1. TEACHING GUIDE FOR SENIOR HIGH SCHOOL
Statistics and Probability
CORE SUBJECT
This Teaching Guide was collaboratively developed and reviewed by educators from public
and private schools, colleges, and universities. We encourage teachers and other education
stakeholders to email their feedback, comments, and recommendations to the Commission on
Higher Education, K to 12 Transition Program Management Unit - Senior High School
Support Team at k12@ched.gov.ph. We value your feedback and recommendations.
Commission on Higher Education
in collaboration with the Philippine Normal University
INITIAL RELEASE: 13 JUNE 2016

2. This Teaching Guide by the
Commission on Higher Education
is licensed under a Creative
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Printed in the Philippines by EC-TEC
Commercial, No. 32 St. Louis
Compound 7, Baesa, Quezon City,
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Published by the Commission on Higher Education, 2016
Chairperson: Patricia B. Licuanan, Ph.D.
Commission on Higher Education
K to 12 Transition Program Management Unit
Office Address: 4th Floor, Commission on Higher Education,
C.P. Garcia Ave., Diliman, Quezon City
Telefax: (02) 441-1143 / E-mail Address: k12@ched.gov.ph
DEVELOPMENT TEAM
Team Leader: Jose Ramon G. Albert, Ph.D.
Writers:
Zita VJ Albacea, Ph.D., Mark John V. Ayaay
Isidoro P. David, Ph.D., Imelda E. de Mesa
Technical Editors:
Nancy A. Tandang, Ph.D., Roselle V. Collado
Copy Reader: Rea Uy-Epistola
Illustrator: Michael Rey O. Santos
Cover Artists: Paolo Kurtis N. Tan, Renan U. Ortiz
CONSULTANTS
THIS PROJECT WAS DEVELOPED WITH THE PHILIPPINE NORMAL UNIVERSITY.
University President: Ester B. Ogena, Ph.D.
VP for Academics: Ma. Antoinette C. Montealegre, Ph.D.
VP for University Relations & Advancement: Rosemarievic V. Diaz, Ph.D.
Ma. Cynthia Rose B. Bautista, Ph.D., CHED
Bienvenido F. Nebres, S.J., Ph.D., Ateneo de Manila University
Carmela C. Oracion, Ph.D., Ateneo de Manila University
Minella C. Alarcon, Ph.D., CHED
Gareth Price, Sheffield Hallam University
Stuart Bevins, Ph.D., Sheffield Hallam University
SENIOR HIGH SCHOOL SUPPORT TEAM
CHED K TO 12 TRANSITION PROGRAM MANAGEMENT UNIT
Program Director: Karol Mark R. Yee
Lead for Senior High School Support: Gerson M. Abesamis
Lead for Policy Advocacy and Communications: Averill M. Pizarro
Course Development Officers:
John Carlo P. Fernando, Danie Son D. Gonzalvo
Teacher Training Officers:
Ma. Theresa C. Carlos, Mylene E. Dones
Monitoring and Evaluation Officer: Robert Adrian N. Daulat
Administrative Officers: Ma. Leana Paula B. Bato,
Kevin Ross D. Nera, Allison A. Danao, Ayhen Loisse B. Dalena

3. Introduction
As the Commission supports DepEd’s implementation of Senior High School (SHS), it upholds the vision
and mission of the K to 12 program, stated in Section 2 of Republic Act 10533, or the Enhanced Basic
Education Act of 2013, that “every graduate of basic education be an empowered individual, through a
program rooted on...the competence to engage in work and be productive, the ability to coexist in fruitful
harmony with local and global communities, the capability to engage in creative and critical thinking,
and the capacity and willingness to transform others and oneself.”
To accomplish this, the Commission partnered with the Philippine Normal University (PNU), the
National Center for Teacher Education, to develop Teaching Guides for Courses of SHS. Together with
PNU, this Teaching Guide was studied and reviewed by education and pedagogy experts, and was
enhanced with appropriate methodologies and strategies.
Furthermore, the Commission believes that teachers are the most important partners in attaining this
goal. Incorporated in this Teaching Guide is a framework that will guide them in creating lessons and
assessment tools, support them in facilitating activities and questions, and assist them towards deeper
content areas and competencies. Thus, the introduction of the SHS for SHS Framework.
The SHS for SHS Framework
The SHS for SHS Framework, which stands for “Saysay-Husay-Sarili for Senior High School,” is at the
core of this book. The lessons, which combine high-quality content with flexible elements to
accommodate diversity of teachers and environments, promote these three fundamental concepts:
SAYSAY: MEANING
Why is this important?
Through this Teaching Guide,
teachers will be able to
facilitate an understanding of
the value of the lessons, for
each learner to fully engage in
the content on both the
cognitive and affective levels.
HUSAY: MASTERY
How will I deeply understand this?
Given that developing mastery
goes beyond memorization,
teachers should also aim for deep
understanding of the subject
matter where they lead learners
to analyze and synthesize
knowledge.
SARILI: OWNERSHIP
What can I do with this?
When teachers empower
learners to take ownership of
their learning, they develop
independence and self-
direction, learning about both
the subject matter and
themselves.

4. The Parts of the Teaching Guide
This Teaching Guide is mapped and aligned to the
DepEd SHS Curriculum, designed to be highly
usable for teachers. It contains classroom activities
and pedagogical notes, and integrated with
innovative pedagogies. All of these elements are
presented in the following parts:
1. INTRODUCTION
• Highlight key concepts and identify the
essential questions
• Show the big picture
• Connect and/or review prerequisite
knowledge
• Clearly communicate learning
competencies and objectives
• Motivate through applications and
connections to real-life
2. INSTRUCTION/DELIVERY
• Give a demonstration/lecture/simulation/
hands-on activity
• Show step-by-step solutions to sample
problems
• Use multimedia and other creative tools
• Give applications of the theory
• Connect to a real-life problem if applicable
3. PRACTICE
• Discuss worked-out examples
• Provide easy-medium-hard questions
• Give time for hands-on unguided classroom
work and discovery
• Use formative assessment to give feedback
4. ENRICHMENT
• Provide additional examples and
applications
• Introduce extensions or generalisations of
concepts
• Engage in reflection questions
• Encourage analysis through higher order
thinking prompts
5. EVALUATION
• Supply a diverse question bank for written
work and exercises
• Provide alternative formats for student
work: written homework, journal, portfolio,
group/individual projects, student-directed
research project
Pedagogical Notes
The teacher should strive to keep a good balance
between conceptual understanding and facility in
skills and techniques. Teachers are advised to be
conscious of the content and performance
standards and of the suggested time frame for
each lesson, but flexibility in the management of
the lessons is possible. Interruptions in the class
schedule, or students’ poor reception or difficulty
with a particular lesson, may require a teacher to
extend a particular presentation or discussion.
Computations in some topics may be facilitated by
the use of calculators. This is encour- aged;
however, it is important that the student
understands the concepts and processes involved
in the calculation. Exams for the Basic Calculus
course may be designed so that calculators are not
necessary.
Because senior high school is a transition period
for students, the latter must also be prepared for
college-level academic rigor. Some topics in
calculus require much more rigor and precision
than topics encountered in previous mathematics
courses, and treatment of the material may be
different from teaching more elementary courses.
The teacher is urged to be patient and careful in
presenting and developing the topics. To avoid too
much technical discussion, some ideas can be
introduced intuitively and informally, without
sacrificing rigor and correctness.
The teacher is encouraged to study the guide very
well, work through the examples, and solve
exercises, well in advance of the lesson. The
development of calculus is one of humankind’s
greatest achievements. With patience, motivation
and discipline, teaching and learning calculus
effectively can be realized by anyone. The teaching
guide aims to be a valuable resource in this
objective.

5. On DepEd Functional Skills and CHED’s College Readiness Standards
As Higher Education Institutions (HEIs) welcome the graduates of the Senior High School program, it is
of paramount importance to align Functional Skills set by DepEd with the College Readiness Standards
stated by CHED.
The DepEd articulated a set of 21st century skills that should be embedded in the SHS curriculum across
various subjects and tracks. These skills are desired outcomes that K to 12 graduates should possess in
order to proceed to either higher education, employment, entrepreneurship, or middle-level skills
development.
On the other hand, the Commission declared the College Readiness Standards that consist of the
combination of knowledge, skills, and reflective thinking necessary to participate and succeed - without
remediation - in entry-level undergraduate courses in college.
The alignment of both standards, shown below, is also presented in this Teaching Guide - prepares
Senior High School graduates to the revised college curriculum which will initially be implemented by
AY 2018-2019.
College Readiness Standards Foundational Skills DepEd Functional Skills
Produce all forms of texts (written, oral, visual, digital) based on:
1. Solid grounding on Philippine experience and culture;
2. An understanding of the self, community, and nation;
3. Application of critical and creative thinking and doing processes;
4. Competency in formulating ideas/arguments logically, scientifically,
and creatively; and
5. Clear appreciation of one’s responsibility as a citizen of a multicultural
Philippines and a diverse world;
Visual and information literacies
Media literacy
Critical thinking and problem solving skills
Creativity
Initiative and self-direction
Systematically apply knowledge, understanding, theory, and skills
for the development of the self, local, and global communities using
prior learning, inquiry, and experimentation
Global awareness
Scientific and economic literacy
Curiosity
Critical thinking and problem solving skills
Risk taking
Flexibility and adaptability
Initiative and self-direction
Work comfortably with relevant technologies and develop
adaptations and innovations for significant use in local and global
communities;
Global awareness
Media literacy
Technological literacy
Creativity
Flexibility and adaptability
Productivity and accountability
Communicate with local and global communities with proficiency,
orally, in writing, and through new technologies of communication;
Global awareness
Multicultural literacy
Collaboration and interpersonal skills
Social and cross-cultural skills
Leadership and responsibility
Interact meaningfully in a social setting and contribute to the
fulfilment of individual and shared goals, respecting the
fundamental humanity of all persons and the diversity of groups
and communities
Media literacy
Multicultural literacy
Global awareness
Collaboration and interpersonal skills
Social and cross-cultural skills
Leadership and responsibility
Ethical, moral, and spiritual values

6. Preface
Prior to the implementation of K-12, Statistics was taught in public high schools in the Philippines
typically in the last quarter of third year. In private schools, Statistics was taught as either an elective,
or a required but separate subject outside of regular Math classes. In college, Statistics was taught
practically to everyone either as a three unit or six unit course. All college students had to take at least
three to six units of a Math course, and would typically “endure” a Statistics course to graduate.
Teachers who taught these Statistics classes, whether in high school or in college, would typically be
Math teachers, who may not necessarily have had formal training in Statistics. They were selected out
of the understanding (or misunderstanding) that Statistics is Math. Statistics does depend on and uses a
lot of Math, but so do many disciplines, e.g. engineering, physics, accounting, chemistry, computer
science. But Statistics is not Math, not even a branch of Math. Hardly would one think that accounting
is a branch of mathematics simply because it does a lot of calculations. An accountant would also not
describe himself as a mathematician.
Math largely involves a deterministic way of thinking and the way Math is taught in schools leads
learners into a deterministic way of examining the world around them. Statistics, on the other hand, is
by and large dealing with uncertainty. Statistics uses inductive thinking (from specifics to generalities),
while Math uses deduction (from the general to the specific).
“Statistics has its own tools and ways of thinking, and statisticians are quite insistent that
those of us who teach mathematics realize that statistics is not mathematics, nor is it even a
branch of mathematics. In fact, statistics is a separate discipline with its own unique ways of
thinking and its own tools for approaching problems.” - J. Michael Shaughnessy, “Research on
Students’ Understanding of Some Big Concepts in Statistics” (2006)
Statistics deals with data; its importance has been recognized by governments, by the private sector,
and across disciplines because of the need for evidence-based decision making. It has become even more
important in the past few years, now that more and more data is being collected, stored, analyzed and
re-analyzed. From the time when humanity first walked the face of the earth until 2003, we created as
much as 5 exabytes of data (1 exabyte being a billion “gigabytes”). Information communications
technology (ICT) tools have provided us the means to transmit and exchange data much faster, whether
these data are in the form of sound, text, visual images, signals or any other form or any combination of
those forms using desktops, laptops, tablets, mobile phones, and other gadgets with the use of the
internet, social media (facebook, twitter). With the data deluge arising from using ICT tools, as of 2012,
as much as 5 exabytes were being created every two days (the amount of data created from the
beginning of history up to 2003); a year later, this same amount of data was now being created every ten
minutes.

7. In order to make sense of data, which is typically having variation and uncertainty, we need the Science
of Statistics, to enable us to summarize data for describing or explaining phenomenon; or to make
predictions (assuming trends in the data continue). Statistics is the science that studies data, and what
we can do with data. Teachers of Statistics and Probability can easily spend much time on the formal
methods and computations, losing sight of the real applications, and taking the excitement out of things.
The eminent statistician Bradley Efron mentioned how diverse statistical applications are:
“During the 20th Century statistical thinking and methodology has become the scientific
framework for literally dozens of fields including education, agriculture, economics, biology, and
medicine, and with increasing influence recently on the hard sciences such as astronomy,
geology, and physics. In other words, we have grown from a small obscure field into a big obscure
field.”
In consequence, the work of a statistician has become even fashionable. Google’s chief economist Hal
Varian wrote in 2009 that “the sexy job in the next ten years will be statisticians.” He went on and
mentioned that “The ability to take data - to be able to understand it, to process it, to extract value from
it, to visualize it, to communicate it's going to be a hugely important skill in the next decades, not only at
the professional level but even at the educational level for elementary school kids, for high school kids,
for college kids. “
This teaching guide, prepared by a team of professional statisticians and educators, aims to assist
Senior High School teachers of the Grade 11 second semester course in Statistics and Probability so that
they can help Senior High School students discover the fun in describing data, and in exploring the
stories behind the data. The K-12 curriculum provides for concepts in Statistics and Probability to be
taught from Grade 1 up to Grade 8, and in Grade 10, but the depth at which learners absorb these
concepts may need reinforcement. Thus, the first chapter of this guide discusses basic tools (such as
summary measures and graphs) for describing data. While Probability may have been discussed prior to
Grade 11, it is also discussed in Chapter 2, as a prelude to defining Random Variables and their
Distributions. The next chapter discusses Sampling and Sampling Distributions, which bridges
Descriptive Statistics and Inferential Statistics. The latter is started in Chapter 4, in Estimation, and
further discussed in Chapter 5 (which deals with Tests of Hypothesis). The final chapter discusses
Regression and Correlation.
Although Statistics and Probability may be tangential to the primary training of many if not all Senior
High School teachers of Statistics and Probability, it will be of benefit for them to see why this course is
important to teach. After all, if the teachers themselves do not find meaning in the course, neither will
the students. Work developing this set of teaching materials has been supported by the Commission on
Higher Education under a Materials Development Sub-project of the K-12 Transition Project. These
materials will also be shared with Department of Education.
Writers of this teaching guide recognize that few Senior High School teachers would have formal
training or applied experience with statistical concepts. Thus, the guide gives concrete suggestions on
classroom activities that can illustrate the wide range of processes behind data collection and data
analysis.

8. It would be ideal to use technology (i.e. computers) as a means to help teachers and students with
computations; hence, the guide also provides suggestions in case the class may have access to a
computer room (particularly the use of spreadsheet applications like Microsoft Excel). It would be
unproductive for teachers and students to spend too much time working on formulas, and checking
computation errors at the expense of gaining knowledge and insights about the concepts behind the
formulas.
The guide gives a mixture of lectures and activities, (the latter include actual collection and analysis of
data). It tries to follow suggestions of the Guidelines for Assessment and Instruction in Statistics
Education (GAISE) Project of the American Statistical Association to go beyond lecture methods, and
instead exercise conceptual learning, use active learning strategies and focus on real data. The guide
suggests what material is optional as there is really a lot of material that could be taught, but too little
time. Teachers will have to find a way of recognizing that diverse needs of students with variable
abilities and interests.
This teaching guide for Statistics and Probability, to be made available both digitally and in print to
senior high school teachers, shall provide Senior High School teachers of Statistics and Probability with
much-needed support as the country’s basic education system transitions into the K-12 curriculum. It is
earnestly hoped that Senior High School teachers of Grade 11 Statistics and Probability can direct
students into examining the context of data, identifying the consequences and implications of stories
behind Statistics and Probability, thus becoming critical consumers of information. It is further hoped
that the competencies gained by students in this course will help them become more statistical literate,
and more prepared for whatever employment choices (and higher education specializations) given that
employers are recognizing the importance of having their employee know skills on data management
and analysis in this very data-centric world.

9. C h a p t e r ( 1 : ( E x p l o r i n g ( D a t a ( – ( L e s s o n ( 1 ( Page(1(
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Chapter 1: Exploring Data
Lesson 1: Introducing Statistics
TIME FRAME:1 hour session
OVERVIEW OF LESSON
In decision making, we use statistics although some of us may not be aware of it. In this
lesson, we make the students realize that to decide logically, they need to use statistics. An
inquiry could be answered or a problem could be solved through the use of statistics. In fact,
without knowing it we use statistics in our daily activities.
LEARNING COMPETENCIES: At the end of the lesson, the learner should be able to
identify questions that could be answered using a statistical process and describe the activities
involved in a statistical process.
LESSON OUTLINE:
1. Motivation
2. Statistics as a Tool in Decision-Making
3. Statistical Process in Solving a Problem
DEVELOPMENT OF THE LESSON
A. Motivation
You may ask the students, a question that is in their mind at that moment. You may write
their answers on the board. (Note: You may try to group the questions as you write them on
the board into two, one group will be questions that are answerable by a fact and the other
group are those that require more than one information and needs further thinking).
The following are examples of what you could have written on the board:
Group 1:
• How old is our teacher?
• Is the vehicle of the Mayor of our city/town/municipality bigger than the vehicle used by
the President of the Philippines?
• How many days are there in December?
• Does the Principal of the school has a post graduate degree?
• How much does the Barangay Captain receive as allowance?
• What is the weight of my smallest classmate?
Group 2:
• How old are the people residing in our town?

10. C h a p t e r ( 1 : ( E x p l o r i n g ( D a t a ( – ( L e s s o n ( 1 ( Page(2(
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• Do dogs eat more than cats?
• Does it rain more in our country than in Thailand?
• Do math teachers earn more than science teachers?
• How many books do my classmates usually bring to school?
• What is the proportion of Filipino children aged 0 to 5 years who are underweight or
overweight for their age?
The first group of questions could be answered by a piece of information which is considered
always true. There is a correct answer which is based on a fact and you don’t need the
process of inquiry to answer such kind of question. For example, there is one and only one
correct answer to the first question in Group 1 and that is your age as of your last birthday or
the number of years since your birth year.
On the other hand, in the second group of questions one needs observations or data to be able
to respond to the question. In some questions you need to get the observations or responses of
all those concerned to be able to answer the question. On the first question in the second
group, you need to ask all the people in the locality about their age and among the values you
obtained you get a representative value. To answer the second question in the second group,
you need to get the amount of food that all dogs and cats eat to respond to the question.
However, we know that is not feasible to do so. Thus what you can do is get a representative
group of dogs and another representative group for the cats. Then we measure the amount of
food each group of animal eats. From these two sets of values, we could then infer whether
dogs do eat more than cats.
So as you can see in the second group of questions you need more information or data to be
able to answer the question. Either you need to get observations from all those concerned or
you get representative groups from which you gather your data. But in both cases, you need
data to be able to respond to the question. Using data to find a