An introduction to
Medical statistics
(L2 presentation of data)
By
Dr. Basma M. Hani
Lecturer of Public Health
Faculty of Medicine
Benha University

DEFINITION
It is a process of putting
collected data in a
concise and
comprehensive form
(table or graph or
mathematical form)so
that the eyes can grasp it
easy. presentation of data 2

The main methods of presentation of
data are:
A. Tabular presentation.
B. Graphical presentation.
C. Mathematical presentation
(Numerical or Parameters).
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- Characteristics of the tables :
A table can be simple or
complex.
The tables should be
numbered.
A brief title must be given to
each table.
The headings of the columns
or rows should be clear and
concise. presentation of data 5

- Characteristics of the tables
:
The data must be presented
according to its importance.
Table should not be too large.
A vertical arrangement is
better than a horizontal one.
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 Some examples of tabulation
are(types):-
 • Simple tables
• Frequency distribution
tables
• Cumulative frequency
distribution tables
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9
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 The data is first split into convenient
groups or class intervals and the
number of items which occur in
each group (Frequency) is shown in
the adjacent column.

The following figures are the ages of patients admitted
to a hospital with gastroenteritis.
Construct a frequency distribution Table, regarding
their age distribution.
8, 24, 18, 5, 12, 4, 3, 3, 2, 3, 23, 9, 18, 16, 1, 2, 3, 5,
11, 31, 9, 11, 11, 7, 19, 6, 9, 5, 16, 20, 4, 3, 3, 3, 10, 3,
2, 1, 6, 9, 3, 7, 14, 8, 1, 4, 6, 4, 15, 22, 2, 1, 4, 7, 1, 12,
3, 23, 4, 19, 6, 2, 2, 4, 14, 2, 2, 21, 3, 2, 9, 3, 2, 1, 7,
19.
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Age (class interval) Number of patients
(frequency)
0 – 4 35
5 – 9 18
10 – 14 11
15 – 19 8
20 – 24 6
Table 2: Age distribution of gastroenteritis patients

In constructing frequency
distribution tables:
 Determine the largest and smallest
numbers in the given set of data i.e.
range.
 divide the range into a convenient
number of class intervals having the
same size.
 Determine the number of observations
falling into each class interval.
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◙ Shows the total number of observations either
less or more than a given level of the variable.
◙ Includes:
* Ascending distribution tables.
* Descending distribution tables.
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a) Ascending cumulative frequency tables:

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b) Descending cumulative frequency tables:

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Criteria of a graph
 The graph must be simple and
legible.
 Not more than 3, preferably only 2,
elements should be compared in a
single graph.
 The graph should be a simple
summary of tabulated data.
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Types of graphs
1. Bar charts.
2. Histogram.
3. Frequency polygon.
4. Line diagrams.
5. Pie (Circular) chart.
6. Pictogram.
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 Bar charts are ways of
presenting a set of numbers by
the length of a bar
 – the length of the bar is
proportional to the magnitude
to be represented.
 Bars may be vertical or
horizontal.
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1. Bar charts

 The bars are usually separated by
appropriate spaces,
 the bars should be of the same
width.
 A suitable scale must be chosen to
present the length of the bars.
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Vertical Bar
charts
horizontal Bar
chartspresentation of data 22

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0
10
20
30
40
50
60
70
80
90
100
Percentage(%)
U. R.
Residence
0
10
20
30
40
50
60
70
80
90
100
Percentage(%)
U. R.
Residence
Males Females
0
10
20
30
40
50
60
70
80
90
100
Percentage(%)
U. R.
Residence
Males Females
Simple Multiple Component

Figure 3.3 Simple bar chart (shows one variable in
one group )of hair color of children receiving
Malathion in nit lotion study
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Figure 3.4 Multiple (Compound) bar chart of hair
color by sex for children
Shows :-
One variables in >one group Or More than one variable in one group
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Component Bar Chart:
 The bars are divided into two or more parts which are
distinguished from each other by coloring, shading or
stippling.
 Each part representing a certain item and proportional to
the magnitude of that particular item.
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Figure 3.6 A component bar chart of hair
color by sex
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2. Histogram.
0
2
4
6
8
10
12
14
16
18
20
10 20 30 40 50 60 70 80
Age (Years)
%
of
the
population
28
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It’s a pictorial diagram
representing the frequency
distribution table.
As bar chart but with no
gaps.
Can represent only one
variable. presentation of data 29

Table(4): Grouped frequency distribution for birth
weight of 30 infants
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Figure 3.8 Histogram of the grouped
birth weight data in Table 4
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3. Frequency polygon
It is obtained by joining the mid-points of the histogram blocks

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4. line diagram:-Line diagram are used to show the trend
of event with the passage of time.
Fig.(3): Infant mortality rate in Egypt during the
period from 1935-1985.
0
50
100
150
200
1935 1945 1955 1965 1975 1985
Year
I.M.R.(per
thousand)

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5. Pie (Circular) chart.The distribution of the
component are based upon a percentage
Fig.(1): Distribution of the studied sample
according to their residence.
Urban
60%
Rural
40%

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6. Pictogram.Pictorial illustrations showing relative and
proportional sizes.
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According to types of data:-
1-Tools to Summarize
Categorical & Discrete Data
 Frequency Table(simple table).
 Bar Chart.
 Pie Chart.
 Pictogram.
2-Tools to Summarize
Continuous Data:
 Frequency Distribution Table.
 Histogram, Frequency Polygon
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Mathematical presentation:-
Measures of central
tendency and Measures
of dispersion

A-Measures of central
tendency
(Statistical averages)
The word “average”:
Is a value tending to lie centrally within a set
of data arranged according to magnitude

A-Measures of central
tendency
1- Mid-range
2- The arithmetic mean
3-The median
4-the mode

1-Mid-range
a-Ungrouped data
=Largest + smallest
2
b-Grouped data
=Lower limit of first interval + the
upper limit of last interval
2

 1-Mid-range
- Used only with quantitative variables
- Rapid, rough and easy
- Not accurate

Ungrouped data:Weights of 5 Persons
is 43, 20, 40, 36, 19 Kg.
Mid-range = (19+43)/2 = 31 Kg.
- Used only with quantitative
variables
- Rapid, rough and easy.
- Not accurate.
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Example
 The following table include the weight of 14
children calculate the mid-range
Mid-range=30+50 =40 Kg
2
Weight Frequency
30- 3
35- 5
40- 4
45-50 2
Total 14

2) The Arithmetic mean:
 Is the sum of the values in a set of data
divided by the number of the values in
the set. It is denoted by the sign X
(called X bar).
X= ∑x
n
X denotes any value of an observation
∑ means sum
n means number of observations

*The advantages of the mean
1- Easy to calculate
2- Easy to understand
*The disadvantages of the mean is that
sometimes may be affected by
abnormal values in the distribuation

Example
 The diastolic blood pressure of 5
individuals was
83, 75, 81, 79, 72 mmHg calculate the
mean
X= ∑x
n
=390 = 78 mmHg
5

3-The median
It is the central value of a set of
observations when those observations are
arranged in order of magnitude

A-Measures of central
tendency
 To obtain the median
a- The data is first arranged in an ascending or
descending order of magnitude
b- If the number of set is odd, the median is the
value
N+1
2
c- If the number of set is even, the middle
values are
N and N +1 and the mean of which is taken
as median
2 2

Example
 The diastolic blood pressure of 9
individuals was
83, 75, 81, 79, 71, 95, 75, 77, 84 calculate
the median
first we arrange the data
71, 75, 75, 77, 79, 81, 83, 84, 95
The number of set is odd
Median= N+1 = 9+1 =5
2 2
So the median is value number 5 in the set
of data=79

Example
 The diastolic blood pressure of 10 individuals
was
83, 75, 81, 79, 71, 95, 75, 77, 84, 90 calculate
the median
first we arrange the data
71, 75, 75, 77, 79, 81, 83, 84, 90, 95
The number of set is even so, the middle
values are
N =10 =5 and N +1= 10 +1 =6
2 2 2 2
The median is average of 5Th and 6Th
observation=79+81
=80
2

4) The mode:
- The mode is the most frequently occurring
value in a series of data.
- It may not exist; no modal.
- It may be unimodal, bimodal, trimodal...
etc.

Example
-2,3,4,4,5,4,7,7,7,9 what is the mode
It has 2 modes 4 and 7 (bimodal)
- 3, 5, 8, 10, 12, 15, 18 what is the mode
- It has no mode

B-Measures of dispersion
1-Range
2-Mean deviation (M.D.)
3-Variance = S2
4-Standard deviation (± S.D.)

B-Measures of dispersion
1- The range is the difference between
highest and lowest value
It depends only on the 2 outlying values e.g.
30, 34, 32, 36, 28. Range = 36 – 28 = 8

2-Mean deviation (M.D.) :-Is the arithmetic
mean of the numerical differences of all
observation from the mean, regardless of
sign around the mean.
=∑(X - X )
n

B-Measures of dispersion
3-Variance = S2
The sum of the squares of the deviation of each measurement in a
series from the mean of the series, divided by the total number of
the observation minus one (The degree of freedom).
=∑(X -X ) 2
n-1

B-Measures of dispersion
4-Standard deviation (± S.D.) it is the
positive square root of the variance

Example
 2,3,4,5,6,7,8 calculate the range,
mean deviation, variance and
standard deviation
1- range = 8-2=6
2- mean deviation
X =35/7= 5
Deviation from the mean=3,2,1,0,-1,-2,-
3
Mean deviation= 12/7= 1.71

Example
3- Variance= ∑ squared deviation from
the mean
n-1
=9+4+1+0+9+4+1 =28/6=4.6
6
4- Standard deviation = is the positive
square root of the variance
=2.1

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