GRADES 1 TO 12 School PIDDIG NATIONAL HIGH SCHOOL Grade 11-AFA, 11-GAS A/B

Level/SECTION
DAILY LESSON LOG
Teacher ANGELENE L. AMBATALI Learning Area Statistics and Probability 11

Teaching Dates and Time February 27-28 to March 1-3 2023 Quarter THIRD Week No. 3
8:30-9:30, 2:00-3:00, 3:00-4:00

Session 1 Session 2 Session 3 Session 4

I. OBJECTIVES
Objectives must be met over the week and connected to the curriculum standards. To meet the objectives, necessary procedures must be followed and if needed, additional lessons, exercises and remedial activities may be done for
developing content knowledge and competencies. These are assessed using Formative Assessment strategies. Valuing objectives support the learning of content and competencies and enable children to find significance and joy in
learning the lessons. Weekly objectives shall be derived from the curriculum guides.

A. Content
The learner demonstrates understanding of key concepts on mean and variance of The learner demonstrates understanding of key concepts of normal probability
Standards a discrete random variables. distribution.
B. Performance
The learner is able to apply an appropriate random variable for a given real-life The learner is able to accurately formulate and solve real-life problems in different
Standards problem (such as in decision making and games of chance). disciplines involving normal distribution.
C. Learning Learning Competency: Interprets the Learning Competency: solve problems Learning Competencies: Illustrates a normal random variable and its
Competencies/Objec mean and variance of a discrete random involving mean and variance of characteristics. (M11/12SP-IIIc-1); constructs a normal curve. (M11/12SP-IIIc-2)
tives variable. (M11/12SP – IIIb-3) probability distribution. (M11/12SP –
IIIb-4) Learning Objectives:
Write the LC code Learning Objectives:
for each Learning Objectives: 1. State the properties of a normal random variable.
1. Interprets the mean of a 2. Illustrate and construct a normal curve.
discrete random variable. 1. Solves problems involving the 3. Recognize the importance of the normal curve in statistical inference.
2. Show willingness in doing the mean of a discrete random
assigned task. variable.
2. Work on the solutions of the
problems involving the mean
and variance of a probability
distributions.
Content is what the lesson is all about. It pertains to the subject matter that the teacher aims to teach. In the CG, the content can be tackled in a week or two.

II. CONTENT Mean and Variance of The Discrete Random Variables. Normal Random Variables and Normal Curve
III. LEARNING List of materials to be used on different days. Varied sources of materials sustain children's interest in the lesson and in learning. Ensure that there is a mix of concrete
RESOURCES and manipulative materials as well as paper-based materials. Hands-on learning promotes concept development.

A. References

1. Teacher’s Guide
pages

2. Learner’s Material
pages

3. Textbook pages Statistics an Probability , REX , Pages Statistics an Probability , REX , Pages Statistics an Probability, REX, Pages 54-71
22-46 22-46

4. Additional
Materials from
Statistics and Probability Module 2 Statistics and Probability Module 2 Statistics and Probability Module 3
Learning Resource
(LR) portal

B. Other Learning Teachers Wraparound Edition Next Teachers Wraparound Edition Next
Resources Century Mathematics Statistics and Century Mathematics Statistics and
Probability Probability Teachers Wraparound Edition Next Century Mathematics Statistics and
https://youtu.be/PP5GVG1llL4? https://youtu.be/PP5GVG1llL4? Probability
list=PLyvLlSwBY36v- list=PLyvLlSwBY36v-
1uE9rzWKt6HvbtKJhTFz 1uE9rzWKt6HvbtKJhTFz

IV. PROCEDURES These steps should be done across the week. Spread out the activities appropriately so that students will learn well. Always be guided by demonstration of learning by the
students which you can infer from formative assessment activities. Sustain learning systematically providing students with multiple ways to learn new things, practice their
learning, question their learning processes and draw conclusions about what they learned in relation to their life experiences and previous knowledge. indicate the time
allotment for each step.

A. Reviewing the Drill: Review/Recall: The teacher will recall the difference
previous lesson 1.Finding the mean and a. Formula for mean of the between discrete and continuous
or presenting the variance of a discrete random probability distribution variables by asking the students the
new lesson variable. μ= ΣX.P(x) following questions.
X.P(x b. Formula for variance of 1. What is a discrete variable?
X P(x) x².P(x)
) probability distribution 2. Give an example of a random
2 4/10 σ² = Σx².P(x) - μ² variable.
3. What is a continuous random
3 2/10
variable?
 4 1/10 4. Give an example of a continuous
random variable.
5 2/10
Answer Key:
1. A random variable is a variable
A. Focus Inquiry: whose value is a numerical outcome of
1. What are the steps in a random phenomenon.
finding the mean of a 2. Possible answer: number of marbles
discrete random variable? in a jar, number of students present or
2. How about finding the number of heads when tossing two
variance of a discrete coins.
random variable? 3. A continuous random variable is a
What are the significant factors in solving random variable where the data can
it? take infinitely many values.
4. Height, weight, answers may vary.
B. Establishing a The teacher lets the students realize that The teacher lets the students realize that The teacher will explain to the students
purpose for the solving problems involving the mean and solving problems involving the mean and how to illustrate a normal random
lesson the variance of a discrete random the variance of a discrete random variable and construct a normal curve.
variable. variable.
C. Presenting Group the students by 5 and let them do / Group the learners into 5 and let them The teacher will explain first what a
examples/ interpret the result of the mean and solve the following problems. normal random variable is and will give
instances for the variance of the following situation: Problem 1: examples related to it. Moreover, below
new lesson The probabilities of a machine is the illustration of normal random
X P(x) X.P(x) x².P(x)
manufacturing are 1, 2, 3, 4, 5 and the variable and the curve.
3 2/52
defective parts are 0.75, 0.17, 0.04,
5 4/52 0.025, and 0.01 respectively.
7 3/52 Find the mean and variance of the The teacher will divide the class into 5
probability distribution. groups and will let them describe the
9 4/52 Problem 2: graph below:
10 2/52 The table shows the number of 1. What does the graph looks like?
computers sold per day at a local 2. Shade the region of between 6.5 and
computer store along with its 8.
corresponding probabilities. Find the 3. Shade the region between 12.5 and
mean and variance of the distribution. 14.
No. of 4. Shade the region between 9.5 to 12.
Comp
uters P(x) X.P(x) x².P(x) Answer Key:
sold 1. The graph looks like a bell-shaped
(X) 2. Answer may refer on the figure
0 0.1 3. Answer may refer on the figure
4. Answer may refer on the figure
 1 0.2
(Contextualization and Localization)
2 0.3 B. Below is the table of scores of the
selected grade 11- AFA of Piddig NHS
3 0.2 who took the remedial quiz in
Mathematics last week.
4 0.2
Construct the graph from the table.

X(score) F
5 1
4 3
3 5
2 3
1 1
N 13
Question:
What does the graph of the data look
like?
Answer: Bell Shape
D. Discussing new The teacher discusses the concept of the The teacher discusses the concept of The teacher will discuss the answers
concepts and mean and variance of a discrete random the mean and variance of a discrete from the group activity above right after
practicing new variable. random variable. the students explain their work.
skills  How do you get the mean? 1. What are the steps in solving The teacher will discuss on the
How about the variance? the mean and variance of a following:
probability distribution of a • Normal random variable
random variable? • Properties of the Normal
2. How it is similar to the Probability Distribution
procedure in solving the mean • Constructing a Normal Curve
and variance of a frequency
distribution?
3. Compare the formulas in
finding the mean and variance
of a frequency distribution and
that of a frequency distribution.
4. How do you interpret the mean
and variance of a probability
distribution?
Which formula is easier to use in finding
the mean and variance of probability
 distribution?
E. Developing Calculate and interpret the mean and By Solve the problem if the probability The students will be given data from The students will do In-Class Activity 5:
mastery ((Leads to variance of the following data shown in distribution of an event X which takes 0, their Mathematics periodical test and Exploring the Graph of a Standard
Formative the table: 1, 2, and with P(x) = 1/8, 3/8, 3/8 will make intervals out of it. After such, Normal Curve
Assessment) respectively.. Find the mean and its they will graph the intervals and Task 1 and Task 2
X P(x) X.P(x) x².P(x) variance describe their observations.
(Answer may vary)
1 1/6

2 2/6

3 5/6

4 1/6
F. Finding practical The students will be answering the The teacher will say, “There are many
applications of following questions: events in real life that generate random
concepts and skills 1. What is the most significant learning variables that have the natural
in daily living you have gained in today’s session? tendency to approximate the shape of a
2. Is learning the mean and variance of a bell. For example, the heights of a large
discrete random variables important to number of seedlings that we see in
your lives? Explain garden normally consist of a few short
3. Construct one “hugot” statement in ones, and most of them having heights
relation to today’s lesson. in between tall and shorts.
G. Making The teacher will discuss the concept and The key points in solving problems for  The normal distribution is the
generalization and interpret the mean and variance of the the mean and variance of a probability most important and most
abstractions about discrete random variable, distribution is to make use of the formula widely used distribution in
the lesson for the mean which is μ=ΣX.P(x) and for statistics. It is sometimes
the variance σ²=Σx².P(x)-μ². called the "bell curve,"
although the tonal qualities of
such a bell would be less than
pleasing. It is also called the
"Gaussian curve" after the
mathematician Karl Friedrich
Gauss.

 A normal curve is a bell-

shaped curve which shows
the probability distribution of a
continuous random variable.
 Moreover, the normal curve
represents a normal
distribution. The total area
under the normal curve
logically represents the sum
of all probabilities for a
random variable. Hence, the
area under the normal curve
is one. Also, the standard
normal curve represents a
normal curve with mean 0 and
standard deviation 1. Thus,
the parameters involved in a
normal distribution is mean ( μ
) and standard deviation ( σ ).

Characteristics of a normal curve:

• The values of mean, median and

mode are same

• It represents a unimodal distribution

as it has only one peak.

• It shows a symmetric distribution as

50% of the data set lies on the left side
of the mean and 50% of the data set
lies on the right side of the mean.

Empirical rule: 68% of the data fall

within μ ±σ, 95% of the data fall within
μ ± 2 σ and 99.7% of the data fall
within μ ± 3 σ
 Some of the examples for normal
distribution are given below:

• Heights/weights of the subjects under

study

• IQ scores of the students

• Test scores of the students

H. Evaluating learning In students’ activity notebook, the
students will fill in the blanks with the
appropriate word or phrase to make
meaningful statements.
1. The curve of a probability distribution
is formed by __________.
2. The area under a normal curve is
____________.
3. The important values that best
describe a normal curve are
______________.
4. There are ________ standard
deviation units at the baseline of a
normal curve.
5. The curve of a normal distribution
extends indefinitely at the tails but does
not ___________.
6. The area under a normal curve may
also be expressed in terms of
________ or __________or
___________.
7. The mean, median, and mode of a
normal curve are ___________
8. A normal curve is used
________________
Answer Key:
1. a distribution of raw scores
2. 1
3. the mean and the standard deviation
4. 6
 5. touch the horizontal axis
6. proportion, probability, percentage
7. equal
8. inferential statistics
I. Additional activities The learners will answer EXTENSION
for application for in their book which will serve as their
remediation performance task for the week.
V. REMARKS

VI. REFLECTION
Reflect on your teaching and assess yourself as a teacher. Think about your students’ progress this week. What works? What else needs to be done to help the students
learn? Identify what help your instructional supervisors can provide for you so that when you meet them, you can ask them relevant questions.

A. No. of learners who

require additional
activities for
remediation who
scored below 80%.

B. Did the remedial

lessons work? No.
of learners who
have caught up with
the lesson.

C. No. of learners who

continue to require
remediation?

D. Which of my
teaching strategies
worked well? Why
did this work?

E. What difficulties did

I encounter that my
principal or
supervisor can help
me solve?

F. What innovation or In the development of the lesson In the development of the lesson In the development of the lesson In the development of the lesson
localized materials (Presenting examples/ instances of (Presenting examples/ instances of (Presenting examples/ instances of (Presenting examples/ instances of
did I use/discover
that I wish to share the new lesson) the new lesson) the new lesson) the new lesson)
with other
teachers?
Prepared by: Checked & Verified: Contents Noted:

ANGELENE L. AMBATALI EMERZON C. GUILLERMO, EdD RIZALINA T. MANZANO, EdD

Teacher I Master Teacher I School Principal IV