3. Collection, Organization and
Presentation of Data
Methods of data collection
Probability and non-probability sampling
Organization of data
Tabular and Graphical Data Presentation
4. At the end of this lesson, you should be able to:
1. Identify, compare and contrast the different sources of
data;
2. Summarize and present data in different forms; and
3. Construct frequency distribution and stem and leaf
display.
6. DATA
COLLECTION
Methods
• Survey
• Observation
• Existing
records
• Simulation
• experiment
Classification of
Data
• Primary Data
• Secondary Data
Non - Probability Sampling/ Non - Random
Sampling
• Haphazard / Accidental Sampling
• Judgment / Purposive Sampling
• Convenience Sampling
• Snowball sampling
Sampling Technique
Probability Sampling/ Random
Sampling
• Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
7. The goal of every statistical study is to collect
information which will be used in making
decisions.
Decision made from the results of any
statistical study is only as good as the process
used to obtain the information. If the process
is flawed, then the resulting decision is
questionable.
8. Methods
• Survey
• Observation
• Existing records
• Simulation
• experiment
Survey - an investigation of one or more characteristics of a population.
Most often, surveys are done by asking questions either thru self-
administered questionnaires or personal interviews. Nowadays, in the
advent of technology online survey becomes prevalent.
https://www.surveymonkey.com/mp/survey-question-types/
9. Kinds of Survey
a.Census – method of gathering the facts of
interest or pertinent data on every unit of the
population.
b.Sample Survey – method by which data from a
small but representative cross-section of the
population are scientifically collected and
analyzed.
Methods
• Survey
• Observation
• Existing records
• Simulation
• experiment
10. a. Speed and timeliness – data collected on the sample can be
gathered faster while ensuring uniformity of data gathering
procedure.
b. Economy – data gathering and analysis are cheaper.
c. Quality and accuracy – when properly conducted, a sample
survey usually yield more accurate results since a small highly
skilled group of workers (enumerators) are likely to make fewer
errors in the collection and handling of data than a large
census force would.
d. Feasibility – for a large population it is difficult or sometimes
impossible to gather all the data from a population. It is more
doable to gather data from a sample compared to a population.
e.g. lifetime of a bulb.
Methods
• Survey
• Observation
• Existing records
• Simulation
• experiment
Advantages of a sample survey over a census:
11. Methods
• Survey
• Observation
• Existing records
• Simulation
• experiment
Observation makes possible the recording of behavior but only at
the time of occurrence.
12. Methods
• Survey
• Observation
• Existing
records
• Simulation
• experiment
Existing records. Data from published
materials like reports, personal files, and
historical records will be utilized.
Existing data may be in the form
of individual records
• academic, medical, financial,
• data sets,
• interview notes,
• biospecimens,
• online profiles and posts (e.g., social
media), and
• audio- or video-recordings
(Duke Research and Innovation, 2024)
13. Methods
• Survey
• Observation
• Existing records
• Simulation
• experiment
Simulation. A simulation is the use of a mathematical or
physical model to reproduce the conditions of a
situation or process.
Simulation is used in a wide number of scenarios. Most often the purpose
of simulation is to prepare for an anticipated event such as with a fire drill
preparing for a real fire. It is also used to teach a skill for example, in
teaching how to perform cardiopulmonary resuscitation (CPR) or deliver a
baby.
14. Methods
• Survey
• Observation
• Existing records
• Simulation
• experiment
Experiment. In performing an experiment, a treatment
is applied to part of a population and responses are
observed. Data are obtained under controlled
conditions.
15. Classification of Data
Primary Data Secondary Data
data that are collected directly
from the subjects/objects of
the study.
– these are previously collected
data that are found in
publications of both government
and non-government institutions,
research papers, books,
periodicals, pamphlets,
computer files, microfilms or the
internet.
17. Generally, it is impossible to study an entire
population. Researchers typically rely on a
sample to obtain the needed information or
data.
Thus, it is important to obtain “good data”
because the inferences made will be based on
the statistics obtained from these data.
18. Sampling Technique is a procedure used
to determine the members of a sample.
Sampling frame is a list, or set of the
elements belonging to the population from
which the sample will be drawn.
To avoid biased data, a researcher must
make sure that the sample is representative
of the population.
19. Determining
the Sample
Size
There is
no absolute
formula in
determining the
sample size.
Slovin’s Formula. This formula is primarily used in the
descriptive studies where the population is known and the
margin of error is pre-identified
where:
n = sample size
N = population size
e = desired margin of error (percent allowance for non-
precision because of the use of the sample instead of
the population)
20. II. According to Gay and Mills (2016), the larger the
population size, the smaller the percentage of the
population required to get a representative sample.
For smaller populations, say, N = 100 or fewer, there is
little point in sampling; survey the entire population.
If the population size is around 500 (give or take 100),
50% should be sampled.
If the population size is around 1,500, 20% should be
sampled.
Beyond a certain point (about N = 5,000), the population
size is almost irrelevant and a sample size of 400 will be
adequate.
21. III. According to Fraenkel and Wallen (2011), the
guideline in selecting a sample size will be as follow:
For descriptive study 100 would be enough;
For correlational studies 50 samples can establish
relationship if there is any;
For experimental or causal-comparative 30 per group
is advise but 15 per group is allowed if the variables
are tightly controlled.
23. A.Probability or Random Sampling
is a procedure wherein every
element of the population is given
an equal chance of being selected in
the sample.
• Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
24. • Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
• giving each sampling unit an equal
chance of being included in the sample.
Fish bowl or lottery method.
Table of random numbers.
25. • Simple Random
• Systematic
Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
• Identify your population/ list will do
• Assign numbers to population
• Determine your sample size
• Determine your sampling interval/ kth interval
• Randomly select a starting point (between 1 and kth
interval)
• now, start identifying samples
26. Samples are selected by using every kth
individual from a population. The first
individual selected is a random number
between 1 and k.
• Simple Random
• Systematic
Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling Procedure in doing Systematic Random Sampling
• Identify your population/ list will do
• Assign numbers to population
• Determine your sample size
• Determine your sampling interval/ kth interval
• Randomly select a starting point (between 1 and kth
interval)
• now, start identifying samples
27. • Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
Separate the population into non-overlapping groups called
strata and then obtaining a simple random sample from each
stratum. The individual within each stratum should be
homogeneous (or similar) in some way (Blay, 2013).
Proportional Allocation – This process chooses sample sizes proportional to the
sizes of the different subgroups or strata.
Equal Allocation – This process chooses the same number of samples from each
group regardless of its size.
28. (stratum) N Relative Weight Sample needed (n)
Male
Female
Total
Stratified Random
Proportional
Allocation
29. b. Equal Allocation can be done by choosing
the same number of samples from each
group regardless of its size.
Say the student government president would like to see if the
opinions of the first-year students differ from those the second-
year students, if your sample size required 100 students then,
each year-level should have 50 respondents that are randomly
selected.
30. • Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
This is sometimes called area sampling because
this is usually applied when the population is large.
Subjects are selected by dividing the population into groups (clusters) and then
some of the groups are selected randomly. The final sample would include all the
subjects in the groups (clusters) randomly selected.
31. Procedure in doing Cluster Sampling
Step 1. Divide the entire population into pre-
existing segments or clusters. The
clusters are often geographic.
Step 2. Obtain a simple random sample of
the clusters.
Step 3. Use all the members of the clusters
obtained in step 2 as the sample.
• Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage sampling
32. • Simple Random
• Systematic Random
• Stratified Random
• Cluster Sampling
• Multi – stage
sampling
- The sample is randomly selected through
two or more steps or stages.
33. Non – Random
Sampling
Non-probability sampling is a method of
selecting units from a population using a
subjective (i.e. non-random) method.
Since non-probability sampling does not
require a complete survey frame, it is a fast,
easy and inexpensive way of obtaining data.
34. Haphazard or Accidental Sampling. Samples are
picked as it comes to the researcher. Many
fields in the social sciences, like archeology, history,
and medicine, picked samples this way, however,
often incorrectly assumed that the samples picked
are typical of the population they come from.
Non –
Random
Sampling
A haphazard sample…
• selection based on no formal predetermined rules
• The “person in the street” approach of television
interviewers usually uses haphazard sampling.
• survey where the interviewer selects any person
who happens to walk by.
35. Judgment or Purposive Sampling. The samples
are selected by the researcher subjectively. The
researcher will pick a sample that he/she believes is
representative to the population of interest.
Non –
Random
Sampling
36. Convenience Sampling. Selecting a sample based on the
convenience of the researcher or using data from population
members that are readily available.
Non –
Random
Sampling
37. Snowball Sampling. A special nonprobability method
used when the desired sample characteristic is rare.
Snowball sampling relies on referrals from initial subjects
to generate additional subjects.
Non –
Random
Sampling
38. Important Points to Consider When Collecting Data
If measurements of some characteristic from people are
being obtained, better results will be achieved if the
researcher does the measuring.
The method of data collection may delay the process.
Choose a method that would not produce a low
response rate.
3. Ensure that the sample size is large enough. Ensure
that the sample is a representative of the population.
40. 10 16 18 20 23 26 29 33
12 16 18 22 25 26 30 33
12 17 20 22 25 27 30 35
15 18 20 23 25 28 32 36
15 18 20 23 26 28 32 38
TEST SCORES OF 40 STUDENTS IN A 50 – TEM
STATISTICS EXAM
RAW DATA – data in the original form
- the data that has been collected directly from a primary source of data
that is not
processed or cleaned by anyone.
41. Class Limits/
Class Interval
Class Boundaries Frequency Class
Midpoint/
Class Mark
Less than
Cumulative
Frequency
Greater than
Cumulative
Frequency
Relative
Frequency
%
35 – 39 34.5 –
39.5
3
37 40 3 7.5
30 – 34 29.5 –
34.5
6
32 37 9 15
25 – 29 24.5 –
29.5
10
27 31 19 25
20 – 24 19.5 –
24.5
9
22 21 28 22.5
15 – 19 14.5 –
19.5
9
17 12 37 22.5
42. Frequency Distribution Table
- Organization of the raw data in table
form using classes and frequencies.
Class Limits Class Boundaries Frequency Class
Midpoint
Less than
Cumulative Frequency
Greater than
Cumulative Frequency
Relative Frequency
%
35 – 39 34.5 – 39.5 3 37 40 3 7.5
30 – 34 29.5 – 34.5 6 32 37 9 15
25 – 29 24.5 – 29.5 10
27 31 19 25
20 – 24 19.5 – 24.5 9 22 21 28 22.5
15 – 19 14.5 – 19.5 9
17 12 37 22.5
10 – 14 9.5 – 14.5 3
12 3 40 7.5
43. Categorical Frequency Distribution
Table
- Used for data that can be placed in the specific
categories, such as nominal or ordinal level data.
Class f Relative frequency
A 5 20
B 7 28
O 9 36
AB 4 16
total 25 100
AB B B AB O
O O B AB B
B B O A O
A O O O
AB
AB A O B A
44. Procedure for Constructing a Frequency
Distribution Table
1. Determine the classes
Range = Highest – Lowest
2. Sturges’ Formula
k = 1 + 3.322 log N
3. Determine the class size/class width
45. Class Limits - represent the smallest and largest data values that can
belong to each class.
• Lower class limit: The smallest data value that can belong to a
class.
• Upper class limit: The largest data value that can belong to a class.
Class Limits/Class Interval
35 – 39
30 – 34
25 – 29
20 – 24
15 – 19
10 – 14
Lower class limit Upper class limit
46. Class boundaries are the numbers used to separate classes.
lower class boundary - subtracting 0.5 from the lower class limit
Upper class boundary - adding 0.5 to the upper class limit
Class Limits Class Boundaries
35 – 39 34.5 – 39.5
30 – 34 29.5 – 34.5
25 – 29 24.5 – 29.5
20 – 24 19.5 – 24.5
15 – 19 14.5 – 19.5
10 – 14 9.5 – 14.5
Lower class boundary upper class boundary
47. Class Limits Class Boundaries Frequency
35 – 39 34.5 – 39.5 3
30 – 34 29.5 – 34.5 6
25 – 29 24.5 – 29.5 10
20 – 24 19.5 – 24.5 9
15 – 19 14.5 – 19.5 9
10 – 14 9.5 – 14.5 3
The frequency (f)
- number of observations in each class interval.
48. The class midpoint (or class mark) is a specific point in the center of
categories in a frequency distribution table
A midpoint is defined as the average of the upper and lower class limits.
Class Limits Class Boundaries Frequency Class Midpoint
35 – 39 34.5 – 39.5 3 37
30 – 34 29.5 – 34.5 6 32
25 – 29 24.5 – 29.5 10 27
20 – 24 19.5 – 24.5 9 22
15 – 19 14.5 – 19.5 9 17
10 – 14 9.5 – 14.5 3 12
49. Class Limits Class Boundaries Frequency Class
Midpoint/
Class Mark
Less than
Cumulative
Frequency
Greater than
Cumulative
Frequency
35 –
39
34.5 – 39.5 3 37 40 3
30 –
34
29.5 – 34.5 6 32 37 9
25 –
29
24.5 – 29.5 10 27 31 19
20 –
24
19.5 – 24.5 9 22 21 28
15 –
19
14.5 – 19.5 9 17 12 37
Cumulative Frequency
- sum of all previous
frequencies of the given data
50. Relative Frequency
the division between individual frequency of a certain
class by the total number of frequencies.
Class Limits Class Boundaries Frequency Class
Midpoint/
Class Mark
Less than
Cumulative
Frequency
Greater than
Cumulative
Frequency
%
Relative Fq
35 –
39
34.5 – 39.5 3 37 40 3 7.5
30 –
34
29.5 – 34.5 6 32 37 9 15
25 –
29
24.5 – 29.5 10 27 31 19 25
20 –
24
19.5 – 24.5 9 22 21 28 22.5
15 –
19
14.5 – 19.5 9 17 12 37 22.5
40
52. In the textual form, the researcher uses the sentences
to convey the information contained in the data. This is
incorporated with important figures only. Textual form
of presentation can be seen on news reports. For
example, an excerpt from news article:
“The new positives increased the region’s cumulative total to 6,884
with 3,194 active cases. Bacolod City still logged the highest number of
new cases with 106 while Negros Occidental has 53. Iloilo City has 45;
Iloilo province, 25; Capiz, 20; Aklan has two; and one each in Antique and
Guimaras. Local cases totaled 238, of whom 11 are locally stranded
individuals (LSIs), two are returning overseas Filipinos, and another two
are authorized persons outside of residence.”
(Source: https://www.pna.gov.ph/articles/1115061)
53. In the tabular form, the data are presented
in rows and columns. This systematic
arrangement of data is called a statistical
table.
Through this presentation, data can easily be
understood. In addition, you can easily
compare and contrast the data.
54. 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.
55. In graphical presentation, the data are presented in
graphs, charts, or diagrams. Graph is a pictorial
representation of a set of data that shows relationship.
Some common types of graphs are line graphs, bar
graph, pie graph and pictograph.
56. Activity:
Instruction Time: The average weekly
instruction time in schools for 5 selected
countries.
Country Time (hrs)
Thailand 31
China 27
France 25
The Philippines 40
United States 22
Use the data below and construct the
following, bar graph, line graph and pie
graph.
57. 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.
Thailand China France Philippines United
States
0
5
10
15
20
25
30
35
40
45
The average weekly instruction time in schools for
5 selected countries
58. Line graph
The line graph shows the relationship between two sets of quantities. Line
graph is similar to the graph drawn in Cartesian plane where the points are plotted
using vertical and horizontal axes. Thus, the points are connected with a line that
makes up the line graph. Line graph is appropriate for variables that predict trends
for a long period of time. Example of line graph:
Thailand China France Philippines United
States
0
5
10
15
20
25
30
35
40
45
31
27
25
40
22
The average weekly instruction time in
schools for 5 selected countries.
59. Pie chart or pie graph
The pie chart or pie graph is appropriate in comparing the parts with
the whole.
21%
19%
17%
28%
15%
The average weekly instruction time in schools for 5
selected countries.
Thailand China France
Philippines United States
60. 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.
61. The Stem-and-Leaf Diagram
Stem-and-leaf diagram
is a visual presentation of raw
data. In this set up, the
numbers (data) are broken into
tens digit and unit digits.
Every row represents the stem
and the numbers on the right
are the leaf.
22 30 19 26 8 8 12 21 15
18 18 12 8 17 11 3 16 5
12 17 4 22 2 8 13 8 2
9 5 19 13 23 7 20 13 7
8 7 18 11 10 22 9 21 16
2 5 8 9 12 13 17 19 22
2 7 8 9 12 15 18 20 22
3 7 8 10 12 16 18 21 23
4 7 8 11 13 16 18 21 26
5 8 8 11 13 17 19 22 30
The first column will be the tens digit followed by the vertical bar. We have to record the single digit
in a stem containing 0 in tens digit. Thus, 2 is written as 0 2. The first two digit number is 10
0 2 2 3 4 5 5 7 7 7 8 8 8 8 8 8 9 9
1 0 1 1 2 2 2 3 3 3 5 6 6 7 7 8 8 8 9 9
2 0 1 1 2 2 2 3 6
3 0
62. Histogram
The histogram is
a series of columns
or vertical
rectangles, each
having as its base
class interval, and
the frequency or
number of cases in
that class as its
height.
Using the
frequency
distribution (1st
Example), the
histogram looks like
34-42 43-51 52-60 61-69 70-78 79-87 88-96
0
5
10
15
20
Graph Showing the test Result of BSED
Students in a 50 item Statistics Exam
Class Limit
Frequency
35 – 39 30 – 34 25 – 29 20 – 24 15 –
19 10 – 14
63. 34-42 43-51 52-60 61-69 70-78 79-87 88-96
0
5
10
15
20
Graph Showing the test Result of BSED
Students in a 50 item Statistics Exam
Class Limit
Frequency
35 – 39 30 – 34 25 – 29 20 – 24 15 –
19 10 – 14
64. 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. Using the same
frequency distribution as
above, the frequency polygon
generated is presented below.
34-42 43-51 52-60 61-69 70-78 79-87 88-96
0
2
4
6
8
10
12
14
16
Graph Showing the test Result of BSED
Students in a 50 item Statistics Exam
38 47 56 65 74 83 92
Frequency
Class Midpoint/Class Mark
65. 34-42 43-51 52-60 61-69 70-78 79-87 88-96
0
2
4
6
8
10
12
14
16
Graph Showing the test Result of BSED
Students in a 50 item Statistics Exam
38 47 56 65 74 83 92
Frequency
Class Midpoint/Class Mark
66. Cumulative frequency distribution
Cumulative frequency
distribution or ogive tells us how
many observations lie above or
below certain values rather than
merely recording the number of
observations within intervals. There
are two types of ogives – the “less
than” and the “greater than” ogives.
The less than ogive is a graph
showing how many values are
below a certain upper class
boundaries. The greater than ogive
is a graph showing how many values
are above a certain upper class
boundary. 0
5
10
15
20
25
30
35
40
45
Graph Showing the test Result of BSED Students in
a 50 item Statistics Exam
less than greater than
9.5 19.5 24.5 29.5 34.5 39.5
Upper Class Boundaries
Frequency
67. 0
5
10
15
20
25
30
35
40
45
Graph Showing the test Result of BSED Students in
a 50 item Statistics Exam
less than greater than
9.5 19.5 24.5 29.5 34.5 39.5
Upper Class Boundaries
Frequency
68. Listed at the right are the salaries (in
thousands) of a sample of instructors to
associate professors in the University of
Antique. Construct a frequency distribution
table for the given data.
68 56 75 34
68 57 76 37
68 58 77 39
70 59 77 42
71 60 78 44
71 60 78 46
71 61 84 49
73 64 85 49
74 64 87 50
74 65 88 50
75 65 90 52
75 66 90 53
95 54
Class
Limits/
Class
Interval
Class
Boundaries
Frequency Class
Midpoint
/ Class
Mark
< c.f. > c.f. Relative Frequency
%
Answer the following.
1. What is the highest and the lowest salary in the
data set?
2. Using sturge’s formula, what is the number of
classes?
3. Determine the class width/ class size.
4. What salary interval (class interval) has the
highest number of employees ?
Editor's Notes
#11:It is also employed when the subjects cannot talk or write. In doing observation, the researchers make use of their senses and observe the condition in the natural state rather than communicating with their respondents.
#13:Simulations allow you to study situations that are impractical or even dangerous to create in real life.
Simulation-based methods involve the creation of artificial models to mimic real-world phenomena.
#15:Primary Data
These subjects/objects may be people, experimental animals, or the environment.
#25:Want to see this sampling method in action? Here is a look at the six systematic sampling steps with a real-world example.
1. Identify Your Population. This is the group from which you are sampling.
You are a small business owner with 2,000 customers. This is your population size.
2. Assign Numbers to the Population. In this step, you give every member of the population a number.
You put your customer list into a spreadsheet and number them from 1 to 2,000.
3. Determine Your Sample Size. Sample size is how many people from the total population you will survey.
Because you don’t have the time or money to survey all 2,000 customers, you choose to survey 10% of them, or 200. This is your sample size.
4. Determine Your Sampling Interval. To do this, divide the population size by the desired sample size.
In our example, 2,000 / 200 = 10. This means you would survey every tenth person from your total population of 2,000.
5. Choose a Starting Point. To be sure the sampling is random, choose a number between 0 and your sampling interval.
You can select a number between 0 and 10, and choose 7. This is your starting point.
6. Identify Sample Members. Now that you have your sampling interval and starting point, you can get started!
Selection begins at 7, and then every tenth person is selected from there (7, 17, 27, 37, and so on). For this reason, systematic sampling may also be referred to as systematic random sampling.
#35:In other words, units are selected “on purpose” in purposive sampling. Also called judgmental sampling, this sampling method relies on the researcher’s judgment when identifying and selecting the individuals, cases, or events that can provide the best information to achieve the study’s objectives.
#37:Also known as chain sampling or network sampling, snowball sampling begins with one or more study participants. It then continues on the basis of referrals from those participants. This process continues until you reach the desired sample, or a saturation point.