Republic of The Philippines

Department of Education
Division of Bukidnon
Cabanglasan II District
CABULOHAN-PARADISE NATIONAL HIGH SCHOOL
Cabulohan, Cabanglasan, Bukidnon
LESSON PLAN ON STATISTICS AND PROBABILITY 11
RANDOM SAMPLING, PARAMETER AND STATISTIC, AND SAMPLING DISTRIBUTION OF STATISTICS
Teaching Date April 25-29, 2024 Learnin Statistics and Probability
g Area
Quarter 4th Quarter Grade 11
Level

I. OBJECTIVES
A. CONTENT STANDARDS The learner demonstrates understanding
of key concepts of sampling and sampling
distributions of the sample mean.
B. PERFORMANCE STANDARDS The learner is able to apply suitable
sampling and sampling distributions of
the sample mean to solve real-life
problems in different disciplines.
C. OBJECTIVES At the end of the lesson, the learner will
be able to:

1. illustrate random sampling

(M11/12SP-IIId-2)
2. distinguish between parameter and
statistic; (M11/12SP-IIId-3) and
3. identify sampling distribution of
statistics (sample mean). (M11/12SP-IIId-
4)
II. LEARNING MATERIALS
A. REFERENCES  Learner’s Material
 Canlapan, R. B. (2016). Statistics
and Probability. DIWA Learning
Town
 Internet
B. ADDITIONAL MATERIALS FOR LEARNING RESOURCES Power point Presentation, Laptop, TV,
Scientific Calculator

C. TEACHING STRATEGIES Problem-solving Exercises

Hands-on activities
Real world examples
III. PROCEDURES
Teacher’s Activity Learner’s Activity
A. Prayer and Greetings In the name of the Father, and of the
Please stand up for our prayer. Dayna, kindly lead the prayer. Son, and of the Holy Spirit. Amen …
(Prayer)
Good morning, learners.
Good morning, ma’am Shine.
Kindly pick up papers and garbage on the floor before you take your sit.
Thank you, ma’am.
B. Attendance
Kindly say present once your name was called.
C. Presenting the Objectives (Learners responded “present”)
If a researcher wants to observe, examine or test a theory or hypothesis, he will
consider the problem by selecting a section of the population of the study using a
method called random sampling. In random sampling, all subjects in the population
listed in the study have the same chances of being chosen for the survey. This
means that, ultimately, each member of the sample retains characteristics, or
impartial characteristics, of the population. With random sampling, the conclusions
of the post-hypothesis tests applied to the sample selection will apply to the entire
population as well. This is due to the fact that the selection of the sample
essentially represents the characteristics of the population from which it is
obtained, since each member of the sample was drawn unbiased from the
population data. When bias in sample selection is avoided, the results of a
particular study are considered more conclusive and the error is minimized.
At the end of this discussion you will be able to:
1. illustrate random sampling (M11/12SP-IIId-2)
2. distinguish between parameter and statistic; (M11/12SP-IIId-3) and
3. identify sampling distribution of statistics (sample mean). (M11/12SP-IIId-4)

D. Motivation
Directions: 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 - 20.2

2. 23, 45, 67, 89, 21, 11 - 42.67
3. 88, 87, 86, 89, 88, 90 - 88
4. 34, 21, 45, 67, 23 -38
5. 12, 9, 6, 5, 32, 40 - 17.33

E. Presenting New Lesson

Random Sampling

The population refers to the whole group under study or

investigation. In research, the population does not always refer to
people. It may mean a group containing elements of anything you
want to study, such as objects, events, organizations, countries,
species, organisms, etc.

The population refers to the whole group under study or

investigation. In research, the population does not always refer to
people. It may mean a group containing elements of anything you
want to study, such as objects, events, organizations, countries,
species, organisms, etc.

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.

Types of Random Sampling Techniques

1. Lottery sampling is a sampling technique in which each

member of the population has an equal chance of being selected.
An instance of this is when members of the population have their
names represented by small pieces of paper that are then
randomly mixed together and picked out. In the sample, the
members selected will be included.

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.

3. Stratified random sampling is a sampling procedure in which

members of the population are grouped on the basis of their
homogeneity. This technique is used when there are a number of
distinct subgroups in the population within which full
representation is required. The sample is constructed by classifying
the population into subpopulations or strata on the basis of 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.

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.

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).

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.

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.

Parameter and Statistic

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.

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.

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.

Sampling Distribution of the Sample Means

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 ❑N C n

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

❑N C n
❑5 C 2 = 10

So, there are 10 possible samples to be drawn.

Example:
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.

This time, let us make a probability distribution of the sample means. This
probability distribution is called the sampling distribution of the sample means.

1
Observe that all sample means appeared only one; thus, their probability is P(x)=
10
or 0.1

Note: A sampling distribution of sample mean is a frequency distribution using the

means computed from all possible random samples of a specific size taken from a
population.

IV. Developing Mastery

Directions: Identify the type of sampling method. Write your answer on the space provided.

Lottery Sampling 1. The teacher writes all the names of students in a piece of paper and puts it in a box for the graded
recitation.
Systematic Sampling 2. The teacher gets the class record and call every 4 names in the list.
Systematic Sampling 3. Every five files out of 500 files will be chosen.
Stratified Sampling 4. There are 20 toddlers, 40 teenagers, 45 middle aged and 55 senior citizens in a certain area. Samples
are taken according to the total number of people in the area.
Lottery Sampling 5. All the names of the employees of the company are put in a raffle box.

V. Application
Directions: Decide whether the statement describes a parameter or statistic. Write your answer on the space provided.

Statistic 1. The average income of 40 out of 100 households in a certain Barangay is P 12, 213.00 a month.
Parameter 2. Percentage of red cars in the Philippines.
Parameter 3. Number of senior high schools in Region 3.
Statistic 4. A recent survey of a sample of 250 high school students reported the average weight of 54.3 kg.
Parameter 5. Average age of students in East High School.

VI. Evaluation
Directions: Construct all random samples consisting three observations from the given data. Arrange the observations in
ascending order without replacement and repetition.

A.
86 89 92 95 98

Solution:

B. Construct all random samples consisting two observations from the given data. You are asked to guess the average
weight of the six watermelons by taking a random sample without replacement from the population.

Watermelon A B C D E F
Weight (in pounds) 19 14 15 9 10 17

VII. Assignment
Instructions: Construct a sampling distribution of sample mean and answer the questions on your answer sheet. Samples of
3 cards are drawn from a population of five cards numbered from 1-5. 1. How many are the possible outcomes? 2. What are
the possible means? 3. What is the probability of getting 4 as a mean? 4. What is the probability of getting 2 as a mean? 5.
What is the probability of getting 3.33 as a mean?

Prepared by: Checked by:

SHINIE LOUISE M. NOYNAY ANGELITO C. SIERAS

School Teacher I Assistant School Principal II