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1. Simple random sampling In a simple random sample, every member of the population has an equal chance of being selected. Your sampling frame should include the whole population. To conduct this type of sampling, you can use tools like random number generators or other techniques that are based entirely on chance. Example You want to select a simple random sample of 100 employees of Company X. You assign a number to every employee in the company database from 1 to 1000, and use a random numbe
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Department of Education
Senior High School Mathematics
LESSON 1: Random Sampling
After exploring this supplementary learning material, you should be able to
illustrate random sampling.
Directions : Read each question carefully, then write the letter of the correct answer.
probability of being chosen to be included in the sample.
A. Simple Random Sampling C. Stratified Sampling
B. Systematic Sampling D. Cluster Sampling
A. Parameter B. Sample C. Sampling D. Statistic
A. Data B. Parameter C. Sample D. Statistic
A. Data B. Parameter C. Sample D. Statistic
sampling. What is the sampling interval?
A population consists of all members of the group with common characteristics
that is the focus of a research and where the sample is drawn. A sample is a portion,
part, or subset of the entire population. Sampling is a procedure in selecting a sample
from the population. This is usually done when the population is too large for
gathering data.
Effectively selecting a sample is essential when a researcher wishes to achieve
unbiased results in his/her study; one of the best ways to fulfill this is by using
random sampling.
Types of Random Sampling
A. Simple random sampling
It is the most basic sampling technique. In this sampling technique, every
member of the population has an equal chance of being chosen to be a part of the
sample. One way to do simple random sampling is by using the Table of Random
Numbers or by using the lottery method.
Senior High School Mathematics
Example: There are 400 families in a barangay in which fifty families are needed as
sample for an experiment.
Solution:
Step 1. Prepare a sampling frame by randomly arranging the 400 families.
Step 2. Assign each family a number from 1 to 400.
Family Number
Santos 1
Garcia 2
Ramos 400
Step 3. Find the sampling interval k. Divide the population size 400 by the sample size
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, 5,
6, 7 and 8. The chosen value is called as the random start.
Step 5. Assume that the randomly selected number is 3. Use 3 as the starting
number.
Step 6. Select every 8
th
families from the sampling frame starting from the 3
rd
families.
st
nd
3rd
∴ The numbers of the sample will then be 3, 11, 19, 27, …
C. Stratified Sampling
In stratified sampling, the population is partitioned into
several subgroups called strata which are based on some
characteristics like year level, gender, age, ethnicity, etc.
Example: A clothing company wants to determine
whether 1000 customers prefer any specific color over
other colors in shirts. How are you going to choose your
sample of 200 customers by using stratified sampling if there are 144, 162, 73, 146,
270, 205 customers per stratum?
Solution:
Senior High School Mathematics
Subdivide the population with their preferred shirt colors into several strata,
then make a table.
Population (N = 1,000) Number of Customers per Stratum
White 144
Blue 162
Black 73
Red 146
Yellow 270
Green 205
Total 1,
To obtain the sample size per color, divide the total number of customers per
stratum by the total number of customers, and then multiply the result by 200. Select
the members of each sample by using simple random sampling.
Computation of sample size:
144
1,
200 = 29 customers should be selected as for white shirt.
Population
Number of Customers
per Stratum
Computation Sample
n = 200
White 144
Blue 162
Black 73
Red 146
Yellow 270
Green 205
Total 1,000 200
D. Cluster or Area Sampling
The population is divided into clusters. From these clusters, random sample
clusters will be drawn. All the elements from the sampled clusters will make up the
sample.
Example:
Suppose some medical researchers want
to study the patients in Metro Manila. How are
they going to do this using the cluster sampling
technique?
Solution:
Senior High School Mathematics
a certain medicine.
A. Simple Random Sampling C. Systematic Random Sampling
B. Cluster Sampling D. Stratified Random Sampling
president.
A. Simple Random Sampling C. Systematic Random Sampling
B. Cluster Sampling D. Stratified Random Sampling
children living in those households.
A. Simple Random Sampling C. Systematic Random Sampling
B. Cluster Sampling D. Stratified Random Sampling
appearances – the male or the female students. She wants to limit her study to
Grade 11 students; however, there are more females than males which are 279 and
250, respectively. If Bea wants her sample to consist only of 50 students, which
sampling method will she use?
A. Simple Random Sampling C. Systematic Random Sampling
B. Cluster Sampling D. Stratified Random Sampling
LESSON 2: Parameters and Statistic
After exploring this supplementary learning material, you should be able to:
Answer the following questions.
A parameter is a measure that describes a population. Parameters are usually
denoted by Greek letters like 𝜇, 𝜎. On the other hand, statistic is a measure that
describes a sample. Statistic is usually denoted by Roman letters x , s. A parameter is
a numerical measurement describing some characteristics of a population. A statistic
is a numerical measurement describing some characteristics of a sample.
Senior High School Mathematics
Example of parameters: 1. Population mean (𝜇)
2
)
The population mean is the mean of the entire population. It is computed using the
formula: 𝜇 =
∑ 𝑥̅
𝑁
where, 𝜇 = population mean
x = given data
N = population size / number of cases
Example 1: The numbers of teachers in 6 departments of a certain high school are 18,
16, 14, 15, 19, and 20. Find the population mean.
Solution:
102
6
Therefore, the population mean is 17.
Population variance and standard deviation are widely used measures of
dispersion of data in research. The population variance 𝜎
2
is the sum of the squared
deviations of each datum from the population mean divided by the population size.
The population standard deviation is the square root of the population variance.
Formula for Population Variance 𝝈
𝟐
: 𝜎
2
=
∑(𝑥̅ −𝜇)
2
𝑁
Formula for Population Standard Deviation 𝝈
2
Example 2: The ages of 9 English teachers in a certain public school are 30, 34, 32,
38, 28, 36, 40, 31, and 35. Compute the following:
a. Population variance b. Population standard deviation
Solution:
Step 1. Compute the population mean. 𝜇 =
∑ 𝑥̅
306
𝑁 9
Step 2. Subtract the population mean from each of the data.
(Refer to table’s 3
rd
column)
Step 3. Square all the deviations of the data from the population mean.
(Refer to table’s 4
th
column)
Step 4. Find the sum of all the squared deviations. (Refer to the last row of the table)
Step 5. Solve for population variance. 𝜎
2
∑(𝑥̅ −𝜇)
2
214
𝑁
Step 6. Solve for population standard deviation.
2
9
where N = population size
x = given data
𝜇= population mean
Senior High School Mathematics
Example 4: Calculate the sample variance and sample standard deviation of the 5
randomly selected data in Example 3.
Teacher Population Age Sample Age (x) 𝑥̅ − 𝑥̅ (𝑥̅ − 𝑥̅ )
2
2
2
2
2
= 14.
2
= 0.
2
Solve for sample variance 𝑠
2
∑(𝑥̅ −𝑥̅ )
2
Solve for sample standard deviation
𝑛− 1 5−1 4
∑(𝑥̅ −𝑥̅ )
2
𝑛− 1 5−1 4
paper. Compute for the average age of your family, then randomly select the members
of the family to be studied using fishbowl method. From the selected family members,
compute for the average age.
Family Member Age
Father 42
Mother 40
st
Sibling 18
nd
Sibling 15
nth Sibling …
Questions:
age?
The population mean is the mean of the entire population. It is represented by
Greek letter mu (𝜇) and is computed using the formula: 𝜇 =
∑ 𝑋
𝑁
Formula for Population Variance 𝜎
2
2
∑(𝑋−𝜇)
2
𝑁
The population standard deviation 𝜎 is the square root of the population
variance 𝜎
2
. That is, 𝜎 =
∑(𝑋−𝜇)
2
𝑁
Senior High School Mathematics
The sample mean (𝑥̅ ) is the average of all the values randomly selected from the
population. 𝑥̅ =
∑ 𝑥̅
𝑛
Directions : Compute for the mean, variance, and standard deviation.
Statistics were 80, 85, 90, 93, and 85.
students in each section: 36, 31, 33, 40, 47, 49, 44, 35, 45, and 42.
POST TEST
subpopulations or strata.
A. Simple Random Sampling C. Cluster Sampling
B. Stratified Random Sampling D. Quota Sampling
population.
A. Stratified Random Sampling C. Cluster Sampling
B. Simple Random Sampling D. Purposive Sampling
population.
A. Stratified Random Sampling C. Cluster Sampling
B. Systematic Random Sampling D. Simple Random Sampling
teachers, and one department head. This statement is an example of a.
A. Statistic B. Parameter C. Random sampling D. Sample
A. Statistic C. Random sampling
B. Parameter D. Sampling technique
