Data analysis

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

2. 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

3. The main methods of presentation of
data are:
A. Tabular presentation.
B. Graphical presentation.
C. Mathematical presentation
(Numerical or Parameters).
presentation of data 3

4. presentation of data 4

5. - 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

6. - 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.
presentation of data 6

7. presentation of data 7

8.  Some examples of tabulation
are(types):-
 • Simple tables
• Frequency distribution
tables
• Cumulative frequency
distribution tables
presentation of data 8

9. 9
presentation of data

10. presentation of data 10
 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.

11. 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.
presentation of data 11
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

12. 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.
presentation of data 12

13. ◙ Shows the total number of observations either
less or more than a given level of the variable.
◙ Includes:
* Ascending distribution tables.
* Descending distribution tables.
presentation of data 13

14. presentation of data 14
a) Ascending cumulative frequency tables:

15. presentation of data 15
b) Descending cumulative frequency tables:

16. presentation of data 16

17. presentation of data 17

18. 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.
presentation of data 22

19. Types of graphs
1. Bar charts.
2. Histogram.
3. Frequency polygon.
4. Line diagrams.
5. Pie (Circular) chart.
6. Pictogram.
presentation of data 19

20.  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.
presentation of data 20
1. Bar charts

21.  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.
presentation of data 21

22. Vertical Bar
charts
horizontal Bar
chartspresentation of data 22

23. presentation of data 23
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

24. Figure 3.3 Simple bar chart (shows one variable in
one group )of hair color of children receiving
Malathion in nit lotion study
presentation of data 24

25. 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
presentation of data 25

26. 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.
presentation of data 26

27. Figure 3.6 A component bar chart of hair
color by sex
presentation of data 27

28. 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
presentation of data

29. 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

30. Table(4): Grouped frequency distribution for birth
weight of 30 infants
presentation of data 30

31. Figure 3.8 Histogram of the grouped
birth weight data in Table 4
presentation of data 31

32. 32
presentation of data
3. Frequency polygon
It is obtained by joining the mid-points of the histogram blocks

33. presentation of data 33
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)

34. presentation of data 34
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%

35. presentation of data 35

36. presentation of data 36

37. 6. Pictogram.Pictorial illustrations showing relative and
proportional sizes.
presentation of data 37

38. 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
presentation of data 38

39. Mathematical presentation:-
Measures of central
tendency and Measures
of dispersion

40. 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

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

42. 1-Mid-range
a-Ungrouped data
=Largest + smallest
2
b-Grouped data
=Lower limit of first interval + the
upper limit of last interval
2

43.  1-Mid-range
- Used only with quantitative variables
- Rapid, rough and easy
- Not accurate

44. 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.
presentation of data 44

45. 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

46. 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

47. *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

48. 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

49. 3-The median
It is the central value of a set of
observations when those observations are
arranged in order of magnitude

50. 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

51. 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

52. 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

53. 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.

54. 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

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

56. 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

57. 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

58. 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

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

60. 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

61. 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

62. 62
presentation of data