalledrawdata.
•Havingcollectedandeditedthedata,thenext
importantstepistoorganizeit.
•Theprocessofarrangingdataintoclassesor
categoriesaccordingtosimilaritiestechnicallyis
calledclassification.
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2. Cont…
•Classificationisapreliminaryanditprepares
thegroundforproperpresentationofdata.
•Mainly,thepurposeofclassificationisto
dividethedataintohomogeneousgroupsor
class.
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3. Cont..
•The classification of the data generally done on
basis on the following:
–Geographical,
–Choronological,
–Qualitative or
–Quantitative.
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3

4. Cont…
1) In geographical classification, data are
arranged according to places, areas or
regions.
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5. Cont…
•2) In chorological classification, data are
arranged according to time i.e., weekly,
monthly, quarterly, half yearly, annually, etc.
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6. Cont…
3) In qualitative classification, the data are
arranged according to attributes like sex,
martial status, educational standard, stage
or intensity of diseases etc.
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7. Cont…
4) In quantativeclassification, the data are
arranged according to certain characteristic
that has been measured like height, weight,
income of persons, vitamin content of in a
substance etc.
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8. Cont…
•Once data is collected, it can be presented as:
–Frequency distribution (table)
–Diagram
–Graph
•Distributionisaposition,arrangement,orfrequencyof
occurrence(asofthemembersofagroup)overanareaor
throughoutaspaceorunitoftime.
•Frequencyis the number of times a certain value or class of
values occurs.
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9. Cont…
•FrequencyDistribution:istheorganizationof
rawdataintableformwithclassesand
frequencies.
Categorical Grouped Ungrouped
Frequency
distribution
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9

10. Cont…
The reasons for constructing a frequency
distribution:
1.Toorganizethedatainameaningful,
intelligibleway.
2.Toenablethereadertodeterminethenature
orshapeofthedistribution.
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11. Cont…
3.Tofacilitatecomputationalproceduresfor
measuresofaverageandspread.
4.Toenabletheresearchertodrawchartsand
graphsforthepresentationofdata
5.Toenablethereadertomakecomparisons
betweendifferentdataset.
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12. Categorical frequency Distribution:
•Used for data that can be placed in to specific categories such
as nominal, or ordinal.
Example 2.1:
–A social worker collected the following data on
marital status for 25 persons.
•where
–M = Married, S = Single, W = Widowed and D = Divorced
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13. Cont…
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14. Cont…
•Solution:
–Since the data are categorical, discrete classes can be used.
–There are four types of marital status M, S, D, and W.
–These types will be used as class for the distribution.
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15. Cont…
Step 1: Tally the data and place the result in
column (2).
Step 2: Count the tally and place the result in
column (3).
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16. Cont…
Step 3: Find the percentagesof values in each class by
using; (f/n) %
Where
f = frequency of the class,
n = total number of value.
•Percentagesarenotnormallyapartoffrequency
distributionbuttheycanbeaddedsincetheyareusedin
certaintypesdiagrammaticsuchaspiecharts.
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16

17. Cont…
Step 4: Find the total for column (2) and (3).
•Combingtheentirestepsonecanconstructthe
followingfrequencydistribution.
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18. Cont…
•.
Class(1) Tally(2)Frequency
(3)
Percent(4)
M //// 5 20
S ////// 7 28
D ////// 7 28
W ///// 6 24
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19. Ungrouped frequency Distribution:
•Is a table of all the potential raw score values
that could possible occur in the data along with
the number of times each actually occurred.
•Is often constructed for small set or data on
discretevariable.
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20. Cont…
Constructing ungrouped frequency distribution:
• First find the smallest and largest raw score in
the collected data.
• Arrange the data in order of magnitude and
count the frequency.
• To facilitate counting one may include a column
of tallies.
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21. Cont…
•Example:
•The following data represent number of new birth
to 20 hospitals per month.
•Construct a frequency distribution, which is
ungrouped.
80 76 90 85 80
70 60 62 70 85
65 60 63 74 75
76 70 70 80 85
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22. Cont…
Solution:
Step 1: Find the range,
Range = Max –Min = 90 –60 = 30.
??????????????????
Step 2: Make a table as shown
Step 3: Tally the data.
Step 4: Compute the frequency.
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23. Cont…
.
#of new birth Tally Frequency
60 // 2
62 / 1
63 / 1
65 / 1
70 //// 4
74 / 1
75 // 2
76 / 1
80 /// 3
85 /// 3
90 / 1
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24. Grouped frequency Distribution:
•Afrequencydistributionwhenseveral
numbersaregroupedinoneclass.
•Whentherangeofthedataislarge,thedata
mustbegroupedintoclassesthataremore
thanoneunitinwidth.
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25. Cont…
Definition of some common terms
Classlimits:Separatesoneclassinagrouped
frequencydistributionfromanother.
Thelimitscouldactuallyappearinthedataandhave
gapsbetweentheupperlimitsofoneclassandlower
limitofthenext.
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26. Cont…
Unitsofmeasurement(U):thedistancebetweentwo
possibleconsecutivemeasures.
Itisusuallytakenas1,0.1,0.01,0.001,-----.
Classboundaries:Separatesoneclassinagroupedfrequency
distributionfromanother.
–Theboundarieshaveonemoredecimalplacesthantherow
dataandthereforedonotappearinthedata.
–Thereisnogapbetweentheupperboundaryofoneclassandlower
boundaryofthenextclass.
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27. Cont…
Class width: the difference between the upper and
lower class boundariesof any class.
✓Itisalsothedifferencebetweenthelowerlimitsof
anytwoconsecutiveclassesorthedifference
betweenanytwoconsecutiveclassmarks.
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28. Cont…
Classmark(Midpoints):itistheaverageofthe
lowerandupperclasslimitsortheaverageof
upperandlowerclassboundary.
Cumulativefrequency:isthenumberof
observationslessthan/morethanorequaltoa
specificvalue.
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29. Cont…
•Cumulative frequency above:it is the total
frequency of all values greater than or equal to
the lower class boundaryof a given class.
•Cumulative frequency blow:it is the total
frequency of all values less than or equal to the
upper class boundaryof a given class.
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30. Cont…
•CumulativeFrequencyDistribution(CFD):it
isthetabulararrangementofclassinterval
togetherwiththeircorrespondingcumulative
frequencies.
Itcanbemorethanorlessthantype,dependingon
thetypeofcumulativefrequencyused.
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31. Cont…
•Relativefrequency(rf):itisthefrequencydivided
bythetotalfrequency.Thisgivesthepercentof
valuesfallinginthatclass.
•Relativecumulativefrequency(rcf):itisthe
cumulativefrequencydividedbythetotal
frequency.Givesthepercentofthevalueswhich
arelessthanormorethantheupper/lowerclass
boundary.
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32. Cont…
Guidelines for classes
–There should be between 5 and 20 classes.
–The class widthshould be an oddnumber.
–The classes must be mutually exclusive.
–The classes must be all inclusive or exhaustive.
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33. Cont…
–Theclassesmustbecontinuous.Therearenogaps
inafrequencydistribution.Classesthathaveno
valuesinthemmustbeincluded(unlessit'sthe
firstorlastclasseswhicharedropped).
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34. Creating a Grouped Frequency Distribution
1. Find the largest and smallest values
2. Compute the Range = Maximum -Minimum
3. Select the number of classes desired.
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35. Cont…
This is usually between 5 and 20 or use Sturgesrule
-K = 1+3.322log(n or N)=> Sturgesrule or
-K=2
??????
>Nornor
-bypersonaljudgment.
where
-kisnumberofclassesdesiredand
-norNistotalnumberofobservation
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36. Cont…
4. Find the class widthby dividing the range by the
number of classes and rounding up
*You must round up, not off.
*Normally 3.2 would round to be 3, but in
rounding up, it becomes 4.
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37. Cont…
5. Pick a suitable starting point less than or equal to
the minimum value.
oThe starting point is called the lower limit of the
first class.
oContinue to add the class width to this lower limit
to get the rest of the lower limits.
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38. Cont…
▪Tofindtheupperlimitofthefirstclass,
subtractUmfromthelowerlimitofthesecond
class.
▪Thencontinuetoaddtheclasswidthtothis
upperlimittofindtherestofthe upper
limits.
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39. Cont…
➢Find the boundaries by subtracting 0.5 U units
from the lower limits and adding 0.5 U units
from the upper limits.
➢The boundaries are also half-way between the
upper limit of one class and the lower limit of
the next class.
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40. Cont…
6. Tally the data.
7. Find the frequencies.
▪Find the cumulative frequencies.
❖If necessary, find the relative frequencies
and/or relative cumulative frequencies.
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41. Cont…
Example:
•Construct a frequency distribution for the following data.
Solutions:
Step 1: Find the highest and the lowest value H = 39, L = 6
Step 2: Find the range; R = H –L = 39 –6 = 33
1129633143122271920
18172238232126343927
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42. Cont…
Step 3: Select the number of classes desired
using Sturgesformula;
K= 1+3.32log (20) = 5.32 = 6 (rounding up)
Step 4: Find the class width;
W = R/K= 33/6 = 5.5 = 6 (rounding up)
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42

43. Cont…
Step 5: Select the starting point, let it be the minimum
observation.
6, 12, 18, 24, 30, 36 are the lower class limits.
Step 6: Find the upper class limit;
E.g. the first upper class = 12 –U = 12 –1 = 11
11, 17, 23, 29, 35, 41are the upper class limits.
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44. Cont…
•So combining step 5 and step 6, one can
construct the following classes.
Class limits
6 –11
12 –17
18 –23
24 –29
30 –35
36 –41
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45. Cont…
Step 7: Find the class boundaries;
E.g. lower class boundary of first class
= 6 -U/2 = 5.5
Upper class boundary = 11 + U/2 = 11.5
* Then continue adding Width on both
boundaries to obtain the rest boundaries.
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45

46. Cont…
•By doing so one can obtain the following
classes.
Class boundary
5.5 –11.5
11.5 –17.5
17.5 –23.5
23.5 –29.5
29.5 –35.5
35.5 –41.5
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47. Cont…
Step 8: Tally the data.
Step 9: Write the numeric values for the tallies in the
frequency column.
Step 10: Find cumulative frequency.
Step 11: Find relative frequency or/and relative
cumulative frequency.
The complete frequency distribution follows:
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48. Cont…
.
CL CB CMTallyFreqLCFGCFRFLRCF
6–115.5–11.58.5// 22200.100.10
12–1711.5–17.514.5// 24180.100.20
18–2317.5–23.520.5//////711160.350.55
24–2923.5–29.526.5////4159 0.200.75
30–3529.5–35.532.5///3185 0.150.90
36–4135.5–41.538.5// 2202 0.101.00
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49. Example
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50. 12/5/2023
50
DIAGRAMMATIC
AND
GRAPHICAL
REPRESENTATION OF
DATA

51. Cont…
•Appropriately drawn graph allows readers to
obtain rapidly an overall grasp of the data
presented.
•The relationship between numbers of various
magnitudes can usually be seen more quickly
and easily from a graph than from a table.
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52. Construction of graphs
•The choice of the particular form among the
different possibilities will depend on personal
choices and/or the type of the data.
–Bar charts and pie chart are commonly used for
qualitative or quantitative discrete data.
–Histograms, frequency polygons are used for
quantitative continuous data.
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53. Cont…
•General rules that are commonly accepted about
construction of graphs.
•Every graph should be self-explanatory and as
simple as possible.
–Titles are usually placed below the graph and it should
again question what ? Where? When? How classified?
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54. Cont…
–Legends or keys should be used to differentiate variables if
more than one is shown.
–The axes label should be placed to read from the left side
and from the bottom.
–The units in to which the scale is divided should be clearly
indicated.
–The numerical scale representing frequency must start at
zero or a break in the line should be shown.
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55. Specific types of graphs include;
•Bar graph
•Pie chart
•Histogram
•Stem-and-leaf plot
•Box-Whisker plot
•Scatter plot
•Line graph
•Others
Nominal, ordinal
data
Quantitative
data
Cont.….
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56. 1. Bar charts
•Categories are listed on the horizontal axis (X-axis)
•Frequencies or relative frequencies are represented
on the Y-axis (ordinate)
•The height of each bar is proportional to the
frequency or relative frequency of observations in
that category
•There are three types of bars
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57. Cont.…
a. Simple bar chart:-used to represent a single
variable.
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58. Method of constructing bar chart
•All the bars must have equal width.
•The bars arenot joined together (leave space between bars)
•The different bars should be separated by equal distances
•All the bars should rest on the same line called the base.
•Label both axes clearly.
Cont…
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59. Cont…
•Example:Construct a bar chart for the
following data
•Distribution of patient in hospital by source of
their referral.
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60. Cont.…
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61. B.Sub-dividedbarchart(component)
•Iftherearedifferentquantitiesformingthesub-divisions
ofthetotals,
•Simplebarsmaybesub-dividedintheratioofthevarious
sub-divisionstoexhibittherelationshipofthepartstothe
whole.
•Theorderinwhichthecomponentsareshownina“bar”
isfollowedinallbarsusedinthediagram.
Cont.…
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62. Example:Plasmodium species distribution for
confirmed malaria cases, Zeway, 20030
20
40
60
80
100
August October December
Percent
2003
Mixed
P. vivax
P. falciparum
Cont.…
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63. C. Multiple bar graph
•Barchartscanbeusedtorepresenttherelationships
amongmorethantwovariables.
•Thefollowingfigureshowstherelationship
betweenchildren’sreportsofbreathlessnessand
cigarettesmokingbythemselvesandtheirparents.
Cont.…
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64. Prevalence of self reported breathlessness among school
childeren, 1998
0
5
10
15
20
25
30
35
Neither One Both
Parents smooking
Breathlessness, per cent
Child never smokedsmoked occassionalychild smoked one/week or more We can see from the graph quickly that the prevalence of the
symptoms increases both with the child’s smoking and with that
of their parents.
Cont.…
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65. 2. Pie chart
•Showstherelativefrequencyforeachcategorybydividinga
circleintosectors,theanglesofwhichareproportionaltothe
relativefrequency.
•Usedforasinglecategoricalvariable
•Usepercentagedistributions
Relative frequency Size of Wedge, in degrees
0.5 50%of 360=180 degrees
0.25 25% of 360=90 degrees
P (P)X(100%)x360degrees
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66. Cont.…
Steps to construct a pie-chart
•Construct a frequency table.
•Change the frequency into percentage (P)
•Change the percentages into degrees, where:degree =
Percentage X 360
o
•Draw a circle and divide it accordingly.
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67. •Example: Distribution of deaths for females, in
England and Wales, 1989
Cause of death No. of death
Circulatory system
Neoplasm
Respiratory system
Injury and poisoning
Digestive system
Others
100 000
70 000
30 000
6 000
10 000
20 000
Total 236 000
Cont..
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68. Distribution fo cause of death for females, in England and Wales, 1989
Circulatory system
42%
Neoplasmas
30%
Respiratory system
13%
Injury and Poisoning
3%
Digestive System
4%
Others
8% Cont…
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69. 3. Histogram
•Histogramsarefrequencydistributionswith
continuousclassintervalsthathavebeenturned
intographs.
•Toconstructahistogram,wedrawtheinterval
boundariesonahorizontallineandthefrequencies
onaverticalline.
•Non-overlappingintervalsthatcoverallofthedata
valuesmustbeused.
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70. Cont.…
•Barsaredrawnovertheintervalsinsuchaway
thattheareasofthebarsareallproportionalin
thesamewaytotheirintervalfrequencies.
•The area of each bar is proportional to the
frequencyof observations in the interval
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71. Example:Distribution of the age of women at the time of
marriage.
Age
group
15-1920-2425-2930-3435-3940-4445-49
Number 11 36 28 13 7 3 2
Cont.…
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72. Cont…
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73. •Two problems with histograms
1.They are somewhat difficult to construct.
2.The actual valueswithin the respective groups are
lost and difficult to reconstruct.
The other graphic display (stem-and-leaf plot)
overcomes these problems
Cont.…
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74. 4. Stem-and-Leaf Plot
•Aquickwaytoorganizedatatogivevisual
impressionsimilartoahistogramwhileretaining
muchmoredetailonthedata.
•Similartohistogramandservesthesame
purposeandrevealsthepresenceorabsenceof
symmetry
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75. Cont…
•Aremosteffectivewithrelativelysmalldatasets
•Arenotsuitableforreportsandother
communications,but
•Helpresearcherstounderstandthenatureof
theirdata.
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76. Example
•43, 28, 34, 61, 77, 82, 22, 47, 49, 51, 29, 36,
66, 72, 41
2 2 8 9
3 4 6
4 1 3 7 9
5 1
6 1 6
7 2 7
8 2
Cont…
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steam Leaf

77. Steps to construct Stem-and-Leaf Plots
1.Separate each data point into a stem and leaf components
•Stem = consists of one or more of the initial digits of the
measurement
•Leaf = consists of the rightmost digit
The stem of the number 483, for example, is 48 and the leaf is 3.
2.Write the smallest stem in the data set in the upper left-hand
corner of the plot
Cont.…
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78. 3. Write the second stem (first stem +1) below the first stem
4. Continue with the remaining stems until you reach the
largest stem in the data set
5. Draw a vertical bar to the right of the column of stems
6.Foreachnumberinthedataset,findtheappropriatestem
andwritetheleaftotherightoftheverticalbar
Cont.…
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79. Example: 3031, 3101, 3265, 3260, 3245, 3200, 3248,
3323, 3314, 3484, 3541, 3649 (BWT in g)
Stem Leaf Number
30
31
32
33
34
35
36
31
01
6560450048
2314
84
41
49
1
1
5
2
1
1
1
Cont.…
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80. What do you see???
Cont.…
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81. 5. Frequency polygon
•Afrequencydistributioncanbeportrayed
graphicallyinyetanotherwaybymeansofa
frequencypolygon.
•Todrawafrequencypolygonweconnectthe
mid-pointofthetopsofthecellsofthe
histogrambyastraightline.
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82. Cont…
•Thetotalareaunderthefrequencypolygonis
equaltotheareaunderthehistogram.
•Usefulwhencomparingtwoormorefrequency
distributionsbydrawingthemonthesame
diagram.
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83. •Frequency polygon for the ages of 2087 mothers with
<5 children, Adami Tulu, 2003N1AGEMOTH
55.050.045.040.035.030.025.020.015.0
700
600
500
400
300
200
100
0
Std. Dev = 6.13
Mean = 27.6
N = 2087.00
Cont.…
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84. •Itcanbealsodrawnwithouterectingrectangles
byjoiningthetopmidpointsoftheintervals
representingthefrequencyoftheclassesas
follows:
•Age of women at the time of marriage
0
5
10
15
20
25
30
35
40
12 17 22 27 32 37 42 47
Age
No of women
Cont.…
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85. 8. Ogive Curve (The Cumulative Frequency Polygon)
•Sometimesitmaybenecessarytoknowthe
numberofitemswhosevaluesaremoreorless
thanacertainamount.
•Wemay,forexample,beinterestedtoknowthe
no.ofpatientswhoseweightis<50Kgor>60
Kg.
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86. Cont…
•Togetthisinformationitisnecessarytochange
theformofthefrequencydistributionfroma
‘simple’toa‘cumulative’distribution.
•Ogivecurve turns a cumulative frequency
distribution in to graphs.
•Are much more common than frequency
polygons
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87. Cumulative Frequency and Cum. Rel. Freq. of Age of 25 ICU
Patients
Age Interval Frequency
Relative
Frequency(%)
Cumulative
frequency
Cumulative Rel.
Freq.(%)
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
3
1
3
0
6
1
9
2
12
4
12
0
24
4
36
8
3
4
7
7
13
14
23
25
12
16
28
28
52
56
92
100
Total 25 100
Cont.…
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87

88. •Cumulative frequency of 25 ICU patients
Cont.…
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88

89. Example: Heart rate of patients admitted to hospital Y, 1998Heart rate No. of patients Cumulative frequency
Less than Method(LM)
Cumulative frequency
More than Method(MM)
54.5-59.5 1 1 54
59.5-64.5 5 6 53
64.5-69.5 3 9 48
69.5-74.5 5 14 45
74.5-79.5 11 25 40
79.5-84.5 16 41 29
84.5-89.5 5 46 13
89.5-94.5 5 51 8
94.5-99.5 2 53 3
99.5-104.5 1 54 1

Cont.…
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90. Heart rate of patients admited in hospital Y, 1998
0
10
20
30
40
50
60
54.5 59.5 64.5 69.5 74.5 79.5 84.5 89.5 94.5 99.5
104.5
Heart rate
Cum. freqency
LM MM Cont.…
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91. Percentiles (Quartiles)
•Suppose that 50% of a cohort survived at least 4
years.
•This also means that 50% survived at most 4 years
•We say 4 years is the median.
•The median is also called the 50th percentile.
•We write: P
50 = 4 years.
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92. Similarlywecouldspeakofotherpercentiles:
–P0:Theminimum
–P25:25%ofthesamplevaluesarelessthanorequaltothisvalue.1
st
Quartile
.P25means25
th
percentile.
–P50:50%ofthesamplearelessthanorequaltothisvalue.2
nd
Quartile.
–P75:75%ofthesamplevaluesarelessthanorequaltothisvalue.3
rd
Quartile
–P100:Themaximum
Cont.…
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93. It is possible to estimate the values of percentiles from a
cumulative frequency polygon.
Cont.…
12/5/2023 93

94. 9. Box and Whisker Plot
•Itisanotherwaytodisplayinformationwhenthe
objectiveistoillustratecertainlocations(skewness)in
thedistribution.
•Canbeusedtodisplayasetofdiscreteorcontinuous
observationsusingasingleverticalaxis–onlycertain
summariesofthedataareshown.
•Firstthepercentiles(orquartiles)ofthedatasetmust
bedefined.
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94

95. •Aboxisdrawnwiththetopoftheboxatthethird
quartile(75%)andthebottomatthefirstquartile(25%).
•Thelocationofthemid-point(50%)ofthedistributionis
indicatedwithahorizontallineinthebox.
•Finally,straightlines,orwhiskers,aredrawnfromthe
centreofthetopoftheboxtothelargestobservationand
fromthecentreofthebottomoftheboxtothesmallest
observation.
Cont.…
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95

96. •Percentile = p(n+1), p=the required percentile
•Arrange the numbers in ascending order
A. 1
st
quartile = 0.25 (n+1)
th
B. 2
nd
quartile = 0.5 (n+1)
th
C. 3
rd
quartile = 0.75 (n+1)
th
D. 20
th
percentile = 0.2 (n+1)
th
C. 15
th
percentile = 0.15 (n+1)
th
Cont.…
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96

97. Cont.…
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98. •The p
th
percentile is a value that is P%of the
observations and the remaining (1-p)
%
.
•The p
th
percentile is:
–The observation corresponding to p(n+1)
th
if p(n+1) is an
integer.
–The average of (k)
th
and (k+1)
th
observations if p(n+1) is not
an integer, where kis the largest integer less than p(n+1).
•If p(n+1) = 3.6, the average of 3
th
and 4
th
observations
Cont.…
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98

99. •Given a sample of size n = 60, find the 10
th
percentile of the data set.
=> p(n+1) = 0.10(60+1) = 6.1
= “Average of 6
th
and 7
th
“
–10% of the observations are less than or equal to this
value and 90% of them are greater than or equal to
the value
Cont.…
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99

100. Cont.…
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100

101. Howcanthelowerquartile,medianandlower
quartilebeusedtojudgethesymmetryofa
distribution?
1.Ifthedistributionissymmetric,thentheupper
andlowerquartilesshouldbeapproximately
equallyspacedfromthemedian.
Cont.…
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102. Cont…
2.Iftheupperquartileisfartherfromthe
medianthanthelowerquartile,thenthe
distributionispositivelyskewed.
3.Ifthelowerquartileisfartherfromthemedian
thantheupperquartile,thenthedistribution
isnegativelyskewed.
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103. Cont.…
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103

104. Boxplotsareusefulforcomparingtwoormoregroupsof
observations
Cont.…
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105. Outlyingvalues
•Thelinescomingoutoftheboxarecalledthe“whiskers”.
•Theendsofthe“whiskers’arecalled“adjacentvalues)[The
largestandsmallestnon-outlyingvalues].
•Upper“adjacentvalue”=Thelargestvaluethatislessthanor
equaltoP75+1.5*(P75–P25).
•Lower“adjacentvalue”=Thesmallestvaluethatisgreaterthan
orequaltoP25–1.5*(P75–P25).
Cont.…
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106. •Theboxplotisthencompleted:
–Drawaverticalbarfromtheupperquartiletothe
largestnon-outliningvalueinthesample
–Drawaverticalbarfromthelowerquartiletothe
smallestnon-outlyingvalueinthesample
Cont.…
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107. Cont…
–Outliersaredisplayedasdots(orsmallcircles)andare
definedby:
Valuesgreaterthan75thpercentile+1.5*IQR
Valuessmallerthan25thpercentile−1.5*IQR
–AnyvaluesthatareoutsidetheIQRbutarenotoutliers
aremarkedbythewhiskersontheplot.
–IQR=P75–P25
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108. Cont.…
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109. •Numberofcigarettessmokedperdaywas
measuredjustbeforeeachsubjectattemptedto
quitsmoking
Cont.…
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110. 10. Scatter plot
•Moststudiesinmedicineinvolvemeasuringmorethanone
characteristic,andgraphsdisplayingtherelationship
betweentwocharacteristicsarecommoninliterature.
•Whenboththevariablesarequalitativethenwecanusea
multiplebargraph.
•Whenoneofthecharacteristicsisqualitativeandtheother
isquantitative,thedatacanbedisplayedinboxand
whiskerplots
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111. •Fortwoquantitativevariablesweusebivariate
plots(alsocalledscatterplotsorscatter
diagrams).
•Inthestudyonpercentagesaturationofbile,
informationwascollectedontheageofeach
patienttoseewhetherarelationshipexisted
betweenthetwomeasures.
Cont.…
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112. •A scatter diagram is constructed by drawing X-and Y-axes.
•Each point represented by a point or dot(•) represents a pair of
values measured for a single study subject
Cont.…
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112

113. •Thegraphsuggeststhepossibilityofapositive
relationshipbetweenageandpercentage
saturationofbileinwomen.
Cont.…
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114. 11. Line graph
•Usefulforassessingthetrendofparticularsituation
overtime
•Helpsformonitoringthetrendofepidemics.
•Thetime,inweeks,monthsoryears,ismarkedalongthe
horizontalaxis,and
•Valuesofthequantitybeingstudiedismarkedonthe
verticalaxis.
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114

115. Cont…
•Valuesforeachcategoryareconnectedby
continuousline
•Sometimestwoormoregraphsaredrawnon
thesamegraphtakingthesamescalesothat
theplottedgraphsarecomparable.
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116. No.ofmicroscopicallyconfirmedmalariacasesby
speciesandmonthatZewaymalariacontrolunit,20030
300
600
900
1200
1500
1800
2100
JanFebMarAprMayJunJulAugSepOctNovDec
No. of confirmed malaria cases
Months
Positive
P. falciparum
P. vivax
Cont.…
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117. •Line graph can be also used to depict the
relationship between two continuous variables like
that of scatter diagram.
•Thefollowinggraphshowslevelofzidovudine
(AZT)inthebloodofAIDSpatientsatseveraltimes
afteradministrationofthedrug,forwithnormalfat
absorptionandwithfatmalabsorption.
Cont.…
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118. Response to administration of zidovudine in two groups of AIDS
patients in hospital X, 1999
0
1
2
3
4
5
6
7
8
10 20 70 80
100 120 170 190 250 300 360
Tim e since adm inistration (Min.)
Blood zidovudine
concentration
Fat malabsorption Normal fat absorption Cont.…
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119. Exercise
Suppose a sample of 38 female university students was asked
their weights in pounds. This was actually done, with the
following results:
130 108 135 120 97 110 105 120
130 112 123 117 170 124 130 120
120 133 87 130 160 128 115 120
110 135 115 127 102 130 100
89 135 87 135 115 110 125
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120. Cont…
(a) Suppose we want 9 class intervals. Find CW.
(b) Construct a frequency distribution.
(c) Construct the corresponding histogram.
(d) Construct a frequency polygon and cumulative
frequency polygon
(e) Construct a stem and leaf plot
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121. Agraphisatool.
Itisnotartworkto
hangaboveyoursofa!
Itismoreimportantthatitis
easytocorrectlyinterpret
thanitisthatitispretty!
Remember:
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122. Exercise
1.Whichpictorialpresentationofdataisappropriatetopresent
theassociationbetweenbloodcholesterollevelandHeartrate?
2.Iftheinvestigatorisinterestedtoseethedistributionofbirth
weightwithregardtosexofthenewbornwhichmethodis
bettertopresentdata?
3.Ifavaluerepresentsthe95
th
percentile,this
means:______________________________
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122

123. Cont…
4.Inanumericaldata,thevalueforQ3can
neverbesmallerthanthevalueforQ1.
5.TheslopeofanOgivecurvecanneverbe
negativeifweusecumulativefrequency
morethanmethod.
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