Organizing & Displaying Data

1. Organizing &
Displaying Data
STUDENTS COLLOQUY
By:
Meenu Saharan
Under Guidance of
Dr. Lokendra Sharma
Prof. Pharmacology
S.M.S. Medical College, Jaipur

2. Introduction
Statistics: Area of study in which we learn how to
collect, organize, and summarize information, and
how to answer research questions and draw
conclusions
Biostatistics: If the information is obtained from
biological and medical sciences, then we use the
term biostatistics.

3. Introduction
Populations: Largest group of people or things in
which we are interested at a particular time and
about which we want to make some statements or
conclusions.
Population Size: The number of elements in the
population is called the population size and is
denoted by N.

4. Introduction
Samples: From the population, we select various
elements (or individuals) on which we collect our
information. This part of the population on which
we collect data is called the sample.
Sample Size: The number of elements in the sample is
called the sample size and is denoted by n.

5. Introduction
Variables: The characteristics to be measured on the
elements of the population or sample are called
variables.
Example of Variables:
- No. of patients ,Height ,Sex, Educational Level
Types of Variables-Variables are classified as:
Quantitative variables
Qualitative variables. Cont…..

6. Types of Variables
Quantitative Variables: The values of a quantitative
variable are numbers indicating how much or how
many of something
Examples: - Family Size ,No. of patients ,Weight ,
height
Types of Quantitative Variables:
-Discrete Variables
-Continuous Variables
cont….

7. Types of Variables
Discrete Variables: A discrete variable can have
countable number of values, i.e., there are jumps
between the values.
Examples: - family size (x = 1, 2, 3, … )
- number of patients (x = 0, 1, 2, 3, … )
Continuous Variables: A continuous variable can
have any value within a certain interval of values.
Examples: - height (140 < x < 190)
- blood sugar level (10 < x < 15) cont….

8. Types of Variables
Qualitative Variables: The values of a qualitative
variable are words or attributes indicating to which
category an element of the population belong.
Examples: Sex, educational level, blood type ,
nationality
Types of Qualitative Variables :
Nominal Variables
Ordinal Variables
cont…..

9. Types of Variables
Nominal Variables: A nominal variable classifies the
observations into various mutually exclusive and
collectively non-ranked categories. The values of a
nominal variable are names or attributes that can not
be ordered or sorted or ranked.
Examples: - Blood type (O, AB, A, B)
- Nationality (Indian,Japness …)
- Sex (male, female)
cont….

10. Types of Variables
Ordinal Variables: An ordinal variable classifies the
observations into various mutually exclusive and
collectively ranked categories. The values of an
ordinal variable are categories that can be ordered,
sorted, or ranked by some criterion.
Examples: Educational level (elementary,intermediate
- Students grade (A, B, C, D, F)
- Military rank

12. Organizing The Data
Ungrouped (or Simple) frequency distributions for:
-Qualitative variables
-Discrete quantitative variables with a few different
values
Grouped frequency distributions for:
-Continuous quantitative variables
-Discrete quantitative variables with large number of
different values

13. Simple (or ungrouped) frequency
distribution
Example: The following data represent he number of
children of 16 women
3, 5, 2, 4, 0, 1, 3, 5, 2, 3, 2, 3, 3, 2, 4, 1
-Variable = X = no. of children (discrete, quantitative)
-Sample size=n=16
- Possible values of the variables are: 0, 1, 2, 3, 4, 5
cont….

14. Simple (or ungrouped) frequency
distribution
Value Frequency
0 1
1 2
2 4
3 5
4 2
5 2
Cont…

15. Simple (or ungrouped) frequency
distribution
The Simple frequency distribution of the no. of
children is:
No. of children (variables) Frequency(no. of women)
0 1
1 2
2 4
3 5
4 2
5 2
Total n=16
Note: Total of the frequencies =The sample size=n cont…

16. Simple (or ungrouped) frequency
distribution
Relative frequency & Percentage frequency
distributions:
-Relative frequency = frequency/n
- Percentage frequency = Relative frequency x100%
cont…..

17. Simple (or ungrouped) frequency distribution
Useful information can be obtained from the table above. For e.g.
6.25% of the women have no children.
Most of the women (31.25% of them) have 3 children.
25% of the women have 2 children.
No. of children
(variable)
Frequency(no. of
women)
Relative Freq.
(R.F.)
(=Freq./n)
Percentage
Freq.(=R.F.x100%)
0 1 0.0625 6.25%
1 2 0.125 12.5%
2 4 0.25 25%
3 5 0.3125 31.25%
4 2 0.125 12.5%
5 2 0.125 12.5%
Total n=16 1.00 100%

18. Graphical Representations of Simple
frequency distributions
There are several graphs representing simple
frequency distributions, one of which is the bar chart
(bar diagram / line chart)

19. Grouped Frequency distribution
Example: Following table gives the level(g/dl) of a sample of 50
men.
17.0 17.7 15.9 15.2 16.2 17.1 15.7 17.3 13.5 16.3
14.6 15.8 15.3 16.4 13.7 16.2 16.4 16.1 17.0 15.9
14.0 16.2 16.4 14.9 17.8 16.1 15.5 18.3 15.8 16.7
15.9 15.3 13.9 16.8 15.9 16.3 17.4 16.0 17.5 16.1
14.2 16.1 15.7 15.1 17.4 16.5 14.4 16.3 17.3 15.8
Variable=X=Hb level ( continuous, quantitative)
Sample size=n=50
Max=18.3, Min=13.5
The range of data is from 13.5 to 18.3
Class intervals: determine suitable intervals dividing the range of the data
For e.g. we may choose the following interval:
12.95-13.95, 13.95-14.95, 14.95-15.95, 15.95-16.95, 16.95-17.95, 17.95-18.95
cont….

20. Grouped Frequency distribution
Notes:
1. Minimum value: first interval
2. Maximum value: last interval
3. The intervals are not overlapped
4. These intervals are called true class intervals.
The end-point ( upper limit) of each interval
equals to the start- point( lower limit) of
following interval.
Class interval =C.I.
cont….

21. Grouped Frequency distribution
Interval Frequency
12.95-13.95 3
13.95-14.95 5
14.95-15.95 15
15.95-16.95 16
16.95-17.95 10
17.95-18.95 1
Interval ( Hb
level)
Frequency (no. of
men)
12.95-13.95 3
13.95-14.95 5
14.95-15.95 15
15.95-16.95 16
16.95-17.95 10
17.95-18.95 1
Total n=50
The grouped frequency distribution
for the Hb level of 50 men
cont…..

22. Grouped Frequency distribution
Mid –points ( class marks) of class intervals:
Mid –point= upper limit+ lower limit
2
Interval Frequency Class mid -point
12.95-13.95 3 13.45
13.95-14.95 5 14.45
14.95-15.95 15 15.45
15.95-16.95 16 16.45
16.95-17.95 10 17.45
17.95 (lower limit)-18.95(( upper limit) 1 18.45
cont….

23. Grouped Frequency distribution
For example:
Mid-point of first interval: (13.0+13.9)/2=13.45
Mid- point of last interval: (18.0+18.9)/2=18.45
Mid-point of a class interval is considered as a
typical ( approximate) value for all values in that
class interval. For example-approximately we
may say that
3 observation with the value of 13.45
5 observations with the value of 14.45
15 observations with the value of 15.45 cont….

24. Grouped Frequency distribution
Width of a class interval (W): The width of a
class interval denoted by (W) and is defined by:
W= upper limit- lower limit
For example: width of the interval in previous table
W = 13.95-12.95=1.0

25. Displaying Grouped Frequency
Distributions
For representing frequency or relative frequency
distributions, we use the following graphs
• Histograms
• Polygons
cont…..

26. Displaying Grouped Frequency
Distributions
Example: Consider the following frequency
distribution of the ages of 100 women
True C.I. Freq. ( no. of
women)
Cumulative
Freq.
Mid-points
14.5-19.5 8 8 17
19.5-24.5 16 24 22
24.5-29.5 32 56 27
29.5-34.5 28 84 32
34.5-39.5 12 96 37
39.5-44.5 4 100 42
Total n=100
Width of interval : W= 19.5-14.5=5 cont…..

27. Displaying Grouped Frequency
Distributions
Histogram: Organizing
& Displaying
Data using Histogram
cont….

28. Displaying Grouped Frequency
Distributions
Polygon: Organizing and Displaying Data using
Polygon (open)
cont….

29. Displaying Grouped Frequency
Distributions
Polygon (Closed)