Module 4
Module 4
Module 4
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A sample is a subset taken from a population,
either by random sampling or by non-random
sampling. A sample is a representation of the
population where it is hoped that valid conclusions
will be drawn from the population.
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Random sampling is a selection of n elements
derived from the N population, which is the
subject of an investigation or experiment, where
each point of the sample has an equal chance of
being selected using the appropriate sampling
technique.
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Types of Random Sampling Techniques
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2. Systematic sampling is a sampling
technique in which members of the population
are listed and samples are selected at intervals
called sample intervals. In this technique,
every nth item in the list will be selected from
a randomly selected starting point. For
example, if we want to draw a 200 sample
from a population of 6,000, we can select
every 3rd person in the list. In practice, the
numbers between 1 and 30 will be chosen
randomly to act as the starting point.
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3. Stratified random sampling is a sampling
procedure in which members of the population are
grouped based on their homogeneity. This technique is
used when there are several distinct subgroups in the
population within which full representation is required.
The sample is constructed by classifying the population
into subpopulations or strata based on certain
characteristics of the population, such as age, gender or
socio-economic status. The selection of elements is
then done separately from within each stratum, usually
by random or systematic sampling methods.
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Example:
Using stratified random sampling, select a sample of 400
students from the population which are grouped according to the
cities they come from. The table shows the number of students per
city.
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Solution:
To determine the number of students to be taken as sample from
each city, we divide the number of students per city by total
population (N= 28,000) multiply the result by the total sample size
(n= 400).
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4. Cluster sampling is sometimes referred to as area sampling
and applied on a geographical basis. Generally, first sampling is
performed at higher levels before going down to lower levels. For
example, samples are taken randomly from the provinces first,
followed by cities, municipalities or barangays, and then from
households.
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5. Multi-stage sampling uses a
combination of different sampling
techniques. For example, when selecting
respondents for a national election
survey, we can use the lottery method
first for regions and cities. We can then
use stratified sampling to determine the
number of respondents from selected
areas and clusters.
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Activity
On your answer sheet, give one situation where each of the sampling
methods is being applied.
1. Lottery Sampling:
_____________________________________________________________
2. Systematic Sampling:
____________________________________________________________
3. Stratified Random Sampling
___________________________________________________________
4. Cluster Sampling
__________________________________________________________
5. Multi-stage sampling
___________________________________________________________
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Activity
Identify the terms being described and write your answer on a separate sheet of
paper.
1. It refers to the entire group that is under study or investigation.
2. It is a subset taken from a population, either by random or non-random sampling
technique. A sample is a representation of the population where one hopes to draw valid
conclusions from about population.
3. This is a selection of n elements derived from a population N, which is the subject of
the investigation or experiment, where each sample point has an equal chance of being
selected using the appropriate sampling technique.
4. A sampling technique where every member of the population has an equal chance of
being selected.
5. It refers to a sampling technique in which members of the population are listed and
samples are selected in intervals called sample intervals.
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Lesson 2. Parameter and Statistic
Determine the statement whether it is true or false. Write T if the
statement is true and F if it is false. Write your answer on a separate
sheet of paper.
_____1. A statistic is a number which describes a sample. _____2. A
parameter is a descriptive measure of population.
_____3. An example of parameter is the sample mean. _____4. The
value of a parameter can be approximated and is not necessarily
equal to the statistic of sample. _____5. An example of statistic is a
population mean
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Study the cases below. Identify which of the cases involves measures from a
population and a sample.
1. A researcher randomly selected a sample of 1000 people in Barangay, 143
and asked if they used a certain coffee product and 40% of them said yes.
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2. A researcher interviewed all the students in a certain school to identify their
insights about their favourite shoe brand.
Analysis: In the first case the researcher measures for a sample. Only 40% out
of 100 said yes. While in the second case the researcher measures the
population because the researcher interviewed all the students of that school.
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A parameter is a descriptive population measure. It is a measure
of the characteristics of the entire population (a mass of all the units
under consideration that share common characteristics) based on all
the elements within that population.
Example:
1. All people living in one city, all-male teenagers worldwide, all
elements in a shopping cart, and all students in a classroom.
2. The researcher interviewed all the students of a school for their
favorite apparel brand.
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Statistic is the number that describes the sample. It
can be calculated and observed directly. The statistic is
a characteristic of a population or sample group. You
will get the sample statistic when you collect the
sample and calculate the standard deviation and the
mean. You can use sample statistic to draw certain
conclusions about the entire population.
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Example:
1. Fifty percent of people living in the U.S. agree with
the latest health care proposal. Researchers can’t
ask hundreds of millions of people if they agree, so
they take samples or part of the population and
calculate the rest.
2. Researcher interviewed the 70% of covid-19
survivors.
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Activity
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Lesson 3. Sampling Distribution of the Sample
Means
Given the set of numbers, compute for the mean. Write your
answer on the space provided in each item. Round off your
answers to two decimal places.
1. 4, 12, 34, 45, 6
2. 23, 45, 67, 89, 21, 11
3. 88, 87, 86, 89, 88, 90
4. 34, 21, 45, 67, 23
5. 12, 9, 6, 5, 32, 40
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A population consists of the five numbers 2, 3, 6, 10, and
12. Consider samples of size 2 that can be drawn from this
population.
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A population consists of the five numbers 2, 3, 6, 10 and 12.
Consider samples of size 2 that can be drawn from this population.
A. How many possible samples can be drawn?
To answer this, use the formula NCn (the number of N objects
taken n at a time), where N is the total population and n is the
sample to be taken out of the population,
In this case N= 5 and n= 2 5C2 = 10 So, there are 10 possible
samples to be drawn.
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B. Construct the sampling distribution of sample means. List all the
possible outcome and get the mean of every sample.
Observe that the means vary from sample to sample. Thus, any mean
based on the sample drawn from a population is expected to assume
different values for samples
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C. This time, let us make a probability distribution of the sample
means. This probability distribution is called the sampling
distribution of the sample means
Observe that all sample means appeared only one; thus, their probability is
P(x)= 1/10 or 0.1
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Construct a sampling distribution of sample mean for the set of
data below.
86 88 90 95 98
Consider a sample size of 3 that can be drawn from a population.
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A.How many possible samples can be drawn?
To answer this, use the formula NCn, where N is the
total population and n is the sample to be taken out of
the population,
In this case N= 5 and n= 3 5C3 = 10 So, there are 10
possible samples to be drawn.
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