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1. DAILY LESSON LOG
School MARCELO H. DEL PILAR NATIONAL HIGH SCHOOL Grade Level 11
Teacher Learning Area STATISTICS AND
PROBABILITY
Teaching Dates & Time Week 2 Quarter 3RD Quarter
Day 1 Day 2 Day 3 Day 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 if remedial
activities may be done for developing content knowledge and competencies. These are assessed using Formative Assessment strategies. Valuing objectives support the learning 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 Standards The learner demonstrates understanding of key concepts of random variables and probability distributions.
B. Performance Standards The learner is able to apply an appropriate random variable for a given real-life problem (such as in decision making and games of chance).
C. Learning Competencies/Objectives
(Write LC code for each area)
The learner …
4. illustrates a probability
distribution for a discrete random
variable and its properties.
(M11/12SP-IIIa-4)
5. constructs the probability mass
function of a discrete random
variable and its corresponding
histogram. (M11/12SP-IIIa-5)
The learner …
4. illustrates a probability
distribution for a discrete random
variable and its properties.
(M11/12SP-IIIa-4)
5. constructs the probability mass
function of a discrete random
variable and its corresponding
histogram. (M11/12SP-IIIa-5)
The learner …
7. illustrates the mean and
variance of a discrete random
variable. (M11/12SP-IIIb-1)
8. calculates the mean and the
variance of a discrete random
variable. (M11/12SP-IIIb-2)
9. interprets the mean and the
variance of a discrete random
variable. (M11/12SP-IIIb-3)
The learner …
7. illustrates the mean and
variance of a discrete random
variable. (M11/12SP-IIIb-1)
8. calculates the mean and the
variance of a discrete random
variable. (M11/12SP-IIIb-2)
9. interprets the mean and the
variance of a discrete random
variable. (M11/12SP-IIIb-3)
II. CONTENT
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.
Probability Distributions of
Discrete Random Variables
– Constructing Histogram
Probability Distributions of
Discrete Random Variables
– QUIZ
Mean of the Probability
Distributions of Discrete
Random Variables
Variance and standard
deviation of the Probability
Distributions of Discrete
Random Variables
A. References
1. Teacher’s Guide pages Pages: 117 – 129 Pages: 117 – 129 Pages: 117 – 129 Pages: 117 – 129
2. Learner’s Material pages
3. Textbook pages RBS Statistics and
Probability
Author: R. Belecina, et. Al.
Pages:
RBS Statistics and
Probability
Author: R. Belecina, et. Al.
Pages:
RBS Statistics and
Probability
Author: R. Belecina, et. Al.
Pages:
RBS Statistics and
Probability
Author: R. Belecina, et. Al.
Pages:
4. Additional Materials from
Learning Resources (LR) portal

2. B. Other Learning Resources
III. PROCEDURE
These steps should be done across the week. Spread out the activities appropriately so that the students will learn well. Always be guided by demonstration of learning of the students which can be inferring from
formative assessment activities. Sustain learning systematically by providing students with multiple ways to learn new thing, 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 to each step.
A. Reviewing previous lessons or
presenting the new lesson
Recall the following:
 Random variables ant types
 Getting the value of the
random variable
 Discrete probability
distribution/ Probability Mass
Function
 Constructing the Discrete
Probability Distribution (give
another example, say, tossing
a coin twice)
Recall the following:
 Random variables ant types
 Getting the value of the
random variable
 Discrete probability
distribution/ Probability Mass
Function
 Constructing the Discrete
Probability Distribution (give
another example, say,
tossing a coin twice)
How to construct a discrete probability
distribution? Histogram?
What was discussed yesterday?
(Mean)
What is a mean?
How can we compute for the mean of
a discrete probability distribution?
B. Establishing a purpose for the
lesson
• Illustrate the probability distribution
for discrete random variables and its
properties
• Compute probabilities
corresponding to a given discrete
random variable
• Construct the probability mass
function of a discrete random variable
and its corresponding histogram
• Illustrate the probability distribution
for discrete random variables and its
properties
• Compute probabilities
corresponding to a given discrete
random variable
• Construct the probability mass
function of a discrete random
variable and its corresponding
histogram
• Illustrate and Compute for the mean
of the discrete probability distribution
• Interpret the mean of a discrete
random variable
• Solve problems involving the mean
of probability distributions
• Illustrate and calculate the variance
and standard deviation of a discrete
random variable
• Interpret the variance and standard
deviation of a discrete random variable
• Solve problems involving variance
and standard deviation of probability
distributions
C. Presenting example/instances
of the new lesson
Introduce the histogram. (Define) A. Given the values of the variables X
and Y, evaluate the following
summations.
𝑋1 = 4 𝑋2 = 2 𝑋3 = 5 𝑋4 = 1
𝑌1 = 2 𝑌2 = 1 𝑌3 = 0 𝑌4 = 2
1. ∑ 𝑋
2. ∑ 𝑌
3. ∑ 𝑋𝑌
4. ∑(𝑋 + 𝑌)
5. ∑ 4𝑋𝑌
Motivation:
Measuring the height of dogs
 The heights (at the shoulder) are:
600mm, 470mm, 170mm, 430mm,
and 300mm. What is the mean
height of the dogs?
 Get the difference of the height of
dogs to the average height. To
measure the amount of variation of
the height of the dogs, square
each difference, then get the
average. (variance)

3.  Get the square root of the variance
(Standard deviation)
 All dogs that has a height within
the two blue lines are considered
normal. Those above or below are
considered tall or short.
D. Discussing new concepts and
practicing new skills #1
Differentiate Histogram and Bar
graph
Ask the students what they know
about the mean
Consider a rolling die. What is the
average number of spots that would
appear?
Define and discuss variance and
standard deviation.
E. Discussing new concepts and
Practicing new skills #2
Construct the histogram in tossing a
coin twice
Present the following steps in
computing for the mean of the discrete
probability distribution:
1. Probability Distribution
Construct a probability
Distribution for the random
variable. Convert the probability
into decimal.
2. Multiply
Multiply the value of the random
variable to the corresponding
probability.
3. Sum up!
Add the result in step 2, then
divide it to the total number of
the sample space in the
probability distribution.
Present the following steps in
computing for the variance and
standard deviation of the discrete
probability distribution:
1. Construct a probability
distribution.
2. Find the mean of the probability
distribution.
3. Subtract the mean from each
value of the random variable.
4. Square ALL the results obtained
in step 3.
5. Multiply the results obtained in
step 4 by the corresponding
probability.
6. Add the results in step 5
Standard Deviation can be obtained by
getting the square root of the
variance.
F. Developing Mastery Two balls are drawn in succession
without replacement from a box
containing 5 red balls and 6 blue
balls. Let Z be the random variable
representing the number of blue
balls. Construct the probability
distribution of the random variable Z
 The probabilities that a customer will
buy 1, 2, 3, 4, or 5 items in a
grocery store are
3 ,
1
,
1
,
2
, 𝑎𝑛𝑑
3
respectively.
10 10 10 10 10
What is the average number of items
that a customer will buy?
Two balls are drawn in succession
without replacement from a box
containing 5 red balls and 6 blue balls.
Let Z be the random variable
representing the number of blue balls.
Construct the probability distribution of
the random variable Z

4.  The probabilities that a surgeon
operates on 3, 4, 5, 6, or 7 patients
in any day are 0.15, 0.10, 0.20,
0.25, and 0.30 respectively. Find the
average number of patients that a
surgeon operates on a day.
G. Finding practical applications of
concepts and skills in daily living
(Mastery and Quiz) (Quiz) Two balls are drawn in succession
without replacement from a box
containing 5 red balls and 6 blue balls.
Let Z be the random variable
representing the number of blue balls.
Construct the probability distribution of
the random variable Z
Two balls are drawn in succession
without replacement from a box
containing 5 red balls and 6 blue balls.
Let Z be the random variable
representing the number of blue balls.
Construct the probability distribution of
the random variable Z
H. Making generalizations and
Abstractions about the lessons
What is the difference between a
histogram and a bar graph?
What do we consider in constructing
the histogram? (random variable and
probability)
What is a mean?
How can we compute for the mean of
a discrete probability distribution?
I. Evaluating Learning The debate society has 8 members
who were qualified to participate the
incoming interschool debate. The
adviser needed to choose three
members out of the 8 qualified to
represent the school in the said
event.
a. Identify all the possible
outcomes in selecting 3
members out of 8
b. Compute for the probabilities
of each outcome
c. Construct the discrete
probability distribution
d. Construct the histogram
Complete the table below and find the
mean of the probability Distribution
Find the mean of the probability
distribution of the random variable X,
which can take only the values 1, 2,
and 3, given that P(1) =
10
, 𝑃(2) =
33
1 , 𝑎𝑛𝑑 𝑃(3) =
12
3 33
J. Additional activities for
application or remediation
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 when you meet them, you can ask them relevant questions.
A. No. of learners who earned 80% in
the evaluation.

5. B. No. of learners who require
additional activities remediation.
C. Did the remedial lessons work? No. of
learners who caught up with the
lesson.
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did these work?
F. What difficulties did I encounter
which my principal or supervisor can
help me solve?
G. What innovation or localization
materials did I use/discover which I
wish to share with other teachers?