Department of Education

8 National Capital Region

SCHOOLS DIVISION OFFICE
MARIKINA CITY

Statistics
Quarter 1 – Module 6
Sampling Procedures

Writer: MYRTLE GWEN D. DELA CRUZ

Layout Illustrator: JOEL ESTUDILLO

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 What I Need to Know
Hello Grade 8 learners! In this module, you will learn the:

SAMPLING PROCEDURES

You can say that you have understood the lesson in this module if you can already:
1. determine an appropriate sample size,
2. differentiate probability from non-probability sampling techniques,
3. describe each of the probability sampling techniques.

What I Know
Read and answer the following questions carefully. Write the letter of the correct answer
in a separate answer sheet.

1. Using published tables, what is the appropriate sample size for a population of 1000
using a precision (e) of ± 7 %?
A. 67 B. 123 C. 169 D. 257

2. Using published tables, what is the appropriate sample size for a population of 200
using a precision (e) of ± 5 %?
A. 84 B. 134 C. 144 D. 164

3. Using Slovin’s Formula what is the appropriate sample size is the population size is
1000 using a 0.05 margin of error?
A. 256 B. 285 C. 286 D.356

4. Using Slovin’s Formula what is the appropriate sample size is the population size is
5000 using a 0.01 margin of error?
A. 333 B. 345 C. 1333 D.3333

5. Using Slovin’s Formula what is the appropriate sample size is the population size is
2000 using a 0.03 margin of error?
A. 714 B. 992 C. 1000 D.1201

6. Using Slovin’s Formula what is the appropriate sample size is the population size is
3000 using a 0.02 margin of error?
A. 256 B.874 C.1323 D.1364

7. Which sampling technique gives every unit of the population an equal chance of being
included in the sample?
A. Stratified Random Sampling
B. Simple Random Sampling
C. Multi-Stage Sampling
D. Cluster Sampling

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8. Which sampling technique selects every kth element from an ordered population?
`A. Cluster Sampling
B. Systematic Sampling
C. Multi- Stage Sampling
D. Stratified Random Sampling

9. Which sampling technique divides the population into heterogeneous groups then
some of groups will be randomly selected to make up the sample?
A. Cluster Sampling
B. Systematic Sampling
C. Multi- Stage Sampling
D. Stratified Random Sampling

10. Which non-probability sampling technique selects sampling units based on their
knowledge of the topics in the study being conducted?
A. Quota Sampling
B. Purposive Sampling
C. Judgement Sampling
D. Convenience Sampling

Lesson
Sampling Procedures
1

What’s In

What are the different sources

of data? How will I collect all
the data that I need?

What’s New
The population is too
big. How will I choose
my sample?

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 What It Is
Determining the Sample Size
There are several approaches to determining the sample size. These include using a
census for small populations, imitating a sample size of similar studies, using published tables,
and applying formulas to calculate a sample size. Each strategy is discussed below.
1. Using a census for small populations
One approach is to use the entire population as the sample. Although cost considerations
make this impossible for large populations, a census is attractive for small populations (e.g.,
200 or less). A census eliminates sampling error and provides data on all the individuals in
the population. In addition, some costs such as questionnaire design and developing the
sampling frame are "fixed," that is, they will be the same for samples of 50 or 200.
2. Imitating a sample size of similar studies
Another approach is to use the same sample size as those of studies similar to the one you
plan. Without reviewing the procedures employed in these studies you may run the risk of
repeating errors that were made in determining the sample size for another study. However,
a review of the literature in your discipline can provide guidance about "typical" sample sizes
which are used.
3. Using Published Tables
A way to determine sample size is to rely on published tables which provide the sample size
for a given set of criteria. Table 1 and Table 2 present sample sizes that would be necessary
for given combinations of precision, confidence levels, and variability.
Please note two things. First, these sample sizes reflect the number of obtained responses,
and not necessarily the number of surveys mailed or interviews planned (this number is
often increased to compensate for nonresponse). Second, the sample sizes in Table 2
presume that the attributes being measured are distributed normally or nearly so. If this
assumption cannot be met, then the entire population may need to be surveyed.

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 4. Applying formulas

Slovin's Formula is used to calculate the sample size (n) given the population size (N) and
a margin of error (e). It is a random sampling technique formula to estimate sampling size

It is computed as
n = N / (1+Ne2).
Where:
n = no. of samples
N = total population
e = error margin / margin of error

To use the formula, first figure out how much error can be tolerated. For example, you may be
happy with a confidence level of 95 percent (giving a margin error of 0.05), or you may require a
tighter accuracy of a 98 percent confidence level (a margin of error of 0.02). Substitute your
population size and required margin of error into the formula. The result will be the sample size
you need to take.

N=1000 and e=0.02

n = 1000 / [1 + (1000)(0.02²)]
n = 1000 / (1 + 0.4)
n = 714.286
n = 714 respondents must be randomly selected from the population

A researcher plans to conduct a survey. If the population in Stat City is 1000 000, find the
sample size if the margin of error is 25%
First: Convert the Margin of Error 2.5% as a decimal
Given:
N = 1000000
e = 2.5% = 0.025

n = 1000000/(1 + 1000000 ·0.025² )

n = 1000000/(1 + 1000000 · 0.000625 )
n = 1000000/(1 + 625 )
n = 1000000/626
n = 1597.44 or approx. 1597

Suppose that you have a group of 1000 city government employees and you want to
survey them to find out which tools are best suited to their jobs. You decide that you are happy
with a margin of error of 0.05. Using Slovin's formula, you would be required to survey
n = N / (1 + Ne2) people:

1000 / (1 + 1000 * 0.052) = 286

Sampling Techniques
1. Probability Sampling Techniques
These sampling procedures give every unit of the population a known nonzero chance of
being included in the sample.

A. Simple Random Sampling

- In simple random sampling, every unit of the population is given an equal chance of
being included in the sample.
Examples
- Using the lottery method is one of the oldest ways and is a mechanical example of
simple random sampling. In this method, the researcher gives each member of the

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 population a number. Researchers draw numbers from the box randomly to choose
samples.
- Use of a table of random numbers

How to use a random number table:

1. Assume you have the test scores for a population of 200 students. Each student has been
assigned a number from 1 to 200. We want to randomly sample only 5 of the students for this
demo.
2. Since the population size is a three-digit number, we will use the first three digits of the
numbers listed in the table.
3. Without looking, point to a starting spot in the table. Assume we land on 75636 (3rd column,
2nd entry).
4. This location gives the first three digits to be 756. This choice is too large (> 200), so we
choose the next number in that column. Keep in mind that we are looking for numbers whose
first three digits are from 001 to 200 (representing students).
5. The second choice gives the first three digits to be 407, also too large. Continue down the
column until you find 5 of the numbers whose first three digits are less than or equal to 200.
6. From this table, we arrive at 070 (07015), 038 (03811), 045 (04594), 055 (05542), and 194
(19428).
7. RESULT: Students 38, 45, 55, 70, and 194 will be used for our random sample.
Our sample set of students has been randomly selected where each student had an equal
chance of being selected and the selection of one student did not influence the selection of
other students.
Note: In today's world, tables of random numbers have been nearly replaced by computational
random number generators. Like the random number tables, these generators use several
different methods for generating random data.
Most calculators cannot generate "truly" random numbers. They use a formula with a number
seed to generate the numbers, which means that the list could potentially be repeated (making
the list not truly random).

B. Stratified Random Sampling

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- The population is divided into homogeneous groups called strata then units are taken
at random from each stratum to complete the sample.

Example:
In a junior high school there are 1200 students.

Using Slovin’s Formula and a 5% margin of error, then the sample size is
n = 1200/[1+1200(0.052)] or n =300

We need to consider the percentage of the number of students per grade level with
respect to the population in selecting the sample.

Grade Level Population Percentage Sample

7 300 300/1200 = 0.25 0.25(300) = 75
= 25%
8 350 350/1200 = 0.2917 0.2917(300) =
= 29.17% 87.51 ≈ 88
9 300 300/1200 = 0.25 0.25(300) = 75
= 25%
10 250 250/1200 = 0.2083 0.2083(300) =
= 20.83% 62.49 ≈ 62
Total 1200 100% 300

Thus, for the random selection of the sample (300), 75 should come from grade 7,
88 from grade 8, 75 from grade 9 and 62 from grade 10.

C. Cluster Sampling

- The population is divided into heterogeneous groups called clusters. Clusters are
chosen at random since each cluster already resembles the population and can
already be considered as a good representative of the population.

Example:
A study about the income of families in Marikina City is conducted. So the
city is divided into barangays, then three barangays were randomly selected. Finally,
censuses for each of the chosen barangays were conducted.

D. Systematic Sampling

- This sampling technique is described as the selection of every kth unit from an ordered
population. K is called the sampling interval determined by dividing the population
size by the expected sample size, then rounding-off the result to the nearest whole
number. The selection process is randomized by drawing a random starting point.
Example:
N = 100 and n = 20 then K = 5
Every 5th element from a randomly chosen starting point are selected until 20 are
taken.

E. Multi – Stage Sampling

- Sampling is done in several stages until the desired number of sampling units are
selected.
Example:
Cluster sampling then stratified random sampling was done in a company to choose
the participants for free leadership trainings overseas.

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2. Non-Probability Sampling Techniques

A. Purposive Sampling
-Sampling units are selected based on their knowledge of the problems of the study

B. Quota Sampling
- Units possessing the characteristics of the population are selected at a first come first
serve basis until the desired number of sampling units are selected.

C. Convenience Sampling
- Sampling units are selected because they are on-hand or are easy or convenient to get
information from.

D. Judgement Sampling
- Sampling units are selected based on an expert’s advice or opinion.

What’s More

Which among the sampling techniques mentioned have you encountered before?
Describe how it was used? _______________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________

What I Have Learned

Which is better to use Probability or Non-Probability Sampling Techniques? Explain your answer.
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________

What I Can Do

1. Find the appropriate sample size for the following populations given the following margins of error. Show
your solution.

1. N = 2500 e = 5%
2. N = 390 e = 2%
3. N = 450 e = 0.03
4. N = 995 e = 0.04
5. N = 2670 e = 0.05

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2. Find the number of respondents to be randomly selected from each stratum if a stratified random sampling
procedure is to be performed for the following populations. Use a 0.05 margin of error.

1. Cases Population Percentage Sample

A 300
B 250
C 320
D 430
Total 1300

2. Animal Kind Animal Rescue Percentage Sample

Population
A 80
B 50
C 70
Total 200

Assessment
Read the following questions carefully. Write the letter of the correct answer in a
separate answer sheet.

1. Using Slovin’s Formula what is the appropriate sample size is the population size is 2000
using a 0.05 margin of error?
A. 333 B. 724 C. 1236 D.1257

2. Using Slovin’s Formula what is the appropriate sample size is the population size is 1000
using a 0.02 margin of error?
A. 286 B.714 C.824 D.828

3. Which sampling technique gives divides the population into homogeneous groups then
elements are randomly drawn from each group to be included in the sample?
A. Stratified Random Sampling
B. Simple Random Sampling
C. Multi-Stage Sampling
D. Cluster Sampling

4. Which sampling technique selects every kth element from an ordered population?
`A. Cluster Sampling
B. Systematic Sampling
C. Multi- Stage Sampling
D. Stratified Random Sampling

5. Which non-probability sampling technique selects sampling units because they are close-
at-hand and are easy to get information from?
A. Quota Sampling
B. Purposive Sampling
C. Judgement Sampling
D. Convenience Sampling
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 Additional Activities
DIALECTIC JOURNAL: Copy this table in a journal. For every new concept or terminology you
learn, fill out a new entry.
Date: ___________ Rate how well you understood
Entry No._______ the concept:

Concept:

Definition/Description:

Illustration/Formula (when applicable):

Examples:

Application in Real Life:

RUBRICS:
Score Requirement
5 Well- defined concepts with illustration/formula (when applicable). Gave
correct examples and good real- life applications, Rated how well you
understood the concept with 5 stars.
4 Well- defined concepts with illustration/formula (when applicable). Gave
good examples and appropriate applications.
3 Well-defined concepts. Gave some good examples but incorrect
applications or vice versa.
2 Gave passable definition to concepts. Gave incorrect examples and
applications.
1 Did not define concepts correctly. Gave incorrect examples and
applications.

Summative Test
Read the following questions carefully. Write the letter of the correct answer
in a separate answer sheet.

1. Using published tables, what is the appropriate sample size for a population of 1000
using a precision (e) of ± 3 %?
A. 237 B. 286 C. 887 D. all

2. Using published tables, what is the appropriate sample size for a population of 3000
using a precision (e) of ± 5 %?
A. 167 B. 234 C. 353 D. 811

3. Using Slovin’s Formula what is the appropriate sample size is the population size is 4000
using a 0.04 margin of error?
A. 243 B. 541 C. 1242 D.2258

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4. Using Slovin’s Formula what is the appropriate sample size is the population size is 1500
using a 0.02 margin of error?
A. 386 B.714 C.824 D.938

5. Which sampling technique gives divides the population into homogeneous groups then
elements are randomly drawn from each group to be included in the sample?
A. Stratified Random Sampling
B. Simple Random Sampling
C. Multi-Stage Sampling
D. Cluster Sampling

6. Which sampling technique gives every unit of the population an equal chance of being
included in the sample?
A. Stratified Random Sampling
B. Simple Random Sampling
C. Multi-Stage Sampling
D. Cluster Sampling

7. Which sampling technique divides the population into heterogeneous groups then some of
groups will be randomly selected to make up the sample?
A. Cluster Sampling
B. Systematic Sampling
C. Multi- Stage Sampling
D. Stratified Random Sampling

8. Which non-probability sampling technique selects sampling units based on their

knowledge of the topics in the study being conducted?
A. Quota Sampling
B. Purposive Sampling
C. Judgement Sampling
D. Convenience Sampling

9. Which non-probability sampling technique selects sampling units because they are close-
at-hand and are easy to get information from?
A. Quota Sampling
B. Purposive Sampling
C. Judgement Sampling
D. Convenience Sampling
10. Which non-probability sampling technique selects sampling units based on an expert’s
advice or opinion?
A. Quota Sampling
B. Purposive Sampling
C. Judgement Sampling
D. Convenience Sampling

References

Almeda, J.V., Capistrano, T. G., & Sarte, G. M. F.(2010). Elementary Statistics. UP Press

Lyla. (2020, May 28). 7 Types of Statistical Analysis: Definition and Explanation. Retrieved
September 29, 2020, from http://www.intellspot.com/types-statistical-analysis/

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Retrieved October 30, 2020 from
https://mathbitsnotebook.com/Algebra2/Statistics/STrandomtable.html

Walpole, R. E., Myers, R. H., & Myers, S. L. (1989). Probability and Statistics for Engineers and
Scientists (9th ed.). Collier Macmillan.

Walpole, R. E. (1997). Introduction to Statistics. Prentice Hall International.

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