This document provides definitions and concepts related to biostatistics. It defines key terms like population, sample, variables, data and measures of central tendency. It describes measures of central tendency like mean, median and mode. It also discusses measures of variation or dispersion like range, variance and standard deviation. The document aims to introduce basic statistical concepts used in health sciences research.

1. INTRODUCTION TO
BIOSTATISTICS
DEFINITIONS

2. Statistics refers to numerical facts.
how data are
 Collected
 Organized
 Summarized
 Presented
 Analyzed
 Interpreted
Application of this knowledge in health
Sciences is Known as Biostatistics

3. Definitions
Population is a set of measurement of interest to
the sample collector. It may or may not be living e.g
population of Karachi, All TB patients in Karachi
Sample is any subset of measurements selected
from the population e.g. All TB patients coming to
CHK during November 2005
Element – Every single unit in the sample is known
as element.It may also be defined as an entity on
which measurements are obtained. Every TB
patient coming to CHK in November 2005
Cont…

4. Observation – Set of measurement
obtained for each element e.g. recording
of age wt, Hb, cholesterol etc
Variables – Any thing which changes
its value in different places or things e.g.
Age, wt Ht, blood sugar, Hb, Electrolyte
etc
Data – Facts and figures collected,
summarised and analysed.

5. MEASURES OF CENTRAL
TENDENCY
• Mean
• Median
• Mode

6. MEAN
The MEAN (or arithmetic mean) is
also known as the AVERAGE. It Is
calculated by totaling the results of
all the observations and dividing by
the total number of observations.
Note that the mean can only be
calculated for numerical data.

7. x  x
n
 6 + 4 + 4 + 3 + 2 + 4 + 5
7

28
7
 4 years
Average age of
children in years
Children 1 2 3 4 5 6 7
Age 6 4 4 3 2 4 5
MEAN
Cont…

8. • Advantages:
1) Familiar and intuitively clear to most people
2) Every data set has one and only one mean
3) Useful for performing statistical procedures
• Disadvantages:
1) May be affected by extreme values
2) Tedious to compute
Advantages / Disadvantages
of the Mean

9. Median
1. Measure of central tendency
2. Middlemost or most central item in
the set of ordered numbers
– If odd n, middle value of sequence
– If even n, average of 2 middle values
3. Not affected by extreme values

10. Calculating Median
Median = item in the data array
( )th
n + 1
2
Number of items in the array

11. Median of
Odd Sample Size
Median
PositioningPoint
Median






n 1
2
7 1
2
4 0
4
.
Number 1 2 3 4 5 6 7
of Child
Age 2 3 4 4 4 5 6
Ages of the
children

12. Median of
Even Sample Size
Median is 4
Positioning Point
Median
   




n 1
2
8 1
2
4.5
4 4
2
4
Ages of
the
children
Number of Child 1 2 3 4 5 6 7 8
Age 2 3 4 4 4 5 6 60

13. MODE
• The MODE is the most
frequently occurring value in a
set of observations.
• The mode is not very useful for
numerical data that are
continuous. It is most useful for
numerical data that have been
grouped into classes.

14. Mode
Examples
• No Mode
Raw Data:10.3 4.9 8.9 11.7 6.3 7.7
• One Mode
Raw Data: 2 3 4 4 4 5 6
• More Than 1 Mode
Raw Data: 21 28 28 41 43 43

15. Range is defined as the difference in
value between the highest (maximum)
and the lowest (minimum) observation
e.g. for previous data the lowest value is
2 and highest is 6
Hence the range is 6-2 = 4
Measures of Variation
Cont…

16. • Variance is defined as the sum of the
squares of the deviation about the
sample mean divided by the total
number of items
• Standard deviation it is the square root
of the variance
Measures of Variation

17. Standard Deviation
• The STANDARD DEVIATION is a
measure, which describes how much
individual measurements differ, on the
average, from the mean.
• A large standard deviation shows that
there is a wide scatter of measured values
around the mean, while a small standard
deviation shows that the individual values
are concentrated around the mean with
little variation among them.

18. Variance &
Standard Deviation
8

19. Computation of Variance &
Standard Deviation
Given a sample consisting of 7
children with following age
distribution compute the variance and
standard deviation.
Ages in complete years
2 3 4
4 4 5
6

20. Solution
s
n
2
1


 (x x)
2

_
Step 1: Compute the
Sample Mean
 x
n
= 4
x =
_
Observations
(x)
(1)
2
3
4
4
4
5
6
28

21. Solution
= 10
(7 - 1)
= 1.66
s = 1.66
= 1.3
s
n
2
1


 (x x)
2

_
Observation Mean
( x ) ( x ) (x – x) (x - x )2
( 1 ) ( 2 ) (1)-(2) [(1)-(2)]2
2 4 -2 4
3 4 -1 1
4 4 0 0
4 4 0 0
4 4 0 0
5 4 1 1
6 4 2 4
10
Step 2: Compute the
sum of (x x )
2

22. OBJECTIVES ?
By the end of session participants are able to
Define Biostatistics, variable, population,
and sample.
Identify different types of variable.
Describe the difference between common
word meanings and the same words if used in
statistics
Compute Measures of Central tendency
Compute Measures of Dispersion
Describe purpose of calculating standard
deviation

23. Tutorial
A population was surveyed to find out
hemoglobin level of 9 females of
reproductive age. The hemoglobin
recorded were as follows
9, 9, 9, 6, 7, 9, 11, 12, 9
a) Compute measures of Central tendency
b) Compute Measures of Dispersion

24. For the data set in the following exercise compute
(a) the mean, (b) the median, (c) the mode, (d) the
range, (e) the variance, (f) the standard deviation,
treat the data set as sample. Select the measure of
central tendency that you think would be most
appropriate for describing the data. Give reasons
to justify your choice
The results of a study by Dosman et al. (A-9) allowed them to
conclude that breathing cold air increases the bronchial reactivity
to inhaled histamine in asthmatic patents. The study subjects
were seven asthmatic patients aged 19 to 33 years. The baseline
forced expiratory values (in liters per minute) for the subjects in
their sample were as follows:
3.94 1.47 2.06 2.36 3.74 3.43 3.78
source: J. A. Dosman, W. G. Hodgson, and D. W.
Cockcroft, “Effect of Cold Air on the Bronchial
Response to Inhaled Histamine in Patients with
Asthma,” American Review of Respiratory Disease, 144
(1991), 45-50.

25. Home Assignment

26. Thankyou