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1. RANDOM
SAMPLING

2. Learning Competencies
The learner will be able to:
1. Calculate the sample size
using the Slovin’s formula.
2. Illustrate random sampling.

3. ORAL EXERCISES
Describe each of the following.
1. Interview method
2. Questionnaire method
3. Observation method
4. Test method
5. Registration method
6. Experimental method
7. Text method
8. Mechanical devices

4. METHODS OF COLLECTING
DATA
INTERVIEW METHOD
The researcher makes direct
and personal contact with the
interviewee. The researcher
gathers data by asking the
interviewee series of questions.

5. INTERVIEW METHOD
DIRECT METHOD
The researcher personally
interviews the respondents.
INDIRECT METHOD
The researcher uses a
telephone to interview the
respondents.

6. METHODS OF COLLECTING
DATA
QUESTIONNAIRE METHOD
The researcher distributes
the questionnaires either
personally or by mail and
collects them by the same
process.

7. QUESTIONNAIRE METHOD
 GUIDED-RESPONSE TYPE
 RECALL TYPE
 RECOGNITION TYPE
 DICHOTOMOUSTYPE
 MULTIPLE-CHOICE TYPE
 MULTIPLE-RESPONSE TYPE
 FREE-RESPONSE TYPE
 RATING SCALE TYPE

8. METHODS OF COLLECTING
DATA
OBSERVATION METHOD
The researcher may observe
subjects individually or group of
individuals to obtain data and
information related to the objectives
of the investigation. It is a method of
obtaining data by seeing, hearing,
testing, touching and smelling.

9. METHODS OF COLLECTING
DATA
TEST METHOD
This method is widely used
in psychological research and
psychiatry. Standard tests are
used because of their validity,
reliability and usability.

10. METHODS OF COLLECTING
DATA
REGISTRATION METHOD
This method of collecting
data is governed by our existing
laws.

11. METHODS OF COLLECTING
DATA
EXPERIMENTAL METHOD
This method of collecting
data is used to find out the
cause and effect relationship of
certain phenomena under
controlled conditions.

12. METHODS OF COLLECTING
DATA
TEXT METHOD
The researcher may ask or
invite individuals to send text
opinions on certain issues or send
in their choices on their brand
preferences on a particular
product using their cellphones.

13. METHODS OF COLLECTING
DATA
MECHANICAL DEVICES
The devices that can be used
when gathering data for social
and educational researchers are
the camera, projector, videotape,
tape recorder, etc.

14. SAMPLING
It is the process or technique of selecting a
representative sample from the entire
population. It is a method used to determine
which element is to be included in the
sample.
POPULATION – refers to the entire group
of individuals or objects known to have
similar characteristics.
SAMPLE – is a subset of the entire
population.

15. DETERMINING THE SAMPLE SIZE
We use Slovin’s formula to determine
the statistically acceptable sample size to be
extracted from the given population.The
Slovin’s formula is
where: n = number of samples needed
N = population size
e = margin of error

16. EXAMPLE
1. A group of researchers was tasked
by the House of Representatives to
survey whether students in Metro
Manila favor the moving of the start of
classes from June to September. If
there are 1,000,000 students and 10%
margin of error is expected, compute
the sample size.

17. EXAMPLE
2. A researcher wants to know
the average of the families living
in Barangay A which has 2,500
residents. Calculate the sample
size the researcher will need if
a 5% margin of error is allowed.

18. EXAMPLE
3.A researcher wants to study the
effects of social media on Grade
11 students in Pulung Santol
National High School. If there are
250 Grade 11 students in the
school, how many students should
there be in his sample if 5% margin
of error is allowed?

19. ACTIVITY 15
Using the Slovin’s formula, determine the
sample size given the population (N) and
the margin of error (e).
1. N=800 e=2% 6. N=75,000 e=6%
2. N=2,000 e=3% 7. N=20,000 e=4%
3. N=10,000 e=5% 8. N=45,000 e=8%
4. N=50,000 e=7% 9. N=30,000 e=9%
5. N=25,000 e=10% 10. N=15,000 e=5%

20. RANDOM SAMPLING
TECHNIQUE or PROBABILITY
SAMPLING TECHNIQUE
It is a part of sampling
technique in which each sample
has an equal chance of being
chosen.

21. RANDOM SAMPLING
TECHNIQUE or PROBABILITY
SAMPLING TECHNIQUE
It is one of the simplest forms
of collecting data from the total
population.

22. RANDOM SAMPLING
TECHNIQUE or PROBABILITY
SAMPLING TECHNIQUE
In order to obtain a genuine
or unbiased sample, each member
of the population must have an
equal chance of being included in
the sample.

23. RANDOM SAMPLING TECHNIQUE
or PROBABILITY SAMPLING
TECHNIQUE
1. SIMPLE RANDOM SAMPLING
It is the most commonly used
random sampling technique. In this
technique, each member of the
population has an equal chance to
be selected as a participant.

24. SIMPLE RANDOM SAMPLING
LOTTERY METHOD
It is the most primitive and
mechanical example of simple random
sampling procedure. This is commonly
known as the “fish bowl method”.

25. SIMPLE RANDOM SAMPLING
LOTTERY METHOD
Steps:
1. List down or write the names of each
member of the population in a separate
pieces of paper.
2. Fold each piece of papers and place in a
bowl.
3. Mix and pick.The names to be randomly
picked from the bowl will form the
sample group.

26. LOTTERY METHOD
SIMPLE RANDOM SAMPLING without
REPLACEMENT
The selection of elements depends
entirely on chance.
SIMPLE RANDOM SAMPLING with
REPLACEMENT
This gives an element of the population
more than one chance to be a part of the
sample and thus, making elements of sample
not distinct with one another.

27. SIMPLE RANDOM SAMPLING
TABLE OF RANDOM NUMBERS
It is a list of numbers that can be used
to generate numbers to stimulate
experiments.

28. SIMPLE RANDOM SAMPLING
RANDOM NUMBER TABLE
Steps:
1. Assign numbers to each member of the
population.
2. Choose a table number randomly.
3. With eyes closed and pencil or pen at hand,
choose the set of numbers from which to start.
4. The number of digits to be considered in the
random numbers selected depends on the
number of digits needed.
5. Repeat the process until you reach the desired
number of members in the sample.

29. RANDOM SAMPLING TECHNIQUE
or PROBABILITY SAMPLING
TECHNIQUE
2. SYSTEMATIC RANDOM SAMPLING
It is a random sampling technique
which considers every element of the
population in the sample with the selected
random starting point for the first
members.

30. SYSTEMATIC RANDOM SAMPLING
Steps:
1. Assign numbers to each member of the
population.
2. Choose a random starting point. Do this by
dividing the number of members in the
population by the desired number of samples.The
quotient (k) will represent the first (k) member
of the population and the random starting point
will be determined by the lottery method.
3. From a student number, skip count by k
repeatedly until the desired number of samples is
completed.

31. SYSTEMATIC RANDOM SAMPLING
Systematic sampling is a random
sampling technique in which every element
of the population is selected until the
desired number of elements in the sample
is obtained. The value of is calculated by
dividing the number of elements in the
desired sample. The value of is the
sampling interval.

32. EXAMPLE
1. In a group of 250 students, how will you
select a sample containing 71 students by
using the systematic sampling technique?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, …, 250

33. EXAMPLE
2. In a group 180 workers, how will you
select a sample of 36 workers by using the
systematic sampling technique?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29,
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, …, 180

34. EXAMPLE
3. The office clerk gave a researcher a list of
500 Grade 10 students. The researcher
selected every 20th
name on the list. How many
respondents that the researcher will have?
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30,
31, 32, 33, 34, 35, 36, 37, 38, 39, 40, …, 500

35. ACTIVITY 16
Identify the sampling interval and list
the assigned number of respondents for the
given data.
1. N=30 n=6
2. N=20 n=4
3. N=25 n=5
4. N=35 n=7
5. N=40 n=10

36. RANDOM SAMPLING TECHNIQUE
or PROBABILITY SAMPLING
TECHNIQUE
3. STRATIFIED RANDOM
SAMPLING
It is a random sampling
technique, which purposively divides a
given population into homogenous
partitions called strata.

37. STRATIFIED RANDOM SAMPLING
Steps:
1. Divide the population into smaller
subgroups or strata based on the numbers’
shared attribute and characteristics.
2. Compute for the number of sample per
strata by dividing the total size per stratum
by the total population. Multiply the
proportion to the total sample size.
3. Randomly select the members of the sample
from each group using either lottery
method or table of random numbers.

38. EXAMPLE
1.You want to interview 200 students in
your school to determine their opinion
on the new school uniform. How are
you going to choose your sample by
using stratified sampling if there are
1,200 students in Grade 7, 1,100 in
Grade 8, 1,050 in Grade 9, 940 in
Grade 10, 900 in Grade 11 and 810 in
Grade 12?

39. SOLUTION
GRADE LEVEL STRATUM SIZE SAMPLE SIZE
7 1200 40
8 1100 37
9 1050 35
10 940 31
11 900 30
12 810 27
TOTAL 6000 200

40. EXAMPLE
2. Marcela, a Statistics student, wants to
determine who care more about their
physical appearances, the male or female
students. She wants to limit her study to
the Grade 10 students. There are unequal
numbers of Grade 10 students: 340 are
male and 500 are female. She wants her
sample to consist only of 50 students. She
chooses the members of her sample using
stratified sampling technique.

41. SOLUTION
GRADE 10 STRATUM SIZE SAMPLE SIZE
MALE 340 20
FEMALE 500 30
TOTAL 840 50

42. EXAMPLE
3. Suppose a researcher wants to
determine the average income of the
families in a barangay having 3,000 families,
distributed in five purok’s. Compute the
sample size at a 5% margin of error and
identify the number of respondents per
purok if there are 800 families in Purok 1,
400 in Purok 2, 500 in Purok 3, 600 in
Purok 4 and 700 in Purok 5.

43. SOLUTION
PUROK STRATUM SIZE SAMPLE SIZE
1 800 94
2 400 47
3 500 59
4 600 71
5 700 82
TOTAL 3000 353

44. ACTIVITY 17
Answer the following.
1. Using the stratified sampling technique,
compute the sample size at a 5% margin of error
for each hospital listed in the table below.
Hospital Population Sample Size
A 560
B 284
C 790
D 1,000
E 366
Total

45. ACTIVITY 17
Answer the following.
2.A researcher wants to know the study habits of
the students of the College of Physical Therapy in
ABC University. Determine the size of the sample
units from each level using a 4% margin of error.
Year Level Population Sample Size
FirstYear 750
SecondYear 600
ThirdYear 550
FourthYear 500
FifthYear 580
Total

46. RANDOM SAMPLING TECHNIQUE
or PROBABILITY SAMPLING
TECHNIQUE
4. CLUSTER RANDOM SAMPLING
It is a random sampling technique which
divides a given population into heterogeneous
groups called clusters. Heterogeneous group
partitions means they are grouped differently
according to the controlling variable of the study.
The sample is taken through a random selection of
cluster(s) and then all members of the chosen
cluster(s) will be a part of the sample.

47. EXAMPLE
1. A doctor wants to make a nationwide study
on the correlation between smoking and death
rate. He decided to focus on the 13 regions of
the country, which can be considered as the
clusters. If three of the clusters or regions are
the desired sample units, the names of the 13
clusters will be written on small pieces of paper,
then three will be picked at random using the
lottery method.All the residents of the selected
three clusters will be included in the study.

48. EXAMPLE
2. A researcher wants to
determine who among the
families in a small town are
using the new detergent
product. How is she going to
do this using the cluster
sampling technique?

49. STRATIFIEDVS CLUSTER
The difference of cluster
sampling from stratified sampling is
that the sample consists of
elements from the selected
clusters only while in stratified
sampling, the sample consists of
elements from all the strata.

50. RANDOM SAMPLING TECHNIQUE
or PROBABILITY SAMPLING
TECHNIQUE
5. MULTI-STAGE SAMPLING
Here, we use combinations of several
random sampling techniques in getting the
sample from a very large population. This is
done by dividing the whole population by area,
and then each area into strata.Thereafter, from
each stratum, we get the sample by using the
simple random sampling technique.

51. NON-PROBABILITY SAMPLING
TECHNIQUE
There are some sampling
techniques which are biased and
therefore not reliable such as those
samples drawn by researchers
based on their own judgment
which are classified as non-
probability sampling technique.

52. NON-PROBABILITY SAMPLING
TECHNIQUE
1. CONVENIENCE SAMPLING
This is used because it is
convenient to the researcher.
This technique is resorted to
by researchers who need the
information the fastest way
possible.

53. CONVENIENCE SAMPLING
EXAMPLE
A researcher may find out which
detergent is the most popular among
households by making phone calls using the
phone numbers found in the telephone
directory. While the data may easily be
obtained, the accuracy of the data may not
be reliable since not all households have
telephone connections.

54. NON-PROBABILITY SAMPLING
TECHNIQUE
2. QUOTA SAMPLING
In this method, the researcher
uses the proportions of different
strata; and from the strata,
selections are done using quota.
This is most commonly used in
opinion polls.

55. QUOTA SAMPLING
EXAMPLE
Suppose a salesman is required to gather
information as to the most common hair shampoo
used by female Filipino clients. If he wants 2,000
sample units and he needs to do the survey within
a short timetable, he can station himself at a public
place, such as park or a mall, then ask the females
what shampoo they usually use. After meeting the
required number of sample points, the researcher
is through with his collection of data.

56. NON-PROBABILITY SAMPLING
TECHNIQUE
3. PURPOSIVE SAMPLING
The researcher gets his sample
from the respondents purposely
related or close to him. The
respondents of the study will be
chosen based on their knowledge of
the information required by the
researcher.

57. PURPOSIVE SAMPLING
EXAMPLE
Suppose a researcher wants to make a
historical study about Town A. The target
population will be the senior citizens of the
town since they are the most reliable persons
who know the history of the town. If there
are 2,000 senior citizens and a 3% margin of
error is allowed, the sample size will be 714.
They will be chosen using any of the methods
discussed previously.

58. GENERALIZATION
Answer the following.
1. State and describe the different
methods of collecting data.
2. How do we determine the sample
size of the given population?
3. State and describe the different
sampling techniques.

59. ACTIVITY 18
A. Identify the most appropriate method/s of gathering
data to be used in each of the following situations.
1. To determine the causes of death from year 2000
to the present.
2. To identify the factors why students fail in Statistics.
3. To find out the relationship between smoking and
lung cancer.
4. To determine the choices of family planning
methods of married couples.
5. To determine the average savings of employees of
company A in a month.

60. ACTIVITY 18
B. Identify the type of sampling technique
used by the researcher in each of the
following situations: simple random
sampling, systematic random sampling,
stratified random sampling or cluster
random sampling.
6.The office clerk gave the researcher a list
of 500 Grade 10 students. The researcher
selected every 20th
name on the list.

61. ACTIVITY 18
7. In a recent research that was conducted in a
private school, the subjects of the study were
selected by using the Table of Random Numbers.
8. A researcher interviewed people from each
town in the province of Albay for his research on
population.
9. A researcher is doing a research work on the
students’ reaction to the newly implemented
curriculum in Mathematics and interviewed every
10th
student entering the gate of the school.

62. ACTIVITY 18
10.A researcher who is studying the effects of
educational attainment on promotion
conducted a survey of 50 randomly selected
workers from each of these categories: high
school graduate, with undergraduate degrees,
with master’s degree, and with doctoral
degree.
11. A researcher selected a sample of n=120
from a population of 850 by using the Table of
Random Numbers.

63. ACTIVITY 18
12. A researcher interviewed all top 10
Grade 11 students in each of 15 randomly
selected private schools in Metro Manila.
13. A researcher randomly selected 10
barangays in a town for her study. She did
this by writing the names of each barangays
on a piece of paper which she folded and
put in a bowl then she draw 10 pieces of
paper from the bowl.

64. ACTIVITY 18
14. A teacher asked her students fall in line. He
instructed one of them to select every 5th
student on the line.
15.A researcher chose the subjects of her study
by selecting every member of the population.
16. A teacher who is conducting a research on
the effects of using calculators in teaching
mathematics decided to divide her students
into male and female and then she selected
students from each gender group.

65. ACTIVITY 18
17. A Statistics student did a research on
the time spent by Grade 11 students in
playing video games. He randomly selected
his subjects by using the Table of Random
Numbers.
18. A statistician selected a sample of
n=100 high school students from a private
school with 2,500 students. He randomly
selected the students from each grade
level.

66. ACTIVITY 18
19. A teacher conducted a study in
her school to determine who were
better in Mathematics: the boys or
the girls.
20. A researcher surveyed all
diabetic patients in each of the 25
randomly selected hospitals in
Metro Manila.