Module 3
Presentation of Data
Introduction
Given a large mass of data, it is very hard for a researcher to
comprehend all the information and implications of such collected data.
Normally, large masses of data or collected data must be organized in
order to show significant characteristics or information.
Objectives:
At the end of this module, you should be able to:
1.
2.
3.
4.
Familiarize with the different methods of data presentation.
Organize data by constructing a frequency distribution table.
Draw the appropriate graph for a given set of data.
Implement the most appropriate method of data presentation for a
given data set.
Methods of Presenting Data:
1. Textual form – where the data are presented in paragraph form
or in sentence form.
2. Tabular form – where the data are presented in row and
columns
3. Graphical form – where the data are presented in pictorial or
visual form.
Textual Method. In this method of data presentation, the researcher
uses the sentences to convey the information contained in the data,
emphasis are only on important figures or the relevance of the other
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figures. This form of presentation is used for a very limited number of
figures to present. Example of such presentation can easily be seen on
newspaper accounts.
Tabular Method. This method of data presentation makes use of the
table where data are arranged systematically into rows and columns. This
systematic arrangement of data is called a statistical table. Through this
process, data can be readily understood and comparisons are more easily
be made.
A good statistical table has four essential parts:
1. Table heading – includes the table number and table title. The
title should briefly explain the contents of the table.
2. Stub – items or classification written on the first column and
identifies what are written on the rows.
3. Caption or box head – includes the items or classifications written
on the first row and identifies what are contained in the columns.
4. Body –the main part of the table and it contains the substance or
the figures of one’s data.
In the construction of a table, the following guidelines should prove
helpful.
1. Every table must be self-explanatory.
2. The title should be clear and descriptive.
3. The title gives information about what, where, how, and when the
data were taken.
Example of a statistical table:
Table 3.1
Population of the Philippines 1877 - 1980
Year
Population
1877
1887
1896
1903
1918
1939
5,567,685
5,984,727
6,261,339
7,635,426
10,314,310
16,000,303
Average Annual
Rate of Increase(%)
2.41
0.72
0.50
2.87
1.89
2.22
19
1948
1960
1970
1975
1980
19,234,182
27,087,685
36,684,486
41,831,045
48,098,000
1.91
3.06
3.01
2.66
2.40
Source of Data: National Statistics Office.
Frequency Distribution. A frequency distribution is an
arrangement of data that shows the frequency of occurrence of the
different values of the variables. There are two types of frequency
distribution.
The qualitative frequency distributions are usually
constructed for discrete variables, while quantitative frequency
distributions are usually constructed for continuous variable.
In constructing a qualitative frequency distribution, the following
steps are considered:
a. Enumerate the categories or classifications and define these
as your classes.
b. Count the number of observations falling under each
category. These are the frequencies of the different classes.
Example of a qualitative frequency (according to a particular category)
Table 3.2
DISTRIBUTION OF STUDENTS IN A PRIVATE SCHOOL
Year Level
First Year
Second Year
Third Year
Fourth Year
Number of Students
694
339
214
111
In constructing a quantitative frequency distribution, the following
steps are considered:
1. Determine the range R.
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R = highest value – lowest value
2. Solve for the number of classes or class intervals, k.
formulas can be used:
Square root method
K=N
Two
Sturges’ Formula
K = 1 + 3.322 log N
3. Determine the class size c.
ć = R/k
c is the nearest number to ć that has the same number of
decimal places as in the raw data.
4. Determine and enumerate the classes. Each class is an interval
of values defined by its lower an upper class limits. There must
be enough classes to include the highest score and the lowest
score. As a rule, the lowest value in the date becomes the lower
class limit (LL) of the first class interval. Adding c to the lower
class limit of the preceding class interval obtains succeeding
lower limits. Upper class limits (UL) are obtained using the
following formula:
UL = LL + c – 1 unit of measure
5. Count the number of observations that fall in each of the class
intervals.
Graphical Method. This method of data presentation makes use of
graphs or charts. A graph is a pictorial representation of a set of data
showing relationships. Some of the most common type of graphs are the
bar graph, line graph, pie graph and pictograph.
Types of graphs:
Line graph
The line graph shows the relationship between two or more sets of
quantities. This type of graph is appropriate for a variable that varies with
time.
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Bar graph
The bar graph consists of vertical or horizontal bars of equal widths. The
length of the bars represent the magnitudes of the quantities being
compared. This type of graph is most appropriate for comparing data at a
particular time.
Pie chart or pie graph
The pie chart or pie graph is appropriate in comparing the parts with the
whole.
Pictograph
Another way of representing numerical values is through the use of
pictographs or picture graphs. In this type of chart, actual pictures or
facsimiles of the objects under study are used to represent values. Each
figure is considered a unit representing a definite number.
Examples of each graph will be presented in class.
Graphical Representation of a Frequency Distribution
There are two graphical methods in the presentation of frequency
distribution.
Histogram
The histogram is a series of columns or vertical rectangles, each
having as its base one class interval, and the frequency or number of
cases in that class as its height.
Frequency polygon
The frequency polygon is the graph of the class mark against the
frequency. The shape of the histogram or the frequency polygon gives an
idea of the shape of the distribution.
Examples of histogram and frequency polygon will be presented in
class.
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Activity
1. Given below are the scores of 44 students in a statistics test.
8
18
12
22
8
2
18
17
30
7
18
12
4
19
18
13
8
22
26
11
23
17
2
8
10
8
11
8
8
22
19
3
13
12
9
13
16
8
21
21
6
5
2
15
16
a. Construct a frequency distribution with the following columns:
class interval, frequency, class mark, cumulative frequencies (less than
and greater than).
data.
b. Construct the histogram and the frequency polygon of the above
2. Below is a comparison of the number and type of nuclear weapons
between the North Atlantic Treaty Organization (NATO) and the
Warsaw Pact countries as of 1987. Draw the graph that best represents
the data.
Number of Weapons
Type of Weapon
Short-range missile
Intermediate-range missile
Artillery (nuclear capable)
Nuclear-capable tactical aircraft
NATO
Countries
Warsaw Pact
Countries
88
18
2924
1382
661
289
5598
2349
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3. Below are monthly data on sales of a department store. What type of
graph will best represent the data? Draw and explain the graph.
Month
Sales
(in thousand pesos)
January
February
March
April
May
June
July
August
September
October
November
December
200
400
600
500
750
750
450
400
350
300
550
1,000
4. The world’s watch production in 1988 was 560 million. The percentage
production of key regions and countries are found below. Draw the
graph that best represents the data.
Region/Country
China
Japan
Western Europe
North America
Eastern Europe & USSR
South and Southeast Asia
Latin America
Others
Percentage
Production
9.2
6.8
21.8
21.6
10.4
12.2
7.2
10.8