The document outlines various random sampling techniques essential for achieving unbiased results in research, including simple random sampling, systematic sampling, stratified sampling, and cluster sampling. Detailed examples illustrate the application of each technique, demonstrating processes for sample selection and the calculations involved. It emphasizes the importance of randomization in various contexts to ensure representative samples.

1. Sampling

2. • A researcher prefers to achieve unbiased results in his
or her study. One of the best ways to fulfill this is
through the use of random sampling.
Types of random sampling
There are four types of random sampling techniques.
1. Simple random sampling (SRS)
2. Systematic sampling
3. Stratified sampling
4. Cluster or Area sampling

3. Simple Random Sampling
The most basic sampling technique. Every member of the population
has an equal chance of being chosen to be part of the sample.
Examples: Table of Random Numbers and Lottery method
For lottery:
1. SRS without Replacement- All the elements bearing the numbers
picked by the researcher become elements of the sample.
2. SRS with Replacement- Involves returning the selected piece of
paper to the box or bowl after it was noted and the next sample is
drawn again from the same number of population. This gives an
element of the population more than one chance to be part of the
sample and thus, making elements of sample not distinct with one
another.

4. Example 1
A researcher wants to study the effects of social
media on Grade 11 students in Davao City
National High School. He wishes to use the
simple random sampling technique in
choosing the members of his sample. If there
are 1,000 Grade 11 students in the school,
how many students should there be in his
sample? Discuss the steps he must take if he
wishes to use the lottery method.

5. Step 1. Determine the number of students that
should be in the sample. Use the Slovin’s
formula as follows.
For the margin of error, use 5% or 0.05

6. Step 2. Assign a number to each member of the
population. In this problem, assign a number to
each of the 1,000 students.
Step 3. Write the number on pieces of paper with
the same size and shape. Fold the pieces of
paper.
Step 4.Put all the folded pieces of paper in a bowl
or box.
Step 5. Without looking, randomly pick out 286
folded pieces from the bowl or box.

7. Example 2.
A Grade 11 student wants to make a study on the
opinions of Grade 8 students concerning the use
of the Filipino language in the teaching of
mathematics. There are 510 Grade 8 students.
She wants to interview only 10% of the Grade 8
students in the school where the study is to be
conducted. If you were the student, how are you
going to do it by using a Table of Random
Numbers?
Solution:

8. Step 1. Multiply 510 by 10% to obtain the members
of the sample.
510x10%=51. The number of students is a three-
digit number; therefore, assign a three-digit
number to each of the 510 students.
Step 2. Randomly select a starting number from the
table. If the table of random numbers contains 5-
digit numbers, consider only the last 3 digits,
since the total number of students in the study is
510 which is a three-digit number. Move down
columns selecting the appropriate number.

9. Continue doing this until 51 students are
selected. If there are no numbers left in the
first column, move to the second column. You
can create your own Table of Random
Numbers by using random number generator.

11. Systematic Sampling
A systematic sampling is a random sampling
technique in which a list of elements of the
population is used as a sampling frame and
the elements to be included in the desired
sample are selected by skipping through the
list at regular intervals.

13. Example 3
In a group of 250 students, how will you select a
sample containing 71 students by using the
systematic sampling technique?
Solution
Step 1. Prepare a sampling frame by randomly
arranging the 250 students.
Step 2. Assign each student a number from 1 to 250
Step 3. Find the sampling interval k. Divide the
population size 250 by the sample size 71.

14. Step 4. Select a number from the whole
numbers between 0 and k+1 by simple
random technique. The numbers that are
between 0 and k+1 are 1,2,3, and 4. This
chosen value is called as the random start.
Step 5. Assume that the randomly selected
number is 2. Use 2 as the starting number.
Step 6. Select every 4th student from the
sampling frame starting from the 2nd student.

15. The numbers of the sample will then be
2,6,10,14,18,...

16. Example 4
In a group of 180 workers, how will you select a
sample of 36 workers by using the systematic
sampling technique?
Solution
Step 1. Prepare a sampling frame by randomly
arranging the 180 workers.
Step 2. Assign each worker a number from 1 to 180.
Step 3. Find the sampling interval k. Divide the
population size 180 by the sample size 36.

17. Step 4. Select a number from the whole
numbers between 0 and k+1 by simple
random technique. The numbers that are
between 0 and k+1 are 1,2,3,4, and 5.
Step 5. Assume that the randomly selcted
number is 4. Use 4 as the starting number.
Step 6. Select every 5th worker from the sample
frame starting from the 4th worker. That is,

18. Stratified Sampling
It is a random sampling technique in which the
population is first divided into strata and then
samples are randomly selected separately
from each stratum.

19. Example 5
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 seven; 1,100
in grade eight; 1,050 in grade nine; and 940 in
grade ten; 900 in grade eleven; and 810 in
grade twelve?

20. Solution
Subdivide the population into several strata. In
this problem, subdivide the population into
year levels. Then, make a table similar to the
following:
Population
N=6000
No of students per Stratum Sample
n=200
Grade 7 1,200 (1200/6000)x200=40
Grade 8 1,100 (1100/6000)x200=37
Grade 9 1,050 (1050/6000)x200=35
Grade 10 940 (940/6000)x200=31
Grade 11 900 (900/6000)x200=30
Grade 12 810 (810/6000)x200=27
Total 6,000 200

21. Sometimes, the computation will result to one
less than the value of the n. If this happens,
round up one of the data to the next integer.
In this problem, n=200. If the of all the
samples per year level is 199 instead of 200,
then round up one of the data which is not a
whole number to the next integer.

22. Example 6
Gwen Grey, a Statistics student, wants to
determine who care more about their physical
appearances, the male or the female students.
She wants to limit her study to the Grade 11
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.

23. Solution
Subdivide the Grade 11 students into two
subgroups using gender. Divide the number of
students per gender by the total number of
students, and then, multiply the resulting
quotient by 50. The computations are shown
below.
Population
N=840
Number of Students Per
Stratum
Sample
n=50
Male 340 (340/840)x50=20
Female 500 (540/840)x50=30
Total 840 50

24. Cluster or Area Sampling
In cluster sampling, the population is divided into clusters.
From these clusters, a random sample of clusters will be
drawn. All the elements from the sampled clusters will
make up the sample. Sometimes, clusters are too large and
there is a need for a second set of smaller clusters to be
taken from the original clusters. For example, a researcher
could divide the province into towns. A sample of towns
will be selected using SRS. She/He could then divide the
towns into barrios. From these towns, a sample of barrios
will be selected at random. From these barrios, a sample of
houses will be identified. This technique is called multi-
stage cluster sampling.

25. Definition of Cluster Sampling
Cluster or area sampling is a random sampling
technique in which the entire population is
broken into small groups, or clusters, and then,
some of the clusters are randomly selected. The
data from the randomly selected clusters are the
ones that are analyzed.
The difference of cluster sampling from a 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.

26. Example 7
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?

27. Solution
Step 1. Divide the population into clusters. Use barrios as
clusters.
Step 2. Not all the barrios of the town will be included in
the sample. Choose the final barrios by using either the
simple random sampling or a systematic sampling
technique.
Step 3. Not all the families in each selected barrio will be
included in the study. Select the final families to be
included in the sample by using either a simple random
sampling or systematic random sampling technique.