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

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.

Advantages of the graphical

method according

to Bacani, et al.

THREE WAYS IN PRESENTING DATA

1. Textual Form- data in paragraph form.

The reader acquires information through reading

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:

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 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

ANSWER:

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:

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

Dr. Dominador Cabrera

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).