Research notes on Distribution of data.ppt

Collection of data
• Types of data
• Primary data: are those which are
collected fresh and for the first time
• Secondary data : are those which have
been collected by someone else and
which have already been passed through
the statistical process

Method of Collection :
Primary data
• 1.Observation Method: observation by
observer
• “Observation may be defined as systematic
viewing ,coupled with consideration of seen
phenomenon - P.V. Young
• 2. Interview method : Oral-verbal responses
• a. Direct Personal interviews
• b. Indirect personal interviews
• c. Telephonic interviews
• d. Group interviews
• g. Postal interviews

Determining the question to be addressed
Constructing a frequency distribution involves:

Collecting raw data

Collecting raw data
Organizing data (frequency distribution)

Collecting raw data
Presenting data (graph)

Collecting raw data
Presenting data (graph)
Drawing conclusions

A Frequency Distribution
Frequency Distribution is a
grouping of data into mutually exclusive
categories showing the number of
observations in each class.

Uses of tabulation:
It facilitates the process of comparison
Statistical tables save space by reducing exploratory and
descriptive statement to a minimum.
Makes it easier to remember the data
Facilitates the summary of items and the detection of
errors and omissions.
Finally it provides a basis for statistical computations.

Class Midpoint
Class Midpoint:
: A point that divides a class
into two equal parts. This is the average of the upper
and lower class limits.
Definitions
Class Frequency
Class Frequency:
The number of
observations in each
class.
Class interval
Class interval: The
class interval is
obtained by subtracting
the lower limit of a
class from the lower
limit of the next class.
The class intervals
should be equal.

t
t
t
t
Step One
Step One:
: Decide on the
number of classes using the
formula 2
2k
k
> n
> n
where k=number of
classes
n=number of observations
Step Two
Step Two: Determine the class interval
or width using the formula
i > H – L
H – L
k
k

EXAMPLE 1
The Survival time in months for 50 patients suffering
from acute myeloblastic leukemia(AML) was given
below
a. Draw a frequency distribution table with proper
class intervals
b. Create a Histogram to show the distributions of
survival time
18 31 28 36 05 39 20 04 45 23
36 22 08 07 27 05 23 32 29 22
37 07 24 18 08 04 14 43 13 42
10 12 24 13 17 28 08 09 16 18
44 25 15 04 34 28 32 17 20 19

oThere are 50 observations so n=50.
oTwo raised to the sixth power is 64.
oTherefore, we should have at least
6classes, i.e., k=6.

where H=highest value, L=lowest value
45– 3
6
= 7
H – L
H – L
k
k
i > =
Round up for an interval of 7
Set the lower limit of the first class at 0, giving a
total of 7 classes.
Example

Step Three
Step Three: Set the individual class limits and
Steps Four and Five
Steps Four and Five: Tally and count the number of
items in each class.
0- 7 IIII
7 -14 IIII
14 -- 21 IIII
21 - 28 II
28 - 35 III
35 - 42 II
42 - 49 I

Presentation of data
The objectives:
Become concise without losing the details
Arouse interest in the reader
Become simple to form impressions
Define the problem and suggest the solution too
Become helpful in further analysis

A Histogram is a graph in which the class
midpoints or limits are marked on the horizontal
axis and the class frequencies on the vertical axis.
The class frequencies are represented by the heights
of the bars and the bars are drawn adjacent to each
other.
The three commonly used graphic forms are
Histograms, Frequency Polygons
Histograms, Frequency Polygons, and a
Cumulative Frequency
Cumulative Frequency distribution.

0
4
10
18
20
19
6
3
0
2
4
6
8
10
12
14
16
18
20
Number
of
cases
Fig 1:Histogram showing the height of the students
140 145 150 155 160 165 170 175

Graphic Presentation of a Frequency
Graphic Presentation of a Frequency
Distribution
Distribution
Graphic Presentation of a Frequency Distribution
A Frequency Polygon
Frequency Polygon consists of
line segments connecting the points
formed by the class midpoint and the
class frequency.

Frequency Polygon
Frequency Polygon for Hours
for Hours
Spent Studying
Spent Studying
0
2
4
6
8
10
12
14
10 15 20 25 30 35
Hours spent studying
Frequency
Frequency Polygon for Hours Spent Studying

Qualitative data:
• Bar charts:A Bar chart can be used to depict any of the level of
measurement(Nominal,ordinal,interval or ratio).
• Bar chart is a popular and easy method adopted for visual
comparison of the magnitude of different frequencies
• in discrete data, such as of morbidity,mortality , vaccinal status
of population in different ages, sexes, professions or places.
Different types of Bar diagrams are-
• 1. Simple bar diagram
• 2. Multiple bar diagram
• 3. Component bar diagram
• 4. Percentage bar diagram
•

•
Type of leprosy Number of patients
Tuberculoid 148
Lepromatous 64
Indeterminate 18
Borderline 10

Research notes on Distribution of data.ppt

Multiple bar chart:
INCOME STATUS

Component Bar chart:
Association between the exposure & the disease

Percentage bar chart:
BURDEN SCALE

46%
24.50%
18.50%
6.50%
4.50%
Group A
Group B
Group C
Group D
Group E
Pie Chart

Ex. 1
• A Psychologist estimates the IQ of 30 students . The values are as
follows:
• 86 98 78 96 79 81 103 85
• 94 100 103 112 76 95 98 94
• 101 99 83 94 64 78 122
• 105 11568 84 90 100 96
• Form a frequency distribution Table with proper class interval. Draw
the suitable diagram

Ex 2
• Represent the following data regarding religion wise break
down
• Hindu 297
• Muslim 99
• Christian 29
• Others 15

Research notes on Distribution of data.ppt

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