The document provides a detailed overview of statistical measures in public health, focusing on descriptive statistics, measures of central tendency (mean, median, mode, midrange), and measures of dispersion (range, variance, standard deviation). It outlines how to compute and interpret these statistics using both ungrouped and grouped data examples, and emphasizes the importance of understanding these concepts in analyzing demographic and health data. Additionally, it discusses demographic studies, including sources of demographic data and the significance of population statistics for policy and planning.

1. By
Bang Chuol (MPH in Epidemiology and Biostatistics)
February, 2024 G.C
Gambella, Ethiopia
GAMBELLA UNIVERSITY
COLLEGE OF NATURAL AND COMPUTATIONAL SCIENCES
DEPARTMENT OF PUBLIC HEALTH
BIOSTATISTICS

2. 2
Bang Chuol (MPH)

3. 3
Statistic vs Parameter
 Statistic: is a descriptive measure computed from the
data of a sample
 Parameter: is a descriptive measure computed from the
data of a population
 Since it is difficult to measure a parameter from the
population, a sample is drawn of size n, whose values are
 1 ,  2 , …,  n
 From such kind of data, we measure the statistic
Bang C. (MPH)

4. 4
A. Measures of Central Tendency
 A measure of central tendency is a measure which
indicates where the middle of the data is.
 The three most commonly used measures of central
tendency are:
 Mean
 Median
 Mode
 Midrange (MR)
Bang C. (MPH)

5. 1. The Mean
A. For ungrouped data
 is the average of the data
 The population mean (µ):
µ =
 This is usually unknown, then we use the sample mean to
estimate or approximate it
5
1
N
i
i
N
X


Bang C. (MPH)

6. 6
 The sample mean ( )
=
Example
 Here is a random sample of size 10 of ages
42, 28, 28, 61, 31, 23, 50, 24, 32, 37
 Meaning  1 = 42,  2 = 28,  3 = 28,  4 = 61,  5 = 31,
 6 = 23,  7 = 50,  8 = 34,  9 = 32,  10 = 37.
= (42 + 28 + … + 37) / 10
= 36.6
x
x
1
n
i
i
n
x


x
Bang C. (MPH)

7. B. For grouped data
7
Bang C. (MPH)

8. Example. Compute the mean age of 169 subjects from the grouped
data.
Class interval Mid-point (mi) Frequency (fi) mifi
10-19
20-29
30-39
40-49
50-59
60-69
14.5
24.5
34.5
44.5
54.5
64.5
4
66
47
36
12
4
58.0
1617.0
1621.5
1602.0
654.0
258.0
Total __ 169 5810.5
8
Bang C. (MPH)

9. 9
Properties of the mean
 Uniqueness: For a given data there is one and only one
mean
 Simplicity: It is easy to understand & to compute
 Affected by extreme values: because all values enter into
the computation
Bang C. (MPH)

10. 10
A. For ungrouped data
 Median is the value that divide the set of observations
into two equal parts after ordering the data according to
increasing or decreasing order of their magnitudes
(I) If n is odd, the median will be the middle of
observations
 It will be the [(n+1)/2]th in ordered observation
(II) If n is even, there are two middle observations
 The median will be the average of [n/2]th and
[(n/2)+1]th
2. The Median ( )
Bang C. (MPH)
x
~

11. 11
Example
 For the following observations, find Median
a. 23, 42, 28, 61, 28, 50, 31, 32, 37, 34
b. 23, 34, 28, 37, 50, 31, 32, 42, 28
Solution (a)
Since n = 10, then the median is
= [n/2]th + [(n/2)+1]th = (5th + 6th)/2
= (32+34)/2 = 33
(b)
 Since n = 9, then the median is
= [(n+1)/2]th
= 5th observation = 32
Bang C. (MPH)
x
~
x
~

12. B. For grouped data
 In calculating the median from grouped data, we assume
that the values within a class-interval are evenly
distributed through the interval
 The first step is to locate the class interval in which the
median is located, using the following procedure
 Find n/2 and see a class interval with a minimum
cumulative frequency which contains n/2
 Then, use the following formula
12
Bang C. (MPH)

13. 






 C
2
n
f
w
L
=
x
~
med
med
where,
Lmed = lower class boundary of the median class
C = cumulative frequency (less than type) before the
median class
fmed = frequency of the interval containing the median
W= class interval width
n = total number of observations
13
Bang C. (MPH)

14. Example: Compute the median age of 169 subjects
from the grouped data
Class interval Mid-point (mi) Frequency (fi) Cum. freq
10-19
20-29
30-39
40-49
50-59
60-69
14.5
24.5
34.5
44.5
54.5
64.5
4
66
47
36
12
4
4
70
117
153
165
169
Total 169
14
Bang C. (MPH)

15.  n/2 = 84.5 meaning the 3rd class is our median class
 Lower class boundary = 29.5
 Frequency of the median class = 47
32.58
70
2
169
47
10
29.5
=
)
x
~
(
Median 








15
Bang C. (MPH)

16. Properties of the Median
 Uniqueness: For a given set of data there is one and only
one median
 Simplicity: It is easy to calculate
 It is not affected by extreme values unlike the mean
16
Bang C. (MPH)

17. 17
3. The Mode ( )
A. For ungrouped data
 It is the value which occurs most frequently
 If all values are different there is no mode
 Sometimes, there are more than one mode
Example
1. Data are: 1, 2, 3, 4, 4, 4, 4, 5, 5, 6
 Mode is 4 “Unimodal”
2. Data are: 1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 8
 There are two modes; 2 & 5 “bi-modal”
3. Data are: 7, 2, 3, 9, 8, 11, 13, 17
 No mode, since all the values are different
Bang C. (MPH)
x̂

18. B. Grouped data
 To find the mode of grouped data, we usually refer to the
modal class, where the modal class is the class interval with
the highest frequency
 If a single value for the mode of grouped data must be
specified, it is taken as the mid-point of the modal class
interval
18
Bang C. (MPH)

19. 19








d2
d1
d1
L
=
x̂ mod w
Try !
Bang C. (MPH)
Where:
class
al
the
following
class
the
of
frequency
f
class
al
the
preceeding
class
the
of
frequency
f
class
al
the
of
frequency
f
f
f
f
f
class
al
the
of
size
the
w
on
distributi
the
of
e
the
X
mo
mo
mo
mod
mod
mod
mod
mod
ˆ
2
1
2
2
1
1











Note: d1 = ∆1 & d2 = ∆2

20. Properties of mode
 It is not affected by extreme values
 It can be calculated for distributions with open end
classes
 Often its value is not unique
 The main drawback of mode is that it may not
exist
20
Bang C. (MPH)

21. 21
4. The Midrange (MR)
A. For ungrouped data
 It is the average of largest and smallest value from the
dataset
B. For grouped data
 It is the average of upper class limit of the last class and
lower class limit of the first class
Bang C. (MPH)

22. 22
Group Assignment with Presentation [20%]
1. Explain in detailed term possible the quartile, decile and
percentile
2. Using your own ungrouped data [for all], calculate and
interpret the;
a. Quartile; Q1, Q2, Q3
b. Decile; D1, D2, D5, D9
c. Percentile; P1, P2, P50, P99
3. Using your own grouped data [for all], calculate and
interpret;
a. Quartile; Q1, Q2, Q3
b. Decile; D1, D2, D5, D9
c. Percentile; P1, P2, P50, P99
Bang C. (MPH)

23. 23
Measures of dispersion [Variation]
 A measure of dispersion conveys information regarding the
amount of variability present in a set of data
Note:
1. If all the values are the same
→ There is no dispersion
2. If some of the values are different
→ There is a dispersion
3. If the values close to each other
→The amount of Dispersion is small
4. If the values are widely scattered
→ The Dispersion is large
Bang C. (MPH)

24. 24
Some measures of dispersion are
 Range (R) and Relative range (RR)
 Variance (S2) or
 Standard deviation (S) or
 Coefficient of variation (C.V)
 Mean Deviation (M.D)…..about mean, median or mode
 Coefficient of Mean Deviation (C.M.D)…………about
mean, median or mode
 Quartile Deviation (Q.D)
 Coefficient of Quartile Deviation (C.Q.D)
2


Bang C. (MPH)

25. 25
1. The Range (R) and RR
 Range = Largest value - Smallest value =
Note (R) =
 Range concern only two values
 Example
Data:43,66,61,64,65,38,59,57,57,50
 Find the range (R) and relative range (RR) ?
 R = 66-38 = 28
 RR =??
S
L x
x 
Bang C. (MPH)

26. 26
2. The Variance:
 It measure dispersion relative to the scatter of the values
bout their mean
a. Sample Variance:
 where is sample mean
Example
 Data: 43,66,61,64,65,38,59,57,57,50, Find Sample
Variance?
 Solution:
 S2 = [(43-56) 2 +(66-56)2+…..+(50-56) 2 ]/10-1
= 810/9 = 90
x
1
1
2
)
(
2





n
n
i
x
i
x
S
Bang C. (MPH)

27. 27
b. Population Variance ( ) :
where , is Population mean
2

N
x
N
i
i



 1
2
2
)
( 


Bang C. (MPH)

28. 3. Standard Deviation:
 is the square root of variance =
a. Sample Standard Deviation (S) =
Example: If sample variance is 16, find the SD ?
S = = 5
b. Population Standard Deviation (σ) =
Example: If population variance is 36, find the SD ?
σ = = 6
28
Varince
2
S
2

Bang C. (MPH)
2
S
2


29. 29
4. Coefficient of Variation (C.V)
 Is a measure used to compare the dispersion between
two sets of data which is independent of the unit of the
measurement
or
%
100
. x
X
S
V
C  %
100
. x
V
C



Bang C. (MPH)

30. 30
Example
 Suppose two samples of human males yield the following
data
 We wish to know which is more variable (dispersed)
Solution
 C.V (Sample 1)= (10/145)*100= 6.9
 C.V (Sample 2)= (10/80)*100= 12.5
 The age of 11-year olds (sample 2) has more
variation that the 25 year olds (sample 1)
Sample 1 Sample 2
Age 25-year-olds 11year-olds
Mean weight 145 pound 80 pound
Standard
deviation
10 pound 10 pound
Bang C. (MPH)

31. 31
Home study….with assistance from instructor!
 Mean Deviation (M.D)…..about mean, median or mode
a. or
b. or
c. or
Bang C. (MPH)

32. 32
 Coefficient of Mean Deviation (C.M.D)…………about
mean, median or mode
 Interquartile Quartile Range (I.Q.R) = Q3 – Q1
 Quartile Deviation (Q.D) =
 Coefficient of Quartile Deviation (C.Q.D)
Bang C. (MPH)
taken
are
deviations
which
about
Average
D
M
D
M
C
.
.
. 
X
X
D
M
X
D
M
C
)
(
.
)
(
.
. 

X
X
D
M
X
D
M
C ~
)
~
(
.
)
~
(
.
. 
X
X
D
M
X
D
M
C
ˆ
)
ˆ
(
.
)
ˆ
(
.
. 

33. Exercising program on various practical questions
A. Measures of Central Tendency
A. Measures of Variation
33
Bang C. (MPH)

34. 34
Bang Chuol (MPH)

35. Demography
 Demography is the scientific study of human
populations, primarily with respect to the size,
distribution, composition, and as well as the causes and
consequences of their change (UN demographic
dictionary)
 Demography- is the study of a population in its static
and dynamic aspects
35
Bang Chuol (MPH)

36. Demography focuses on five aspects of human population
1. Size = number of persons in a given area at a given
time.
2. Distribution = the way the population is dispersed in
Geographic space at a given time.
3. Composition (static) = the numbers of person in sex,
age, and other “demographic” categories.
4. Population dynamics = fertility, mortality, migration
5. Socioeconomic determinants and consequences of
population change.
36
Bang Chuol (MPH)

37. Demographic aspects
Static aspects
 These are all characteristics that do not essentially
change at a point in time such as composition
 They are so-called ascribed characteristics
Dynamics aspects
 Are the movement of population
 When populations change in size, composition, or
distribution, the changes depend exclusively on one or
more of the three “demographic processes “namely
Fertility, Mortality & Migration
 These are continues processes that determine population
size, composition and distribution
37
Bang Chuol (MPH)

38. Population Studies
 The definition of demography can be extended
to include and cover:
 The social
 Economical
 Historical and
 Political characteristics of the population and related
processes
 This broader aspect is known as population
studies
38
Bang Chuol (MPH)

39.  Population studies is the study of the
relationships between demographic
variables and other variables such as
social, historical, political and economics
variables
 Population studies = Technical
demography + Substantive demography
 Population studies is at least as broad as
interest in the determinants and
consequences of population trends
39
Bang Chuol (MPH)

40.  Demographic data are important in providing
factual basis for decisions on matters of public
policy and actions concerning social and
economic affairs
 Moreover, population data has many uses for
policy makers, planners, educators, political
parties, business organizations, the media, and
researchers
40
Demographic Data
Bang Chuol (MPH)

41. Sources of demographic data
 Conventional sources
 Censuses
 Vital registration
 Surveys
 Non-conventional sources
 Population registers- (registration of the
movement of the population)
 Administrative records- (health facility
records, school enrollment, etc)
 Parish register- (baptismal and burial
registers)
41
Bang Chuol (MPH)

42. A. Census
 Census is an important and extensive source
of demographic information, both at the
national and sub-national levels
 It is called the inventory of the human
population of a country at a specified period
of time
42
Bang Chuol (MPH)

43.  A comprehensive definition of a modern
census
 Census is the total process of collecting,
compiling, analyzing, and publishing or
otherwise disseminating demographic,
economic, and social data pertaining to all
persons in a country at a specified time
43
Bang Chuol (MPH)

44.  It has involved the following essential characteristics;
(a) a complete enumerations of the entire population;
(b) the collection of information about some important
features of each person;
(c) the counting of people at regular intervals; and
(d) obtaining knowledge about the trends in population
growth and its structure and characteristics.
44
Bang Chuol (MPH)

45. The recommended variables included in census can be put into
three groups:
(i) Demographic characteristics : place where at the time of
census, place of usual residence, place of birth, duration of
residence, place of previous residence, place of work etc…
(ii) Personal and household characteristics: sex, age,
relationship to head of household, relationship to head of
family, marital status, age at marriage, duration of marriage,
children born alive, ….
(iii) Economic Characteristics: type of activity, occupation,
industry, status (as employer, employee, etc.) etc…
45
Variables in census
Bang Chuol (MPH)

46. Salient Features of Census
 Sponsorship
 because of the complex administrative arrangements it requires,
large amount of money and the authority required to collect
information, sponsored by an agency that has adequate
 administrative apparatus
 substantial financial resources and
 supreme legal authority over the entire population
 Territoriality
 The census has to clearly define the territory (whether it is national
or regional) with in which the population count is to be made
 This is more necessary because political and administrative
boundaries are often subjected to adjustments
46
Bang Chuol (MPH)

47. Universality
 There should be inclusion of all persons irrespective of
their ethnic and socio-economic characteristics
Periodicity
 Assess changes, to update estimates and to project them
to the future
 Carried out in a certain interval in most cases 10 years
47
Bang Chuol (MPH)

48. Comparability
 Concepts and definitions of terms vary within
a country from census to census
 Ensuring maximum comparability is possible
on a national basis and additional questions
are added to suit regional needs
48
Bang Chuol (MPH)

49. Techniques of census taking
 Census can be conducted using either of the following
procedures;
The De-jure approach
 It is an approach in which the registration of individuals takes place at
the normal place of residence
 Hence, temporary residents are not included while the permanent
members are counted whether or not are present at the time of
enumeration
 Usually census work is completed within a period of 2 to 3 weeks
called period enumeration
49
Bang Chuol (MPH)

50. Merits of the De-jure Approach
 It gives the picture of permanent population of a given
community in a given nation
 Gives more realistic and useful family and household
statistics
 Data can be used for the allocation of the representatives to
the congresses or parliaments, for planning community social
and welfare programs and so on
Discuss its demerits??
50
Bang Chuol (MPH)

51. The De-facto Approach
 All persons present in a place at the time of
enumeration are counted (registered)
irrespective of whether they belong to the
place or not
 Those who have been counted once
somewhere else will not be counted again.
 This system lasts only for one night
51
Bang Chuol (MPH)

52. Merits of the De-facto approach
 It offers less chance for double count and omission as
compared to the de-jure approach
 As persons are counted at any place they are found
during the time of enumeration, the de-facto approach
could present a true picture of the total population of a
given country
Discuss its demerits??
 The major steps in conducting census are;
1. Planning and preparation
2. Collecting information
3. Compiling and analyzing
4. Evaluation
52
Bang Chuol (MPH)

53. Enumeration /recording
 It is the process of collecting information concerning
each individual and their household
 The quality of census data depends up on:
 The cooperation of the public
 The efficiency of the enumerations
 The arrangements done for the field work
53
Bang Chuol (MPH)

54. Methods of Census Enumeration
Canvasser Method
 A trained person employed by the census called
enumerator or canvasser visits each of the households in
the enumeration area
 Collects information about all the persons in the
household from the responsible member of the
household through interviews using the standard
schedule, in a particular sequence, as instructed
54
Bang Chuol (MPH)

55. Householder Method
 the census questionnaires with the related instructions are
distributed well in advance of the census date to all the
households
 The responsibility of having the schedules duly completed and
returned to the census in time is entrusted with the head of the
household
55
Bang Chuol (MPH)

56. B. Vital Registration/civil
registration
 It is the continuous, obligatory and legal recording
of vital events, like births, deaths, marriages, divorces,
separations and adoptions
 vital registration becomes the only reliable tool to
understand dynamics of population if it is registered
continually
 The continuous nature of registering and data analysis
in vital registration remains the basic difference
between this method and the census
56
Bang Chuol (MPH)

57. History of vital registration
 Relatively modern concept in its present format.
 Churches have long maintained baptism and burial
registries
Data collection procedures
 Active: registrars visit every household
 Recommended among illiterate societies
 Passive: informants report to registrars
 Informants can be health facilities or family
members
 A combination of them
57
Bang Chuol (MPH)

58. Purpose
 The primary purpose is administrative to give
routine service to the community
 Certificates generated by the system can be used
to testify occurrence of events, which has legal use
 We can calculate various statistical index to
adjust the magnitude of population attributes
58
Bang Chuol (MPH)

59. Advantages
 Continuous monitoring of vital rates
 May provide both numerator and denominator for
some rates
 Small area data are available
 The information can be used as a base for testing the
accuracy of censuses and national surveys
Disadvantages
 Difficult to ensure registration of all the events
 Time reference is often contradictory with
denominator definition
 Information may come from the third party
59
Bang Chuol (MPH)

60. C. Sample Survey
 A sample survey is another source of demographic data
carried out in a scientifically selected area which covers
only a section or portion (sample) of the population
under consideration
 Surveys are usually undertaken during a period of
transition between two consecutive censuses
 Surveys are of a smaller size than a census, which allows
for collection of more in-depth information that can then
be generalized
Types of Survey
a. Single-round (retrospective/Cross-sectional)
b. Multi-round follow-up (prospective)
60
Bang Chuol (MPH)

61. Demographic Measurements (Migration, Fertility
and Mortality rates)
 Migration is a movement of individuals or groups which
involves a permanent or semi-permanent change of
usual residence
 Mobility is used for all forms of spatial movement,
whether permanent or temporary
 Migration is one of the three basic factors affecting
changes in the population of an area following births and
deaths
61
Bang Chuol (MPH)