METHODS OF REPRESENTATION OF DATA . pptx

METHODS
OF
REPRESENTATION OF DATA
PRESENTED BY :
Dr. G Charu Chitra
Reader, Dept of Public Health dentistry
Rama Dental College
1

TABLE OF CONTENT
1. Introduction
a) What do you mean by data
b) Types of statistical data
i. Qualitative data
ii. Quantitative data
2. Methods of representation of data
a) Tabulation
b) Drawings/Graphs
I. Presentation of Quantitative data through graphs
i. Histogram
ii. Frequency Polygon
iii. Frequency Curve
iv. Line chart or graph
v. Cumulative frequency diagram
vi. Scatter/Dot diagram
2

TABLE OF CONTENT
II. Presentation of Qualitative data through graphs
i. Bar diagram
ii. Pie/Sector diagram
iii. Pictogram/Picture diagram
iv. Map diagram / Spot map
3. Summary
4. Conclusion
3

INTRODUCTION
 DATA :
 Data, the plural of datum ,are facts expressed in
numerical terms .
 Information in raw or unorganized form (such as
alphabets, numbers, or symbols) that refer to, or
represent, conditions, ideas, or objects.
5
Indrayan A, Sarmukaddam SB. Medical Biostatistic.1st ed. (Marcel Dekker,Inc. New York)
chapter-3.p.66-78

INTRODUCTION Contd.
 Statistical data can be divided into broad categories :
1. Qualitative data
2. Quantitative data
6
Dixit JV.Principles and practice of biostatistics.4th ed.In:M/s Banarsidas bhanot publishers
2009.chapter-2.Collection and presentation of data.p.5-24

INTRODUCTION Contd.
1. Qualitative Data :
 Is also called as enumeration data.
 It represents a particular quality or attribute.
 These are expressed as numbers without units of
measurements.
 Examples : Religion,Sex,blood group, (Tall/Short)
etc
7

INTRODUCTION Contd.
2. Quantitative Data:
 Is also called as measurement data.
 These are expressed as number with or without units
of measurements.
 Example : Height in cm,Weight in kg,Blood pressure
(mm of Hg)
8
Dixit JV.Principles and practice of biostatistics.4th ed.In:M/s Banarsidas bhanot publishers 2009.chapter-
2.Collection and presentation of data.p.5-24

NEED FOR PRESENTATION OF DATA
 The information collected from various sources is
called as raw data .
 It does not lead to any understanding of the situation
 Hence it should be compiled, classified & presented in
a purposive manner to bring out important points
clearly and strikingly
9
Mahajan B.K.Methods in Biostatistics.6th ed. Jaypee Brothers,Medical publishers(p)
Ltd.chapter-6.p.88-102

PRINCIPLES OF PRESENTATION OF
DATA
10

PRINCIPLES OF PRESENTATION OF
DATA
 Data should be presented in such a way that data
should:
 arouse interest in reader
 Become concise without losing important details.
 Become simple & meaningful
 Facilitate further statistical analysis
 Define problem & suggest the solution too.
11

METHODS OF REPRESENTATION OF
DATA
12

METHODS OF
 There are two important methods for presenting the
data:
1. Tabulation
2. Diagrams/Graphs
13
Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing house
2009.chapter-14.Research methodology and biostatistics 365-384.

METHODS OF
1. Tabulation
14

DATA
1. TABULATION:
 Tables are simple devices used for presentation of
statistical data
General principles that are accepted for table construction:
 Tables should be as simple as possible
 It should be self-explanatory
 Each row & column should be labeled concisely & clearly
15

DATA
1. TABULATION Contd.:
 Table must be numbered
 Title should be clear,concise,and to the point.
 Tables should not be too large
 Foot notes be given wherever necessary
providing additional information, source or
explanatory notes.
16

TYPES OF TABLES
1. Master Table
2. Simple Table
3. Frequency Distribution Table
17

TYPES OF TABLES
1. Master Table:
 They are tables, which contain all the data obtained
from a survey.
18
Sl.No. Age Sex Education D M F DMF PI
001
002
003
004

TYPES OF TABLES
2. Simple Table
 They are one way tables which supply answers to
questions about one characteristic of data only.
19

TYPES OF TABLES
 Example of a simple table :
Number of students in colleges of RSS
Trust in 2011.
20
Name Of College No.Of Students
Dental College 540
Nursing College 675
College of Physiotherapy 586
College of Management 1025
Total 2826

TYPES OF TABLES
3. Frequency Distribution Table
 The simplest table is a two column frequency table
 The first column lists the classes into which the data
are grouped
 The second column lists the frequency for each
classification
21

TYPES OF TABLES
3. Frequency Distribution Table Contd.:
Example of a Frequency Distribution table :
Anemia in boys and girls of RV Dental
College
22
Sex Type Of Anemia Total
Mild Moderate Severe
Boys 615 85 15 260
Girls 190 120 45 355
Total 350 205 60 615

Table Of Content
1. Introduction
a) Tabulation
b) Drawings/Graphs
I. Presentation of Quantitative data through
graphs
II. Presentation of Qualitative data through
graphs
3. Summary
4. Evaluation Of Learning Objective
5. Conclusion
23

METHODS OF
2. Diagrams/Graphs
24

DIAGRAMS/GRAPHS
 Diagrams & graphs are one of the most convincing and
appealing ways of depicting results.
They are extremely useful because:
 They are attractive to the eyes.
 Gives a bird’s eye view of the entire data.
 Has a lasting impression on the mind of the layman
 Facilitates comparison of data
25

DIAGRAMS/GRAPHS
Principles in the construction of Diagrams & Graphs:
 Every diagram must be given a title that is self
explanatory.
 It should be simple & consistent with the data.
 The no. of lines drawn in any graph should not be
many. This makes it look clumsy.
 The scale of presentation for the X-axis & Y-axis
should be mentioned
26

PRESENTATION OF
QUANTITATIVE DATA
27

PRESENTATION OF
QUANTITATIVE DATA
 Presentation of quantitative data is through
graphs.
 The common graphs in use are:
1. Histogram
2. Frequency Polygon
3. Frequency Curve
4. Line chart or graph
5. Cumulative frequency diagram
6. Scatter/Dot diagram
28

PRESENTATION OF QUANTITATIVE
DATA
1. Histogram
29

DATA
1. HISTOGRAM :
 It’s a pictorial diagram of frequency distribution.
 The histogram is a series of columns or vertical
rectangles, each having as its base one class interval,
and the frequency or number of cases in that class as
its height
 The class intervals are given on the X axis and the
frequencies along the Y axis.
30

DATA
1. HISTOGRAM Contd.:
 There is no space between the cells on a
histogram.
 This graph is not to be confused with a
bar chart, which has space between the
cells.
31

HISTOGRAM :
Example : The following is the frequency
distribution of weights of 30 students of I
year dental students of a dental college .
Draw a histogram to represent the data.
32
Classes 45-50 50-55 55-60 60-65 65-70 Total
Frequency 3 7 12 5 3 30

Solution :
 For drawing a histogram we go through the steps similar to those of a
bar graph.
They are given below :
 Step 1 : On a paper, we draw two perpendicular lines and call them
horizontal and vertical axes.
 Step 2 : Along the horizontal axis, we take classes of equal width :45–
50, 50–55, ...... As the axis starts from 45–50, we take one interval 40–
45 before it and put a kink on axis before that
 Step 3 : Choose a suitable scale on the vertical axis to represent the
frequency. It can start from 0 to 12, with a step of 2, i.e., 0, 2, 4, 6, ....,
12, 14
 Step 4 : Draw the rectangles as shown in Fig.
33

PRESENTATION OF
QUANTITATIVE DATA
2. FREQUENCY POLYGON:
35

PRESENTATION OF
QUANTITATIVE DATA
2. FREQUENCY POLYGON:
 Its an area diagram of frequency distribution
developed over a histogram.
 The X axis depicts the categories of data and the Y
axis depicts the frequency of data in each category.
 Frequency polygon can be obtained from histogram by
joining mid points of blocks or rectangles of the
histogram.
36

FREQUENCY POLYGON:
EXAMPLE : The daily earnings of 100 Private
dental practioners are given below :
37
Daily
Earnings
in Rs.
200-300 300-
400
400-500 500-600 600-700 700-800 800-900
No. of
Dental
Clinics
3 12 15 30 25 12 3

PRESENTATION OF QUANTITATIVE DATA
3. FREQUENCY CURVE :
39

PRESENTATION OF
QUANTITATIVE DATA
3. FREQUENCY CURVE :
 As the number of observations become very large
& class intervals very much reduced, the frequency
polygon loses its angulation and gives rise to a
smooth curve known as frequency curve.
 Such frequency curves are often encountered
when we study the distribution of most of the
biological variables.
40

NOTE:
 Frequency polygon and frequency curves
are same except frequency curve is drawn
using free hand and frequency polygon is
drawn using scale. (Each point is joint
using scale)
42

4. LINE CHART OR GRAPH
43

PRESENTATION OF
QUANTITATIVE DATA
4. LINE CHART OR GRAPH
 Line charts are used to show the trend of
events with the passage of time.
 It is nothing but a frequency polygon
presenting variations by a line.
 The class interval can be a week, a month,
a year or 100 years.
 Scale used can change shape of line
diagram but not its trend
44

LINE CHART OR GRAPH
EXAMPLE:
The table below shows daily temperatures for Bangalore
City, recorded for 6 days, in degrees Fahrenheit.
45
Temperature in Bangalore City
Day Temperature
1 43
2 53
3 50
4 57
5 59
6 67

LINE CHART OR GRAPH
46
Temperature In Bangalore City

PRESENTATION OF
QUANTITATIVE DATA
5. CUMULATIVE FREQUENCY DIAGRAM/OGIVE
47

DATA
5. CUMULATIVE FREQUENCY DIAGRAM/OGIVE:
 Its also a representation of continuous and
ordered data
 In this case, the frequency of data in each
category represents the sum of the data from the
category and from the preceding category.
 Cumulative frequencies are plotted opposite the
group limits of the attribute or variable.
 These points are joined by a smooth free hand
curve to get a cumulative frequency diagram or
“ogive”.
48

DATA
Example :
A Professor arranged the marks gained by all year 10
pupils in a Anatomy test in a table as shown below:
49
Marks Frequency of
pupils
11-20 2
21-30 11
31-40 19
41-50 36
51-60 42
61-70 31
71-80 13
81-90 6

CUMULATIVE FREQUENCY
DIAGRAM/OGIVE:
 This table shows the number of pupils (called
the frequency) who gained marks in the
various mark bands, eg 31-40.
 For example, the number of pupils who scored
between 21 and 30 marks was 11.
 No pupil scored fewer than 11 marks or more
than 90 marks.
50

CUMULATIVE FREQUENCY DIAGRAM/OGIVE:
 To create a cumulative total for the frequency of
pupils in each group (called the cumulative frequency)
a third column is created as shown below:
51
Marks Frequency Cumulative
Total
Cumulative
frequency
11-20 2 2 2
21-30 11 2+11 13
31-40 19 13+19 32
41-50 36 32+36 68
51-60 42 68+42 110
61-70 31 110+31 141
71-80 13 141+13 154
81-90 6 154+6 160

CUMULATIVE FREQUENCY
DIAGRAM/OGIVE:
 The cumulative frequency column makes it
easy to see at a glance that 68 pupils
scored 50 marks or fewer, and that 32
pupils scored 40 marks or fewer.
52
Cumulative Frequency Graph for year 10 anatomy
results

PRESENTATION OF
QUANTITATIVE DATA
6. SCATTER/DOT DIAGRAM:
53

6. SCATTER/DOT DIAGRAM:
 These show relationship between two
variables
 Also called as correlation diagram
 Perpendicular drawn from each scatter point
on x & y axis gives value of two variables
associated with it.
 Depending on the clustering of scatter points
this diagram can provide evidence of positive,
negative or no correlation
54
2009.chapter-14.Research methodology and biostatistics 365-384

SCATTER/DOT DIAGRAM:
Example
The Prosthodontics and Periodontics results of ten dental
students are shown in the table below:
55
Name Sal Kim Bill Tom Gita Alex Bev Ken Alen Jo
Prostho 20 71 60 52 80 32 47 90 49 80
Perio 30 80 65 50 81 38 40 87 55 70

 To see whether there is a correlation
between the Prostho and Perio marks, you
could plot a scatter diagram.
 The Prostho mark is on the horizontal scale
and the corresponding Perio mark on the
vertical scale.
 Bill's Prostho mark was 60 and his Perio mark
was 65, so his results are represented by the
orange point at coordinates (60, 65).
56

57
Prosthodontics Mark
Periodontics
Marks

SCATTER PLOT
Things to look for:
 If the points cluster in a band running from lower left
to upper right, there is a positive correlation (if x
increases, y increases).
 If the points cluster in a band from upper left to
lower right, there is a negative correlation (if x
increases, y decreases).
58

 Imagine drawing a straight line or curve through the
data so that it "fits" as well as possible. The more the
points cluster closely around the imaginary line of
best fit, the stronger the relationship that exists
between the two variables.
 If it is hard to see where you would draw a line, and if
the points show no significant clustering, there is
probably no correlation.
59

Table Of Content
1. Introduction
a) Tabulation
b) Drawings/Graphs
I. Presentation of Quantitative data
through graphs
II. Presentation of Qualitative data
through graphs
3. Summary
4. Evaluation Of Learning Objective
5. Conclusion
60

PRESENTATION OF QUALITATIVE DATA
61

PRESENTATION OF QUALITATIVE
DATA
 Presentation of qualitative data is through
diagrams.
 The common diagrams in use are :
1. Bar diagram
2. Pie or sector diagram
3. Pictogram or Picture diagram
4. Map diagram or spot map
62

PRESENTATION OF
QUALITATIVE DATA
1. BAR DIAGRAM :
63

PRESENTATION OF QUANLITATIVE
DATA
1. BAR DIAGRAM :
 Bar diagram is a popular & easy method adopted
for visual comparison of the magnitude of
different frequency such as
morbity,mortality,immunization status of
population in different ages, sexes or places
 There are three types of bar diagrams:
a) Simple bar diagram
b) Multiple bar diagram
c) Proportional bar diagram
64

PRESENTATION OF QUANLITATIVE DATA
a) Simple bar diagram:
 It represents only one variable.
Example :
Age-wise prevalence of dental caries (in
percentage)
65

Simple bar diagram:
0
20
40
60
80
100
5-9 years 10-14 years 15-19 years
Caries
Caries
66
Age-wise prevalence of dental caries (in percentage)

DATA
b) Multiple bar diagram:
 This diagram is similar to the bar diagram except that
for each category of the variable there are set of
bars of the same width corresponding to the
different sections without any gap in between
Example:
Prevalence of dental caries based on age & gender
67

Multiple bar diagram:
0
20
40
60
80
100
5-9 years 10-14 years 15-19 years
Males
Females
68
Prevalence Of Dental Caries Based On Age & Gender

DATA
c) Proportional bar diagram:
 The individual bars are divided into two or more
parts.
 This diagram is used to compare the sub-groups
between different major groups of observations.
Example:
Prevalence of dental caries based on age and gender
69

Proportional bar diagram:
0 50 100 150 200
5-9 years
10-14 Years
15-19 years
Females
Males
70
Prevalence of dental caries based on age and gender

PRESENTATION OF
QUALITATIVE DATA
2. PIE/SECTOR DIAGRAM:
71

DATA
2. PIE/SECTOR DIAGRAM:
 They are so called because the entire graph
looks like a pie & its component represent
slices cut from a pie.
 The total angle at the Centre of a circle is
equal to 360 & it represents the total
frequency.
 It is divided into different sectors
corresponding to the frequencies of the
variables in the distribution.
 Eg.: Distribution of dental disease in 30-40
year olds.
72

DATA
2. PIE/SECTOR DIAGRAM Contd.:
 The segments are then shaded with
different shades or color and an index is
provided for these shade colors
 This diagram cannot be used to represent
two or more data sets.
73

PIE/SECTOR DIAGRAM:
Dental Diseases
Caries
Gingivitis
Periodontitis
30
35
45
74
Distribution of dental diseases in 30-40 year olds

PRESENTATION OF
QUALITATIVE DATA
3. PICTOGRAM OR PICTURE DIAGRAM:
75

DATA
3. PICTOGRAM OR PICTURE DIAGRAM:
 These diagrams are used for a layman man
those who cannot understand technical charts
like bar charts.
 Here pictures or symbols are used to present
the data.
Example:
 For physically disabled person the symbol of
person sitting on wheelchair is used in public
places.
76
Peter S. Essentials of community and preventive dentistry;4th ed.Arya publishing
house 2009.chapter-14.Research methodology and biostatistics 365-384.

Pictogram
77
India
Singapore
Bangladesh
Dentist population Ratio
7500
10000
1,50000

PRESENTATION OF
QUALITATIVE DATA
4. MAP DIAGRAM OR SPOT MAP:
78

DATA
4. MAP DIAGRAM OR SPOT MAP:
 These maps are used to show geographical
distribution of frequencies of a
characteristic.
 It is a map of an area with the location of
each case of an illness,death,abnormality or
condition identified by a spot ,dot or other
symbol on the map
79

CONCLUSION
 "A picture is worth a thousand words" refers
to the notion that a complex idea can be
conveyed with just a single still image.
 Representation of data through charts &
diagrams also aptly characterizes one of the
main goals of visualization, namely making it
possible to absorb large amounts of data
quickly.
81

REFERENCES
1. Dixit JV.Principles and practice of
biostatistics.4th ed.In:M/s Banarsidas bhanot
publishers 2009.chapter-2.Collection and
presentation of data.p.5-24
2. Mahajan B.K.Methods in Biostatistics.6th ed.
Jaypee Brothers,Medical publishers(p)
3. Hiremath SS.Textbook of preventive and
community dentistry.1st ed.Elsevier
2007:chapter-48. Biostatistics,p.483-488
82

REFERENCES
4. Peter S. Essentials of community and
preventive dentistry;4th ed.Arya
publishing house 2009.chapter-
14.Research methodology and
biostatistics 365-384
5. Indrayan A, Sarmukaddam SB. Medical
Biostatistic.1st ed. (Marcel Dekker,Inc.
New York) chapter-3.p.66-78
83

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