2. Data organization and presentaion.ppt

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Data organization
Data organization
and
and
Presentation
Presentation
Biostatistics lecture note
Uquba G (MPH, MSc EMCC)

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Learning objectives
Learning objectives
 At the end of this lecture the students will be able to:
 Identify different ways of data organization & presentation
 Familiar with constructing different methods of data organization and
presentation

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Methods of data organization
Methods of data organization
 The data collected in a survey is called raw data
 Information is not immediately evident from the mass of unsorted raw data
 Needs to be organized in such a way as to condense information to show patterns
and variations
 Techniques of data organization & presentation
 Ordered array
 Tables &
 Graphs

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Ordered array
Ordered array
 A serial arrangement of numerical data in an ascending or descending
order
 Tells as the ranges of data and their general distributions
 Appropriate only for small data (<20)
 If it is beyond 20 we need to use frequency distributions or Tables

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Frequency distributions
Frequency distributions
 A frequency distribution is a summary of how often each value
occurs in a dataset.
 Is a table that shows data classified in to a number of classes with a
corresponding number of times falling in each categories (frequency)
 Frequency is the number of times a certain value of the variable is
separated in a given class.
 Two types
 Categorical frequency distribution
 Numerical frequency distribution

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Categorical frequency distribution
Categorical frequency distribution
 Used for data that can be placed in specific categories
 Used for nominal & Ordinal
 E.g. blood type, marital status etc.
 Example: A health worker collected data on blood type of 30
individuals and recorded as follows (Hypothetical)
 O, A, AB, B, O, O, O, A, B, O, AB, B, B, A, AB, O, O, O, B, AB, O, A,
AB, B, O, O, O, A, B, O

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Procedures to construct the frequency distribution
Procedures to construct the frequency distribution
There are 4 types of blood group, so we have four classes
Step 1: Make a table
Step 2: Tally the data & place the result in Tally column
Step 3: count the tally and Place the result in frequency
column
Step 4: calculate the % for each class
% = f/n*100
Where f= frequency of the class &
n= total number of values

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Numerical frequency distribution
Numerical frequency distribution
Here the classification criterion is quantitative
It has two forms
 Ungrouped frequency distribution
 For discrete quantitative data
 Grouped frequency distribution
 For continues quantitative data

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Ungrouped frequency distribution
Ungrouped frequency distribution
 Is a table of all the potential raw score values that could
possibly occur in the data along with the number of times
each actually occurred
 Often used for small set of data on discrete variables

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Constructing ungrouped freq. distri.
Constructing ungrouped freq. distri.
 1st
find the smallest & the largest values in the data
 Arrange the data in order of magnitude and count the frequency
 To facilitate counting one may include column of tallies.
 Steps in constructing
 Step 1: make the table
 Step 2: Tally the data
 Step 3: Count the frequency
 Step 4: compute the percentage
 E.g. the following hypothetical data represent family size of 50 households.
4, 6, 4, 3, 5, 2 , 8, 10, 4, 4, 5, 3, 5, 8, 4, 4, 6, 2, 6, 4, 3, 5, 2 , 8, 10, 4, 4, 5, 3, 5, 8,
4, 4, 6, 2, 5, 2 , 8, 10, 4, 4, 5, 3, 10, 4, 5, 6, 3, 5, 6

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Grouped frequency distribution (GFD)
Grouped frequency distribution (GFD)
 A frequency distribution when several numbers are grouped in one
class
 Usually used when the range of the data is large
 Two types
 Inclusive
 the upper limit of one class coincides with the lower limit of the next class
 Exclusive
 the upper limit of one class does not coincides with the lower limit of the
next class

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Grouped freq. distr….
 Example: Consider the following ungrouped marks of 30 students of
AMC Biostatistics course (out of 50%)
24 30 36 35 42 40 26 23
36 36 12 45 29 21 34 40
16 47 28 32 33 44 19 34
30 36 35 47 20 14
• Construct grouped frequency distribution for the above data

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Guidelines for creating classes
Guidelines for creating classes
1. There should be b/n 6-20 classes
2. The classes must be mutually exclusive.
i.e. no data value fall into two d/t classes
3. The classes must be all inclusive or exhaustive. i.e. all data values must
be included
4. The classes must be continues.
i.e. No gaps in a frequency distribution
5. The classes must be equal in width.
• The exception here is the first or the last classes
• Possible to have ‘Below…’ or ‘…and above’ class.
• Often used in ages.

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Steps in constructing Grouped freq. distr
Steps in constructing Grouped freq. distr.
.
1. Find the largest & smallest value
2. Compute range (R) = Maximum –Minimum
• From above example R = 47-12 =35
3. Select number of classes (usually 6-20) or use
 Sturge’s rule k = 1+ 3.322 logn
Where k is desired number of classes &
n is total number of observations
K will be round up if there are values after decimal
From the example above (n =30)
K = 1+ 3.322 log30 (log30 = 1.48)
K = 1 + 3.322(1.48) = 5.9, round up to 6
So we need to have 6 classes

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Steps…
Steps…
4. Find the class width (w) by dividing the range by the number of
classes and roundup not round off.
From ex. Above w = R/k = 35/6 = 5.8, rounded to 6
5. Form a suitable starting point which is equal to the minimum value.
 Starting point is called the lower limit of the 1st
class
 Continue to add the class width to this lower limit to get the rest of lower limits.

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Steps..
Steps..
 From the above example the lower class limits (LCL) will be:
 The starting point is Small value = 12, so,
 1st
lower limit = 12
 2nd
lower limit = 12 +6 =18
 3rd
lower limit = 18+6 = 24
 4th
 5th
lower limit= 30+6 = 36
 6th

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Steps…
Steps…
 1st
UCL = 12 + 5 = 17
 2nd
UCL = 18 + 5 = 23
 3rd
UCL = 24 + 5 = 29
 4th
UCL = 30 + 5 = 35
 5th
UCL = 36 + 5 = 41
 6th
UCL = 42 + 5 = 47
Classes Tally Freq %
12-17
18-23
24-29
30-35
36-41
42-47
Total
6. Find the upper class limit (UCL),
UCL= LCL + (w-1)
From the above ex. W= 6,
so, W-1 = 5

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Steps …
Steps …
7. Make tally
8. Count the tally & fill frequency
9. Calculate & fill percentages
10. Find relative frequency (rf)
Rf=f/n
11. Find cumulative frequency (cf):
 Lcf : Less than cumulative frequency (<UCB)
 Gcf: Greater than cumulative frequency (>LCB)

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By combining all the steps
By combining all the steps
Classes Tally Freq % rf Cf
(less than)
Cf (greater than)
12-17 /// 3 10.0 0.10 3 30
18-23 //// 4 13.3 0.13 7 27
24-29 //// 4 13.3 0.13 11 23
30-35 //// /// 8 26.7 0.27 19 19
36-41 //// / 6 20.0 0.20 25 11
42-47 //// 5 16.7 0.17 30 5
Total 30 100.0 1.00

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Common terms used in grouped freq. distr. (GFD)
 Class interval: range of scores grouped together in a GFD
 Class limits: the first & the last elements in the given class interval
 Units of measurement (U): the distance between two consecutive measures
 U = (n+1)th
LCL – nth
UCL
Example 12-17,
 18-23, U = 18-17 =1
 U is usually taken as; 1, 0.1, 0.01, 0.001….
Example 1: Unit of Measurement U = 0.1
 Intervals:
 12.0 - 12.1
 12.1 - 12.2
 Calculation:
 U=12.1−12.0=0.1U = 12.1 - 12.0 = 0.1U=12.1−12.0=0.1

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 Example 2: Unit of Measurement U = 0.01
 Intervals:
 12.00 - 12.01
 12.01 - 12.02
 Calculation:
 U=12.01−12.00=0.01U = 12.01 - 12.00 = 0.01U=12.01−12.00=0.01
 Example 3: Unit of Measurement U = 0.001
 Intervals:
 12.000 - 12.001
 12.001 - 12.002
 Calculation:
 U=12.001−12.000=0.001U = 12.001 - 12.000 = 0.001U=12.001−12.000=0.001

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Terms….
Terms….
12. Class boundaries: separates one class in GFD from another
 The boundaries have one more decimal places than the raw data and therefore do not
appear in the data
 There is no gap b/n the upper boundary of one class and the lower bounder of the next
class
 LCB = LCL-U/2
 UCB = UCL + U/2
 Eg. 12-17, 18-23, U = 18-17 =1
 LCB for 18-23, 18-1/2 = 18-0.5 =17.5
 UCB for 18-23, 23 + ½ = 23 +0.5 =23.5

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Terms…
Terms…
Classes Class boundaries Freq %
12-17 11.5-17.5
18-23 17.5-23.5
24-29 23.5-29.5
30-35 29.5-35.5
36-41 35.5-41.5
42-47 41.5-47.5
Total
Classes Boundaries
• Class width (w) = UCB-LCB

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Terms…
Terms…
13. Class mark (Xc)
 The mid point of the class
 The average of LCL & UCL or the average
of LCB + UCB
 Xc = LCL + UCL
2
Eg. Xc1 = 12+17 = 29/2 = 14.5
2
Classes Class marks
(Xc)
12-17 14.5
18-23 20.5
24-29 26.5
30-35 32.5
36-41 38.5
42-47 44.5
Total

------------------------------------------------------------------------------------
Cholesterol level
Mg/100ml freq Relative freq Cum freq Cum.rel. freq
-------------------------------------------------------------------------------------------
80-119 13 1.2 13 1.2
120-159 150 14.1 163 15.3
160-199 442 41.4 605 56.7
200-239 299 28.0 904 84.7
240-279 115 10.8 1019 95.5
280-319 34 3.2 1053 98.7
320-359 9 0.8 1062 99.5
360-399 5 0.5 1067 100
-------------------------------------------------------------------------------------------
Total 1067 100
Table xx. Frequencies of serum cholesterol levels for 1067 US males of ages 25-34 1976-1980

Example: the following data represent the amount of S. urea
(Mg/dl) of some patients
15,18,22,27,30,35,40, 18, 22, 24, 26, 45, 30, 17, 12, 32, 27, 41,
25, 15, 10, 12, 27, 26, 21, 20, 30, 28, 22, 25, 28, 42, 44, 48, 37,
25, 23, 24, 19, 20, 17, 13, 11, 15, 17, 32, 12, 14, 18, 11
i. Represent the above observations by a frequency table
ii. Find number of persons who have S. Urea 25 and above
iii. find percentage of persons who have S. Urea less than 30.

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Rules in constructing tables
Rules in constructing tables
1. Table should be as simple as possible (6-20 categories)
2. Tables should be self explanatory
• Title should be clear and to the point (answers: What, when, where, how
classified)
e.g. Table 1: Marks of 30 Medical students of AAU, March 2011, AA, Ethiopia.
• Placed above the table
3. Each raw & column should be labelled
4. Numerical entities of zero should be explicitly written rather than indicating by dash,
as dashes are reserved for missing or unobserved data.
5. Totals should be indicated (last raw last column)
6. If the data are not original, their source should be given in foot notes.

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Types of tables
Types of tables
 We have three d/t types of tables based on the number of variables included
1. Simple or one way table
 Single variable involved
2. Two way table
- Two variables cross tabulated
3. Higher ordered table
- Three or more variables involved

Brief
1. Immunization status of children in xxx woreda
2. Immunization status by sex of children in xxx woreda
3. Immunization status by sex and residence of children in xxx
woreda

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Eg. One way
Eg. One way
 Table 2: Immunization status of children in xxx woreda, 2010
(hypothetical)
Immunization status Number Percent
Immunized 135 64.3
Not immunized 75 35.7
Total 210 100.0

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Eg. Two way table
Eg. Two way table
 Table 3: Immunization status by sex of children in xxx woreda, 2010
(hypothetical)
Sex of children Immunization status Total
Immunized Not immunized N %
N % N %
Male 85 65.4 45 34.6 130 100.0
Female 50 62.5 30 37.5 80
Total 135 64.3 75 35.7 210 100.0

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Eg. Higher ordered table
Eg. Higher ordered table
•Table 4: Immunization status by sex and residence of children in xxx woreda, 2010 (hypothetic
Sex & residence of children
Immunization status Total
N % N %
Male Urban 55 68.7 25 31.3 80 100.0
Rural 30 60.0 20 40.0 50 100.0
Female Urban 40 66.7 20 33.3 60 100.0
rural 10 50.0 10 50.0 20 100.0
Total 135 64.3 75 35.7 210 100.0

Diagrammatic/Graphical
presentation of data

Objectives
 At the end of the class the students will be able to:
 Identify the different types of graphs
 Chose among the graphs based on the data
 Familiar with constructing the different types of graphs
 Identify importance and limitation of using graphs

Graphical presentation of data
 Techniques for presenting data in visual displays using geometric and pictures.
 Importance
 Greater attraction
 Easily understandable
 Facilitate comparison
 May reveal unsuspected patterns in complex set of data
 Greater memorizing value
Limitation
 Used only for purpose of comparison
 Not an alternative to tabulation
 Can give only an approximate idea
 They fail to bring to light to small differences

Graphs
 Graph should be CONISTENT
 With the size of the paper in w/c the diagram is to be drawn
 With value of the variable to be presented
 Sob the scale is chosen that the diagram is not looked too small
or too big
 It should be neat and clean
 Index to explain the symbols, colours, lines
 Explanatory notes to explains the important points at the bottom
or corner of the diagram.

Types of graphs
 For qualitative & quantitative discrete data
 Bar chart
 Pie chart
 For quantitative continues data
 Histograms
 Frequency polygon
 Cumulative frequency polygon ((ogive)
 Stem and leaf plot
 Scatter diagram
 Line graph

Bar chart
 A series of equally spaced bars having equal width (base) where
the height of the bar represents the frequency of (amount)
associated with each category.
 It could be either vertical or horizontal
 Three types based on number of variables involved
 Simple bar chart
 Multiple bar chart
 Component bar chart

Simple bar chart
 From our previous example
Table 2: Immunization status of children in xxx woreda, 2010
(hypothetical)
Immunization
status
Freq %
Immunized 135 64.3
Not immunized 75 35.7
Total 210 100.0
0
20
40
60
80
100
120
140
160
Immunized Not immunized
Immunization Status
num
ber
of
children
Figure 1: Immunization status of children in xxx woreda,
2010 (hypothetical)

Multiple bar chart
 From the previous example
Table 3: Immunization status by sex of children in xxx woreda, 2010
(hypothetical)
Sex of children Immunization status Total
N % N %
Male 85 65.4 45 34.6 130 100.0
Female 50 62.5 30 37.5 80
Total 135 64.3 75 35.7 210 100.0

Multiple bar chart…
0
10
20
30
40
50
60
70
80
90
Immunized not immunized
Immunization
N
o.
of
childern
Male
Female
Figure 2: Immunization status by sex of children in xxx woreda, 2010 (hypothetical)
0
10
20
30
40
50
60
70
Immunized not immunized
Immunization
%
of
children
Male
Female

Component bar chart
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
Male Female
Sex
%
of
children
0
20
40
60
80
100
120
140
Male Female
Sex
NO.
of
children
Figure 3: Immunization status by sex of children in xxx woreda, 2010 (hypothetical)
We can also construct component bar chart for the above table

.
. .
Bar charts showing frequency distribution of the variable ‘BWT’ described in
Table
0
1000
2000
3000
4000
5000
6000
Very low Low Normal Big
BWT
Freq.
0
20
40
60
80
100
Very low Low Normal Big
BWT
Rel.
Freq.

.
. .
Bar charts for comparison
 In order to compare the distribution of a variable for two or more groups,
bars are often drawn along side each other for groups being compared in a
single bar chart
9
88.9
2.1
7.9
89
3.1
0
10
20
30
40
50
60
70
80
90
100
Low Normal Big
BWT
Percen
t
Yes
No
BWT
Big
Normal
Low
Freq.
6000
5000
4000
3000
2000
1000
0
Antenatal Care
No
NNo
Yes
Bar chart indicating categories of birth weight of 9975 newborns grouped by antenatal follow-up of the
mothers

Pie chart
 A circle divided in to sectors so that the areas of the sectors
are proportional to the frequencies.
 Distribution of angles (360o
) is made based on the proportion
of each frequency’s share from the total observation.
 fi/n * 360o
or % of each class * 360o

Pie chart…
Blood Type Freq. %
A 5 16.7
B 7 23.3
AB 5 16.7
O 13 43.3
Total 30 100
A = 5/30*360o
=60o
B = 7/30*360o
=84o
AB = 5/30*360o
=60o
O = 13/30*360o
=156o
Example:
Table 4: Blood type of 30 individuals in xxx woreda, 2010
(hypothetical)

Pie chart
17%
23%
17%
43%
A
B
AB
O
Figure 4: Blood type of 30 individuals in XXXX Woreda, 2010 (hypothetical)

Line graph (diagram)
 The diagram is usually used to represents the time series data, where time is
plotted horizontal axis (x-axis) and the value of the variables against time is
plotted in variable axis (Y- axis) with appropriate scale
 Example: the following data represent the number of data patients of a
hospital in different years
Year 2006 2007 2008 2009 2010 2011
# of dead
patients
725 680 550 650 540 500

Histograms
 Graph consists of series of rectangles whose bases are equal to the class width of
the corresponding class & whose heights are proportional to class frequencies
 Used for quantitative Continues data
1. The horizontal axis is continues scale running from one extreme end
to the other
 Should be labelled with the name of the variable & units of measurement
2. For each class in the distribution, a vertical rectangle is drawn with:
 There will never be gaps b/n the histogram rectangles
 Bases of rectangle will be determined by the class width

Eg. Conseder the data on student marks
Classes Class marks (Xc) Frequency
12-17 14.5 3
18-23 20.5 4
24-29 26.5 4
30-35 32.5 8
36-41 38.5 6
42-47 44.5 5
Total 30
Table 5: Marks of 30 students, AMC Biostatistics course (out of 50%) , Ethiopia, 2021 (hypothetical data)

Histograms
Figure 4: Histograms showing students’ mark, AMC, 2021 (hypothetical data)

Frequency Polygon
 Join the mid points of the tops of the adjacent rectangles of the
histogram with segments
 When it is joined with x-axis the area under the polygon is equal to the
area under the histogram.
 The scales should be marked in the numerical values of the midpoints
(Xc)
 The length of the ordinates represent the class frequency.

2. Data organization and presentaion.ppt

Figure 5: Frequency polygon showing mark of 30 students, AAU, 2010, (Hypothetical data

Cumulative frequency polygon (Ogive)
 Line graph obtained by plotting the cumulative frequency
distribution (Y-axis) against class boundaries (x-axis)
 Two types
 Cumulative frequency Less than the UCB (Lcf)or
 Cumulative frequency More than the LCB (Mcf)
 We can also use the intersection of the two.

Construct Ogive by using the table from the above Example
Classes Class
boundaries
Freq Less
than cF
More than cf
12-17 11.5-17.5 3 3 30
18-23 17.5-23.5 4 7 27
24-29 23.5-29.5 4 11 23
30-35 29.5-35.5 8 19 19
36-41 35.5-41.5 6 25 11
42-47 41.5-47.5 5 30 5
Total 30

Less than Ogive
Figure 6: Less than Ogive showing mark of 30 students, AAU, 2010, (Hypothetical data)

More than Ogive
Figure 7: More than Ogive showing mark of 30 students, AAU, 2010, (Hypothetical data)

Scatter plot
 Used to show the relation ship between two variables.
 The symbol usually a dot is used to show the data pair.
 X-axis – independent variables (factors, cause)
 Y- axis dependent variables (out-come )

Summary
Data Type Graph Type Description Example
Qualitative Bar Chart Frequency of categories Types of fruits sold
Qualitative Pie Chart Proportions of categories Market share of smartphone
brands
Qualitative Stacked Bar
Chart
Composition of categories Students by major and year
Quantitative Discrete Bar Chart Counts of discrete numeric values Number of students in
grades
Quantitative Discrete Histogram Distribution of discrete values Scores in a test
Quantitative Discrete Dot Plot Individual occurrences of values Books read by each student
Quantitative
Continuous
Histogram Distribution of continuous data Heights of students
Quantitative
Continuous
Line Graph Trends over time Temperature changes over a
week
Quantitative
Continuous
Box Plot Summary of data distribution Test scores across classes
Quantitative
Continuous
Scatter Plot Relationship between two
continuous variables
Hours studied vs. exam
scores

Quiz
What is the most appropriate graphical method to display for
the following data?
1. The distribution of pain level status
2. The height measurement of 20 individuals
3. The age of pregnant women attending ANC
4. Treatment outcome among RTA patients

2. Data organization and presentaion.ppt

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