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# Analysis, Presentation, and Interpretation of Data

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## Gie Ranay

on 24 May 2014

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#### Transcript of Analysis, Presentation, and Interpretation of Data

Summarizing Quantitative Data
Quantitative research involves measurements, usually of a number of variables, across a sample.
Main Concepts:
Other Constituent Parts:
Preparing Data for Presentation
Talligram
How to construct a talligram:
1. Determine the classes and their respective subclasses along with their respective numbers.
2. Make rows for the classes by drawing horizontal lines with appropriate spaces between the lines and the number of the rows and should be two more than the number of classes.
3. Make columns for the subclasses by drawing vertical lines with appropriate spaces between the lines and the number of columns should be two more than the number of subclasses.

Techniques for Summarizing
and
Presenting Quantitative Data

Central Tendency
Frequency Distribution
Variation
Two features of the mean:

The first technical is the point in a distribution about which the sum of the squared deviations is at a minimum. This makes it important for estimating variance, and for least squares analysis.

The second feature is that the mean is very effective statistic when there is a great variance.
Several Ways to measure the Variance:
• The Range
 Highest score in the sample
minus the lowest score. (R=HS-LS)

• Standard Deviation
 Most common measure of variability.

Variance gives us numerical estimate of the amount of spread in the data. While the standard deviation is commonly used in descriptive statistics, the variance is more commonly used in statistical inference. But we can always obtain one from the other.
Figure 7.1, approximately:
 68% of all cases fall within one standard deviation
either side of the mean.
 95% of all cases fall within two standard deviations either side of the mean.
 99% of all cases fall within three standard deviations either side of the mean.
• Their calculation is straightforward.
• The individual scores in the distribution are tabulated
according to how many respondents achieved each score, or gave each response, or fell into each category.
• Absolute numbers and/or percentages may be used.
• Depending on the overall score range, it will sometimes be useful to group scores in ranges, to easily see the distribution of the frequencies.
• Results can be shown as frequency distribution tables, or as graphs.
• Histograms and frequency polygons are the most usual.
• Other graph forms are also possible such as pie charts or horizontal bar charts.

Example:
Analysis

– is the process of breaking
up the whole study into its
constituent parts of categories
according to the specific questions
under the statement of the problem.

- This is to bring out into focus
the essential features of the study.

- Usually precedes presentation.

Example:
In the study of teaching Science in the
high schools of Province A, the whole study
may be divided into constituent parts as
follows according to the specific questions:

1. Educational qualifications of the Science
teachers
2. Methods and strategies used in the teaching
of Science
3. Facilities available for the teaching of Science
4. Forms of supervisory assistance

Each constituent part may still be divided into its essential categories.

Example:
The educational qualifications of
the teachers may further be subdivided
into the following:

1. Degrees earned in pre-service
education
2. Major or specialization
3. Units earned in Science
4. Teacher’s examinations and
other examinations passed

Then under degrees earned are
1. Bachelor of Arts
2. Bachelor of Science in Education
3. Master of Arts
4. Etc.

Classification of data- is grouping together data with similar characteristics.

Bases of Classification:
a. Qualitative (kind) – those having the same quality or are the same kind are grouped together.
b. Quantitative – data are grouped according to their quantity.
c. Geographical – data may be classified according to their location.
d. Chronological – data are classified according to the order of occurrence.

Cross-classification – this is further classifying a group of data into subclasses.
Arrangement of data or classes of data – the bases of arrangement of data or groups of data are the same
as those of classification.
a. Qualitative – data may be arranged alphabetically or
from the biggest class to the smallest class.
b. Quantitative – this is arranging data according to their numerical magnitudes, from the greatest to the smallest number of vice versa.
c. Geographical – data may be arranged according to their geographical location or according to direction.
d. Chronological – this is listing down data that occurred
first and last those that occurred last, or vice versa
according to the purpose of presentation.

a. Teacher A is an AB graduate with a science major. Enter a tally in the cell which is the intersection of the AB row and the Science column. The tally is a short vertical bar. See Entry (1) in Figure 2.
b. Teacher B is an AB graduate with a science major. Enter a tally in the cell which is the intersection of the AB row and the Science column. See Entry (2) in Figure 2.
c. Teacher C is a BSE graduate with a science major. Enter a tally in the cell which is the intersection of the BSE row and the Science column. See Entry (3)
in Figure 2.
d. Teacher D is a BSE graduate with mathematics major. Enter a tally in the cell which is the intersection of the BSCE row and the Mathematics column. See Entry (4)
in Figure 2.
e. Teacher E is a BSCE graduate with mathematics major. Enter a tally in the cell which is the intersection of the BSCE row and the Mathematics column. See Entry (5) in Figure 2.
f. Continue the process until all the data needed are entered.
How to tally data (responses) gathered through a questionnaire. Tallying responses
to a questionnaire in a talligram follows. Suppose a questionnaire gives the following data:

Figure 2 may now be converted into a
statistical table for data presentation.
Generally, all quantified data are tallied first
in talligram which are then converted
into statistical tables for data
presentation using Hindu-Arabic numerals
in the cells in place of tallies.
GRAPHICAL PRESENTATION OF DATA
A graph is a chart representing the
quantitative variations or changes
of a variable itself, or quantitative
changes of a variable in
comparison with those of
another variable or variables
in pictorial or diagrammatic
form.
The purpose of graphing
is to present the variations,
changes, and relationships
of data in a most
attractive, appealing,
effective and
convincing way.

method according
to Bacani, et al.
THREE WAYS IN PRESENTING DATA
1. Textual Form- data in paragraph form.
the gathered data.
It can be presented using paragraphs or sentences.
It involves enumerating important characteristics, emphasizing significant figures and identifying
important features of data.

EXAMPLE:
in the statistics test. The following are the test scores of your class:
34 42 20 50 17 9 34 43 50 18
35 43 5023 23 35 37 38 38 39
38 38 39 24 29 25 26 28 27 44
44 49 48 46 45 45 46 45 46
Below is the rearrangement of data from lowest to highest:
9 23 28 35 38 43 45 48
17 24 29 37 39 43 45 49
18 25 34 38 39 44 46 50
20 26 34 38 39 44 46 50
23 27 35 38 42 45 46 50

In the statistics class of 40 students, 3 obtained the perfect score of 50.
Sixteen students got a score of 40 and above, while only 3 got 19 and
Below. Generally, the students performed well in the test with23 or 70%
Getting a passing score of 38.

2. TABULAR FORM
Frequency table or table of distribution.
Systematic and orderly presentation of data
in rows and columns.

EXAMPLE:
1. It attracts attention more effectively than do tables, and therefore, is less likely to be overlooked.

2. The use of colors and pictorial diagrams makes a list of figures in business reports more meaningful.

3. It gives a comprehensive view of quantitative data.

4. Graphs enable the busy executive of a business concern to grasp the essential facts quickly and without much trouble.

5. Their general usefulness lies in the simplicity they add to the presentation of numerical data.

Limitations of graphs according to Bacani, et al.
Graphs do not show as much information at a time as do tables.

Graphs do not show data as accurately as the tables do.

Charts require more skill, more time, and more expense to prepare than tables.

Graphs cannot be quoted in the same way as tabulated data.

Graphs can be made only after the data have been tabulated.

Graphs may be classified into the following types:
1. Bar graph
It is a diagram consisting of line showing the variations, relationships of data in different ways. It is generally used to make comparison of simple magnitudes very much more clearly and more distinctly perceptible to the eye.
Classifications of Bar graphs
a. Single vertical bar graph

b. Single horizontal bar graph
c. Grouped (Multiple or Composite)
Bar graph
d. Histogram
1. Number. Charts are numbered for reference purposes. The general practice is to write the number as Figure 1, figure 2, Figure 3, etc. at the bottom of the graph.

2. Title. The same principles hold in graphs as in tables. The title is usually written above the graph.

3. Scale. The scale indicates the length or height unit that a certain amount of the variable which is the subject of the graph. The scale enables the reader to interpret the significance of a number of length or height units.

4. Classification and arrangement. The principles of classification and arrangement are the same in graphs and as in tables.

5. Classes, categories, or time series are indicated at the x-axis and the scale units are indicated at the Y-axis.

6. Symmetry of the graph. The whole chart or graph should be about square, otherwise the length should be a little greater than the height.
Essentials of a graph:
7. Footnote. The footnote,
if there is any, should be placed immediately below the graph
aligned with the left side of
the graph.

8. Source. The source of data,
if there is any, should be written
just below the chart at the lower
left immediately below the
footnote if there is any, but
it should be above the
graph number.

2004
2007
2013
2010
2001
2. Linear graphs
a. Time series linear charts (single line)
b. Time series composite or multilinear charts
c. Frequency polygon
d. The ogive
Advantages of linear graphs or charts according to Bacani et al.:
1. The curve shows data as a continuous line; hence, it is continuous in its effect.

2. The wandering line of the curve tells the whole story.

3. Its preparation requires less time and skill.

3. The pie chart or circle graph
The circle is subdivided into portions whose number is equal to the number of components part. The size of each chart is proportional to the percent of the component part it represents. It is equated to 100% and because the circle has 360 0, 1% is equated to 3.6 0 so that 60% must be equal to 216 0 (3.6 x 60).

Construction
First, make a scale, that is, each picture or symbol must represent a definite number of units. So, to find the number of pictures or symbols to represents a magnitude, divide the magnitude by the number of units represented by each picture or symbol. The pictures or symbols must be of the same size and arranged in row or rows. The symbols should suggest the nature of the subject matter of the data being presented.

4. Pictograms
The pictograms or pictograph is used to portray data by means of pictures or symbols. Since the pictogram cannot portray data accurately, its only purpose is to make the comparison of magnitudes more vivid and clear. Besides, it is very attractive and never fails to catch attention.

Five elements of the
Implications of the Findings:

1. The existence of a condition. This condition is a finding discovered in the research.

2. The probable cause of the condition. If there is a condition there must be a cause and there must be a logical relationship between the condition and the cause, otherwise the cause may not be a valid one.

3. The probable effect of the condition. There is a probable effect of the condition and there must be a logical relationship between the condition and its probable effect.

4. The measure to remedy the unsatisfactory condition or to continue to strengthen the favourable one.

APPLICATION
Example:
You are asked to present the performance of your section in the Statistics test. The following are the test scores of your class: 34 42 20 50 17 9 34 43 50 18 35 43 50 23 23 35 37 38 38 39 39 38 38 39 24 29 25 26 28 27 44 44 49 48 46 45 45 46 45 46

Textual Form
Below is the rearrangement of data from lowest to highest:
9 23 28 35 38 43 45 48
17 24 29 37 39 43 45 49
18 25 34 38 39 44 46 50
20 26 34 38 39 44 46 50
23 27 35 38 42 45 46 50
In the Statistic Class of 40 students, 3 obtained the perfect score of 50. Sixteen students got a score of 40 and above, while only 3 got 19 and below. Generally, the students performed well in the test with 23 or 70% getting a passing score of 38.

Tabular Form
Frequency Distribution Table of the Performance
of 50 students in the Statistics Test

Graphical Form
Total= 40
Reporters:
Kristina Marie S. Ravelas
Virgie Lyn A. Ranay
Daniel S. Delos Reyes
Gerwayne M. Palomar

Professor
MR 200 Methodology of Research

3. The pie chart or circle graph
The circle is subdivided into portions
whose number is equal to the number
of components part. The size of each
chart is proportional to the percent
of the component part it represents.
It is equated to 100% and because
the circle has 360 0, 1% is equated
to 3.6 0 so that 60% must be equal
to 216 0 (3.6 x 60).
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