STATISTICS AND PROBABILITY (TEACHING GUIDE)

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

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Commission on Higher Education
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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

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.

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 encouraged;
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.

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

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.

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.

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.

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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?

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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 an answer or a solution to a
problem or an inquiry is actually using the statistical process or doing it with statistics.
Now, let us formalize what we discussed and know more about statistics and how we use it in
decision-making.
B. Main Lesson
1. Statistics as a Tool in Decision-Making
Statistics is defined as a science that studies data to be able to make a decision. Hence, it is a
tool in decision-making process. Mention that Statistics as a science involves the methods of
collecting, processing, summarizing and analyzing data in order to provide answers or
solutions to an inquiry. One also needs to interpret and communicate the results of the
methods identified above to support a decision that one makes when faced with a problem or
an inquiry.
Trivia: The word “statistics” actually comes from the word “state”— because governments
have been involved in the statistical activities, especially the conduct of censuses either for
military or taxation purposes. The need for and conduct of censuses are recorded in the
pages of holy texts. In the Christian Bible, particularly the Book of Numbers, God is
reported to have instructed Moses to carry out a census. Another census mentioned in the

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Bible is the census ordered by Caesar Augustus throughout the entire Roman Empire before
the birth of Christ.
Inform students that uncovering patterns in data involves not just science but it is also an art,
and this is why some people may think “Stat is eeeks!” and may view any statistical
procedures and results with much skepticism. (See Figure 1-1.)
Make known to students that Statistics enable us to
• characterize persons, objects, situations, and phenomena;
• explain relationships among variables;
• formulate objective assessments and comparisons; and, more importantly
• make evidence-based decisions and predictions.
And to use Statistics in decision-making there is a statistical process to follow which is to be
discussed in the next section.
2. Statistical Process in Solving a Problem
You may go back to one of the questions identified in the second group and use it to discuss
the components of a statistical process. For illustration on how to do it, let us discuss how we
could answer the question “Do dogs eat more than cats?”
As discussed earlier, this question requires you to gather data to generate statistics which will
serve as basis in answering the query. There should be plan or a design on how to collect the
data so that the information we get from it is enough or sufficient for us to minimize any bias
in responding to the query. In relation to the query, we said earlier that we cannot gather the
data from all dogs and cats. Hence, the plan is to get representative group of dogs and another
representative group of cats. These representative groups were observed for some
characteristics like the animal weight, amount of food in grams eaten per day and breed of the
animal. Included in the plan are factors like how many dogs and cats are included in the
group, how to select those included in the representative groups and when to observe these
animals for their characteristics.
After the data were gathered, we must verify the quality of the data to make a good decision.
Data quality check could be done as we process the data to summarize the information
extracted from the data. Then using this information, one can then make a decision or provide
answers to the problem or question at hand.
To summarize, a statistical process in making a decision or providing solutions to a problem
include the following:
• Planning or designing the collection of data to answer statistical questions in a way that
maximizes information content and minimizes bias;
• Collecting the data as required in the plan;
• Verifying the quality of the data after they were collected;
• Summarizing the information extracted from the data; and
• Examining the summary statistics so that insight and meaningful information can be
produced to support decision-making or solutions to the question or problem at hand.

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Hence, several activities make up a statistical process which for some the process is simple
but for others it might be a little bit complicated to implement. Also, not all questions or
problems could be answered by a simple statistical process. There are indeed problems that
need complex statistical process. However, one can be assured that logical decisions or
solutions could be formulated using a statistical process.
KEY POINTS
• Difference between questions that could be and those that could not answered using
Statistics.
• Statistics is a science that studies data.
• There are many uses of Statistics but its main use is in decision-making.
• Logical decisions or solutions to a problem could be attained through a statistical process.
REFERENCES
Albert, J. R. G. (2008).Basic Statistics for the Tertiary Level (ed. Roberto Padua, Welfredo
Patungan, Nelia Marquez), published by Rex Bookstore.
Handbook of Statistics 1 (1st
and 2nd
Edition), Authored by the Faculty of the Institute of
Statistics, UP Los Baños, College Laguna 4031
Workbooks in Statistics 1 (From 1st
to 13th
Edition), Authored by the Faculty of the Institute
of Statistics, UP Los Baños, College Laguna 4031
https://www.illustrativemathematics.org/content-standards/tasks/703
http://www.cartoonstock.com
ASSESSMENT
Note: Answers are provided inside the parentheses and in bold face.
1. Identify which of the following questions are answerable using a statistical process.
a. What is a typical size of a Filipino family? (answerable through a statistical process)
b. How many hours in a day? (not answerable through a statistical process)
c. How old is the oldest man residing in the Philippines? (answerable through a
statistical process)
d. Is planet Mars bigger than planet Earth? (not answerable through a statistical
process)
e. What is the average wage rate in the country? (answerable through a statistical
process)
f. Would Filipinos prefer eating bananas rather than apple? (answerable through a
statistical process)
g. How long did you sleep last night? (not answerable through a statistical process)

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h. How much a newly-hired public school teacher in NCR earns in a month? (not
answerable through a statistical process)
i. How tall is a typical Filipino? (answerable through a statistical process)
j. Did you eat your breakfast today? (not answerable through a statistical process)
2. For each of the identified questions in Number 1 that are answerable using a statistical
process, describe the activities involved in the process.
For a. What is a typical size of a Filipino family? (The process includes getting a
representative group of Filipino families and ask the family head as to how many
members do they have in their family. From the gathered data which had undergone
a quality check a typical value of the number of family members could be obtained.
Such typical value represents a possible answer to the question.)
For c. How old is the oldest man residing in the Philippines? (The process includes getting
the ages of all residents of the country. From the gathered data which had undergone
a quality check the highest value of age could be obtained. Such value is the answer to
the question.)
For e. What is the average wage rate in the country? (The process includes getting all
prevailing wage rates in the country. From the gathered data which had undergone a
quality check a typical value of the wage rate could be obtained. Such value is the
answer to the question.)
For f. Would Filipinos prefer eating bananas rather than apple? (The process includes
getting a representative group of Filipinos and ask each one of them on what fruit
he/she prefers, banana or apple? From the gathered data which had undergone a
quality check the proportion of those who prefers banana and proportion of those
who prefer apple will be computed and compared. The results of this comparison
could provide a possible answer to the question.)
For i. How tall is a typical Filipino? (The process includes getting a representative group
of Filipinos and measure the height of each member of the representative group.
From the gathered data which had undergone a quality check a typical value of the
height of a Filipino could be obtained. Such typical value represents a possible answer
to the question.)
Note: Tell the students that getting a representative group and obtaining a typical value are
to be learned in subsequent lessons in this subject.

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Lesson 2: Data Collection Activity
OVERVIEW OF LESSON
As we have learned in the previous lesson, Statistics is a science that studies data. Hence to
teach Statistics, real data set is recommend to use. In this lesson,we present an activity where
the students will be asked to provide some data that will be submitted for consolidation by the
teacher for future lessons. Data on heights and weights, for instance, will be used for
calculating Body Mass Index in the integrative lesson. Students will also be given the
perspective that the data they provided is part of a bigger group of data as the same data will
be asked from much larger groups (the entire class, all Grade 11 students in school, all Grade
11 students in the district). The contextualization of data will also be discussed.
LEARNING COMPETENCIES: At the end of the lesson, the learner should be able to:
• Recognize the importance of providing correct information in a data collection activity;
• Understand the issue of confidentiality of information in a data collection activity;
• Participate in a data collection activity; and
• Contextualize data
LESSON OUTLINE:
1. Preliminaries in a Data Collection Activity
2. Performing a Data Collection Activity
3. Contextualization of Data
A. Preliminaries in a Data Collection Activity
Before the lesson, prepare a sheet of paper listing everyone’s name in class with a “Class
Student Number” (see Attachment A for the suggested format). The class student number
is a random number chosen in the following fashion:
(a) Make a box with “tickets” (small pieces of papers of equal sizes) listing the numbers 1 up
to the number of students in the class.
(b) Shake the box, get a ticket, and assign the number in the ticket to the first person in the
list.
(c) Shake the box again, get another ticket, and assign the number of this ticket to the next
person in the list.
(d) Do (c) until you run out of tickets in the box.

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At this point all the students have their corresponding class student number written across
their names in the prepared class list. Note that the preparation of the class list is done before
the class starts.
At the start of the class, inform each student confidentially of his/her class student number.
Perhaps, when the attendance is called, each student can be provided a separate piece of
paper that lists her/his name and class student number. Tell students to remember their class
student number, and to always use this throughout the semester whenever data are requested
of them. Explain to students that in data collection activity, specific identities like their
names are not required, especially because people have a right to confidentiality, but there
should be a way to develop and maintain a database to check quality of data provided, and
verify from respondent in a data collection activity the data that they provided (if necessary).
These preliminary steps for generating a class student number and informing students
confidentially of their class student number are essential for the data collection activities to be
performed in this lesson and other lessons so that students can be uniquely identified, without
having to obtain their names. Inform also the students that the class student numbers they
were given are meant to identify them without having to know their specific identities in the
class recording sheet (which will contain the consolidated records that everyone had
provided). This helps protect confidentiality of information.
In statistical activities, facts are collected from respondents for purposes of getting aggregate
information, but confidentiality should be protected. Mention that the agencies mandated to
collect data is bound by law to protect the confidentiality of information provided by
respondents. Even market research organizations in the private sector and individual
researchers also guard confidentiality as they merely want to obtain aggregate data. This way,
respondents can be truthful in giving information, and the researcher can give a commitment
to respondents that the data they provide will never be released to anyone in a form that will
identify them without their consent.
B. Performing a Data Collection Activity
Explain to the students that the purpose of this data collection activity is to gather data that
they could use for their future lessons in Statistics. It is important that they do provide the
needed information to the best of their knowledge. Also, before they respond to the
questionnaire provided in the Attachment B as Student Information Sheet (SIS), it is
recommended that each item in the SIS should be clarified. The following are suggested
clarifications to make for each item:
1. CLASS STUDENT NUMBER: This is the number that you provided confidentially to the
student at the start of the class.
2. SEX: This is the student’s biological sex and not their preferred gender. Hence, they have
to choose only one of the two choices by placing a check mark (√) at space provided
before the choices.
3. NUMBER OF SIBLINGS: This is the number of brothers and sisters that the student has
in their nuclear or immediate family. This number excludes him or her in the count. Thus,
if the student is the only child in the family then he/she will report zero as his/her number
of siblings.

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4. WEIGHT (in kilograms): This refers to the student’s weight based on the student’s
knowledge. Note that the weight has to be reported in kilograms. In case the student
knows his/her weight in pounds, the value should be converted to kilograms by dividing
the weight in pounds by a conversion factor of 2.2 pounds per kilogram.
5. HEIGHT (in centimeters): This refers to the student’s height based on the student’s
knowledge. Note that the height has to be reported in centimeters. In case the student
knows his/her height in inches, the value should be converted to centimeters by
multiplying the height in inches by a conversion factor of 2.54 centimeters per inch.
6. AGE OF MOTHER (as of her last birthday in years): This refers to the age of the
student’s mother in years as of her last birthday, thus this number should be reported in
whole number. In case, the student’s mother is dead or nowhere to be found, ask the
student to provide the age as if the mother is alive or around.You could help the student in
determining his/her mother’s age based on other information that the student could
provide like birth year of the mother or student’s age. Note also that a zero value is not
an acceptable value.
7. USUAL DAILY ALLOWANCE IN SCHOOL (in pesos): This refers to the usual
amount in pesos that the student is provided for when he/she goes to school in a weekday.
Note that the student can give zero as response for this item, in case he/she has no
monetary allowance per day.
8. USUAL DAILY FOOD EXPENDITURE IN SCHOOL (in pesos): This refers to the
usual amount in pesos that the student spends for food including drinks in school per day.
Note that the student can give zero as response for this item, in case he/she does not spend
for food in school.
9. USUAL NUMBER OF TEXT MESSAGES SENT IN A DAY: This refers to the usual
number of text messages that a student send in a day. Note that the student can give zero
as response for this item, in case he/she does not have the gadget to use to send a text
message or simply he/she does not send text messages.
10. MOST PREFERRED COLOR: The student is to choose a color that could be considered
his most preferred among the given choices. Note that the student could only choose one.
Hence, they have to place a check mark (√) at space provided before the color he/she
considers as his/her most preferred color among those given.
11. USUAL SLEEPING TIME: This refers to the usual sleeping time at night during a
typical weekday or school day. Note that the time is to be reported using the military way
of reporting the time or the 24-hour clock (0:00 to 23:59 are the possible values to use)
12. HAPPINESS INDEX FOR THE DAY : The student has to response on how he/she feels
at that time using codes from 1 to 10. Code 1 refers to the feeling that the student is very
unhappy while Code 10 refers to a feeling that the student is very happy on the day when
the data are being collected.
After the clarification, the students are provided at most 10 minutes to respond to the
questionnaire. Ask the students to submit the completed SIS so that you could consolidate the
data gathered using a formatted worksheet file provided to you as Attachment C. Having the

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data in electronic file makes it easier for you to use it in the future lessons. Be sure that the
students provided the information in all items in the SIS.
Inform the students that you are to compile all their responses and compiling all these records
from everyone in the class is an example of a census since data has been gathered from every
student in class. Mention that the government, through the Philippine Statistics Authority
(PSA), conducts censuses to obtain information about socio-demographic characteristics of
the residents of the country. Census data are used by the government to make plans, such as
how many schools and hospitals to build. Censuses of population and housing are conducted
every 10 years on years ending in zero (e.g., 1990, 2000, 2010) to obtain population counts,
and demographic information about all Filipinos. Mid-decade population censuses have also
been conducted since 1995. Censuses of Agriculture, and of Philippine Business and
Industry, are also conducted by the PSA to obtain information on production and other
relevant economic information.
PSA is the government agency mandated to conduct censuses and surveys. Through Republic
Act 10625 (also referred to as The Philippine Statistical Act of 2013), PSA was created from
four former government statistical agencies, namely: National Statistics Office (NSO),
National Statistical Coordination Board (NSCB), Bureau of Labor and Employment of
Statistics (BLES) and Bureau of Agricultural Statistics (BAS). The other agency created
through RA 10625 is the Philippine Statistical Research and Training Institute (PSRTI) which
is mandated as the research and training arm of the Philippine Statistical System. PSRTI was
created from its forerunner the former Statistical Research and Training Center (SRTC).
C. Contextualization of Data
Ask students what comes to their minds when they hear the term “data” (which may be
viewed as a collection of facts from experiments, observations, sample surveys and
censuses, and administrative reporting systems).
Present to the student the following collection of numbers, figures, symbols, and words, and
ask them if they could consider the collection as data.
3, red, F, 156, 4, 65, 50, 25, 1, M, 9, 40, 68, blue, 78, 168, 69, 3, F, 6, 9, 45, 50, 20,
200, white, 2, pink, 160, 5, 60, 100, 15, 9, 8, 41, 65, black, 68, 165, 59, 7, 6, 35, 45,
Although the collection is composed of numbers and symbols that could be classified as
numeric or non-numeric, the collection has no meaning or it is not contextualized, hence it
cannot be referred to as data.
Tell the students that data are facts and figures that are presented, collected and
analyzed. Data are either numeric or non-numeric and must be contextualized. To
contextualize data, we must identify its six W’s or to put meaning on the data, we must know
the following W’s of the data:
1. Who? Who provided the data?
2. What? What are the information from the respondents and What is the unit of
measurement used for each of the information (if there are any)?
3. When? When was the data collected?

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4. Where? Where was the data collected?
5. Why? Why was the data collected?
6. HoW? HoW was the data collected?
Let us take as an illustration the data that you have just collected from the students, and let us
put meaning or contextualize it by responding to the questions with the Ws. It is
recommended that the students answer theW-questions so that they will learn how to do it.
1. Who? Who provided the data?
• The students in this class provided the data.
2. What? What are the information from the respondents and What is the unit of
measurement used for each of the information (if there are any)?
• The information gathered include Class Student Number, Sex, Number of Siblings,
Weight, Height, Age of Mother, Usual Daily Allowance in School, Usual Daily Food
Expenditure in School, Usual Number of Text Messages Sent in a Day, Most
Preferred Color, Usual Sleeping Time and Happiness Index for the Day.
• The units of measurement for the information on Number of Siblings, Weight, Height,
Age of Mother, Usual Daily Allowance in School, Usual Daily Food Expenditure in
School, and Usual Number of Text Messages Sent in a Day are person, kilogram,
centimeter, year, pesos, pesos and message, respectively.
3. When? When was the data collected?
• The data was collected on the first few days of classes for Statistics and Probability.
4. Where? Where was the data collected?
• The data was collected inside our classroom.
5. Why? Why was the data collected?
• As explained earlier, the data will be used in our future lessons in Statistics and
Probability
6. HoW? HoW was the data collected?
• The students provided the data by responding to the Student Information Sheet
prepared and distributed by the teacher for the data collection activity.
Once the data are contextualized, there is now meaning to the collection of number and
symbols which may now look like the following which is just a small part of the data
collected in the earlier activity.

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Class
Student
Number
Sex
Number
of
siblings
(in
person)
Weight
(in kg)
Height
(in
cm)
Age of
mother
(in
years)
Usual
daily
allowance
in school
(in pesos)
Usual daily
food
expenditure
in school
(in pesos)
Usual
number
of text
messages
sent in a
day
Most
Preferred
Color
Usual
Sleeping
Time
Happiness
Index for
the Day
1 M 2 60 156 60 200 150 20 RED 23:00 8
2 F 5 63 160 66 300 200 25 PINK 22:00 9
3 F 3 65 165 59 250 50 15 BLUE 20:00 7
4 M 1 55 160 55 200 100 30 BLACK 19:00 6
5 M 0 65 167 45 350 300 35 BLUE 20:00 8
: : : : : : : : : : : :
: : : : : : : : : : : :
KEY POINTS
• Providing correct information in a government data collection activity is a responsibility of
every citizen in the country.
• Data confidentiality is important in a data collection activity.
• Census is collecting data from all possible respondents.
• Data to be collected must be clarified before the actual data collection.
• Data must be contextualized by answering six W-questions.
REFERENCES
Albert, J. R. G. (2008). Basic Statistics for the Tertiary Level (ed. Roberto Padua, Welfredo
and 2nd
to 13th
https://www.khanacademy.org/math/probability/statistical-studies/statistical-
questions/v/statistical-questions
https://www.illustrativemathematics.org/content-standards/tasks/703

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ATTACHMENT A: CLASS LIST
STUDENT NAME
CLASS
STUDENT
NUMBER
STUDENT NAME
CLASS
STUDENT
NUMBER
1. 36.
2, 37.
3. 38.
4. 39.
5. 40.
6. 41.(
7. 42.(
8. 43.(
9. 44.(
10. 45.(
11. 46.(
12. 47.(
13. 48.(
14. 49.(
15. 50.(
16. 51.(
17. 52.(
18. 53.(
19. 54.(
20. 55.(
21. 56.(
22. 57.(
23. 58.(
24. 59.(
25. 60.(
26. 61.(
27. 62.(
28. 63.(
29. 64.(
30. 65.(
31. 66.(
32, 67.(
33. 68.(
34. 69.(
35. 70.(

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ATTACHMENT B: STUDENT INFORMATION SHEET
Instruction to the Students: Please provide completely the following information. Your
teacher is available to respond to your queries regarding the items in this information
sheet, if you have any. Rest assured that the information that you will be providing will
only be used in our lessons in Statistics and Probability.
1. CLASS STUDENT NUMBER: ______________
2. SEX (Put a check mark, √): ____Male __ Female 3. NUMBER OF SIBLINGS: _____
4. WEIGHT (in kilograms): ______________ 5. HEIGHT (in centimeters): ______
6. AGE OF MOTHER (as of her last birthday in years): ________
(If mother deceased, provide age if she was alive)
7. USUAL DAILY ALLOWANCE IN SCHOOL (in pesos): _________________
8. USUAL DAILY FOOD EXPENDITURE IN SCHOOL (in pesos): ___________
9. USUAL NUMBER OF TEXT MESSAGES SENT IN A DAY: ______________
10. MOST PREFERRED COLOR (Put a check mark, √. Choose only one):
____WHITE ____RED ____ PINK ____ ORANGE ____YELLOW ____GREEN
____BLUE ____PEACH ____BROWN ____GRAY ____BLACK ____PURPLE
11. USUAL SLEEPING TIME (on weekdays): ______________
12. HAPPPINESS INDEX FOR THE DAY:
On a scale from 1 (very unhappy) to 10 (very happy), how do you feel today? : ______

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ATTACHMENT C: CLASS RECORDING SHEET (for the Teacher’s Use)
Class
Student
Number
Sex
Number
of
siblings
(in
person)
Weight
(in kg)
Height
(in cm)
Age of
mother
(in
years)
Usual
Daily
allowance
in school
(in pesos)
Usual Daily
food
expenditure
in school
(in pesos)
Usual
number of
text
messages
sent in a
day
Most
Preferred
Color
Usual
Sleeping
Time
Happiness
Index for
the Day

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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 ! 3 ! Page!1"
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Chapter 1:Exploring Data
Lesson 3: Basic Terms in Statistics
OVERVIEW OF LESSON
As continuation of Lesson 2 (where we contextualize data) in this lesson we define basic
terms in statistics as we continue to explore data. These basic terms include the universe,
variable, population and sample. In detail we will discuss other concepts in relation to a
variable.
LEARNING OUTCOME(S): At the end of the lesson, the learner is able to
• Define universe and differentiate it with population; and
• Define and differentiate between qualitative and quantitative variables, and between
discrete and continuous variables (that are quantitative);
LESSON OUTLINE:
1. Recall previous lesson on ‘Contextualizing Data’
2. Definition of Basic Terms in Statistics (universe, variable, population and sample)
3. Broad of Classification of Variables(qualitative and quantitative, discrete and continuous)
A. Recall previous lesson on ‘Contextualizing Data’
Begin by recalling with the students the data they provided in the previous lesson and how
they contextualized such data. You could show them the compiled data set in a table like this:
Class
Student
Number
Sex
Number
of
siblings
(in
person)
Weight
(in kg)
Height
(in
cm)
Age of
mother
(in
years)
Usual
Daily
allowance
in school
(in pesos)
Usual Daily
food
expenditure
in school
(in pesos)
Usual
number
of text
messages
sent in a
day
Most
Preferred
Color
Usual
Sleeping
Time
Happiness
Index for
the Day
1 M 2 60 156 60 200 150 20 RED 23:00 8
2 F 5 63 160 66 300 200 25 PINK 22:00 9
3 F 3 65 165 59 250 50 15 BLUE 20:00 7
4 M 1 55 160 55 200 100 30 BLACK 19:00 6
5 M 0 65 167 45 350 300 35 BLUE 20:00 8
: : : : : : : : : : : :
: : : : : : : : : : : :

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Recall also their response on the first Ws of the data, that is, on the question “Who provided
the data?” We said last time the students of the class provided the data or the data were taken
from the students.
Another Ws of the data is What? What are the information from the respondents? and What
is the unit of measurement used for each of the information (if there are any)? Our responses
are the following:
• The information gathered include Class Student Number, Sex, Number of Siblings,
Weight, Height, Age of Mother, Usual Daily Allowance in School, Usual Daily Food
Expenditure in School, Usual Number of Text Messages Sent in a Day, Most
Preferred Color, Usual Sleeping Time and Happiness Index.
• The units of measurement for the information on Number of Siblings, Weight, Height,
Age of Mother, Usual Daily Allowance in School, Usual Daily Food Expenditure in
School, and Usual Number of Text Messages Sent in a Day are person, kilogram,
centimeter, year, pesos, pesos and message, respectively.
B. Main Lesson
1. Definition of Basic Terms
The collection of respondents from whom one obtain the data is called the universe of the
study. In our illustration, the set of students of this Statistics and Probability class is our
universe. But we must precaution the students that a universe is not necessarily composed of
people. Since there are studies where the observations were taken from plants or animals or
even from non-living things like buildings, vehicles, farms, etc. So formally, we define
universe as the collection or set of units or entities from whom we got the data. Thus, this
set of units answers the first Ws of data contextualization.
On the other hand, the information we asked from the students are referred to as the variables
of the study and in the data collection activity, we have 12 variables including Class Student
Number. A variable is a characteristic that is observable or measurable in every unit of the
universe. From each student of the class, we got the his/her age, number of siblings, weight,
height, age of mother, usual daily allowance in school, usual daily food expenditure in
school, usual number of text messages sent in a day, most preferred color, usual sleeping time
and happiness index for the day. Since these characteristics are observable in each and every
student of the class, then these are referred to as variables.
The set of all possible values of a variable is referred to as a population. Thus for each
variable we observed, we have a population of values. The number of population in a study
will be equal to the number of variables observed. In the data collection activity we had, there
are 12 populations corresponding to 12 variables.
A subgroup of a universe or of a population is a sample. There are several ways to take a
sample from a universe or a population and the way we draw the sample dictates the kind of
analysis we do with our data.

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We can further visualize these terms in the following figure:
VARIABLE 1 VARIABLE 2 VARIABLE 12
UNIVERSE POPULATION
OF VARIABLE 1
POPULATION
OF VARIABLE 2
POPULATION OF
VARIABLE 12
2. Broad Classification of Variables
Following up with the concept of variable, inform the students that usually, a variable takes
on several values. But occasionally, a variable can only assume one value, then it is called a
constant. For instance, in a class of fifteen-year olds, the age in years of students is constant.
Variables can be broadly classified as either quantitative or qualitative, with the latter further
classified into discrete and continuous types (see Figure 3.3 below).
Unit!1!
Unit!2!
Unit!3!
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Unit!N!
Value!1!
Value!2!
Value!3!
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Value!N!
Value!1!
Value!2!
Value!3!
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Value!N!
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Value!1!
Value!2!
Value!3!
:!
:!
Value!N!
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OR!
Unit!1!
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:!
Unit!n!
Value!1!
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Value!n!
SAMPLE
Figure 3.3 Broad Classification of Variables
A SAMPLE OF UNITS A SAMPLE OF
POPULATION VALUES
Figure 3.1 Visualization of the relationship among universe, variable, population and sample.

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(i) Qualitative variables express a categorical attribute, such as sex (male or female),
religion, marital status, region of residence, highest educational attainment. Qualitative
variables do not strictly take on numeric values (although we can have numeric codes for
them, e.g., for sex variable, 1 and 2 may refer to male, and female, respectively).
Qualitative data answer questions “what kind.” Sometimes, there is a sense of ordering in
qualitative data, e.g., income data grouped into high, middle and low-income status. Data
on sex or religion do not have the sense of ordering, as there is no such thing as a weaker
or stronger sex, and a better or worse religion. Qualitative variables are sometimes
referred to as categorical variables.
(ii) Quantitative (otherwise called numerical) data, whose sizes are meaningful, answer
questions such as “how much” or “how many”. Quantitative variables have actual units of
measure. Examples of quantitative variables include the height, weight, number of
registered cars, household size, and total household expenditures/income of survey
respondents. Quantitative data may be further classified into:
a. Discrete data are those data that can be counted, e.g., the number of days for
cellphones to fail, the ages of survey respondents measured to the nearest year, and
the number of patients in a hospital. These data assume only (a finite or infinitely)
countable number of values.
b. Continuous data are those that can be measured, e.g. the exact height of a survey
respondent and the exact volume of some liquid substance. The possible values are
uncountably infinite.
With this classification, let us then test the understanding of our students by asking them to
classify the variables, we had in our last data gathering activity. They should be able to
classify these variables as to qualitative or quantitative and further more as to discrete or
continuous. If they did it right, you have the following:
VARIABLE
TYPE OF
VARIABLE
TYPE OF
QUANTITATIVE
VARIABLE
Class Student Number Qualitative
Sex Qualitative
Number of Siblings Quantitative Discrete
Weight (in kilograms) Quantitative Continuous
Height (in centimeters) Quantitative Continuous
Age of Mother Quantitative Discrete
Usual Daily Allowance in School (in
pesos)
Quantitative
Discrete
Usual Daily Food Expenditure in School
(in pesos)
Quantitative
Discrete
Usual Number of Text Messages Sent in
a Day
Quantitative
Discrete
Usual Sleeping Time Qualitative
Most Preferred Color Qualitative
Happiness Index for the Day Qualitative

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Special Note:
For quantitative data, arithmetical operations have some physical interpretation. One can add
301 and 302 if these have quantitative meanings, but if, these numbers refer to room
numbers, then adding these numbers does not make any sense. Even though a variable may
take numerical values, it does not make the corresponding variable quantitative! The issue is
whether performing arithmetical operations on these data would make any sense. It would
certainly not make sense to sum two zip codes or multiply two room numbers.
KEY POINTS
• A universe is a collection of units from which the data were gathered.
• A variable is a characteristic we observed or measured from every element of the
universe.
• A population is a set of all possible values of a variable.
• A sample is a subgroup of a universe or a population.
• In a study there is only one universe but could have several populations.
• Variables could be classified as qualitative or quantitative, and the latter could be further
classified as discrete or continuous.
REFERENCES
Albert, J. R. G. (2008). Basic Statistics for the Tertiary Level (ed. Roberto Padua,
WelfredoPatungan, Nelia Marquez), published by Rex Bookstore.
and 2nd
Takahashi, S. (2009). The Manga Guide to Statistics. Trend-Pro Co. Ltd.
to 13th

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ASSESSMENT
1. A market researcher company requested all teachers of a particular school to fill up a
questionnaire in relation to their product market study. The following are some of the
information supplied by the teachers:
• highest educational attainment
• predominant hair color
• body temperature
• civil status
• brand of laundry soap being used
• total household expenditures last month in pesos
• number of children in the household
• number of hours standing in queue while waiting to be served by a bank teller
• amount spent on rice last week by the household
• distance travelled by the teacher in going to school
• time (in hours) consumed on Facebook on a particular day
a. If we are to consider the collection of information gathered through the completed
questionnaire, what is the universe for this data set? (The universe is the set of all
teachers in that school)
b. Which of the variables are qualitative? Which are quantitative? Among the quantitative
variables, classify them further as discrete or continuous.
• highest educational attainment (qualitative)
• predominant hair color (qualitative)
• body temperature (quantitative: continuous)
• civil status (qualitative)
• brand of laundry soap being used (qualitative)
• total household expenditures last month in pesos (quantitative: discrete)
• number of children in a household (quantitative: discrete)
• number of hours standing in queue while waiting to be served by a bank teller
(quantitative: discrete)
• amount spent on rice last week by a household (quantitative: discrete)
• distance travelled by the teacher in going to school (quantitative: continuous)
• time (in hours) consumed on Facebook on a particular day(quantitative: continuous)
c. Give at least two populations that could be observed from the variables identified in (b).
(Possible answer: The population is the set of all values of the highest educational
attainment and another population is {single, married, divorced, separated,
widow/widower})
2. The Engineering Department of a big city did a listing of all buildings in their locality. If
you are planning to gather the characteristics of these buildings,
a. what is the universe of this data collection activity? (Set of all buildings in the big city)
b. what are the crucial variables to observe? It would also be better if you could classify the
variables as to whether it is qualitative or quantitative. Furthermore, classify the
quantitative variable as discrete or continuous. (A possible answer is the number of
floors in the building, quantitative, discrete)

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3. A survey of students in a certain school is conducted. The survey questionnaire details
the information on the following variables. For each of these variables, identify whether
the variable is qualitative or quantitative, and if the latter, state whether it is discrete or
continuous.
a. number of family members who are working (quantitative: discrete)
b. ownership of a cell phone among family members (qualitative)
c. length (in minutes) of longest call made on each cell phone owned per month
(quantitative: continuous)
d. ownership/rental of dwelling (qualitative)
e. amount spent in pesos on food in one week (quantitative: discrete)
f. occupation of household head (qualitative)
g. total family income (quantitative: discrete)
h. number of years of schooling of each family member (quantitative: discrete)
i. access of family members to social media (qualitative)
j. amount of time last week spent by each family member using the internet
(quantitative: continuous)
Explanatory Note:
• Teachers have the option to just ask this assessment orally to the entire class, or to group
students and ask them to identify answers, or to give this as homework, or to use some
questions/items here for a chapter examination.

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Lesson 4: Levels of Measurement
OVERVIEW OF LESSON
In this lesson we discuss the different levels of measurement as we continue to explore data.
Knowing such will enable us to plan the data collection process we need to employ in order
to gather the appropriate data for analysis.
LEARNING OUTCOME(S): At the end of the lesson, the learner is able to identify and
differentiate the different levels of measurement and methods of data collection
LESSON OUTLINE:
1. Motivational Activity
2. Levels of Measurement
3. Data Collection Methods
A. Motivational Activity
Ask the students first if they believe the following statement:
“Students who eat a healthy breakfast will do best on a quiz, students who eat an unhealthy
breakfast will get an average performance, and students who do not eat anything for
breakfast will do the worst on a quiz”
You could further ask one or more students who have different answers to defend their
answers. Then challenge the students to apply a statistical process to investigate on the
validity of this statement. You could enumerate on the board the steps in the process to
undertake like the following:
1. Plan or design the collection of data to verify the validity of the statement in a way that
maximizes information content and minimizes bias;
2. Collect the data as required in the plan;
3. Verify the quality of the data after it was collected;
4. Summarize the information extracted from the data; and
5. Examine the summary statistics so that insight and meaningful information can be
produced to support your decision whether to believe or not the given statement.

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Let us discuss in detail the first step. In planning or designing the data collection activity, we
could consider the set of all the students in the class as our universe. Then let us identify the
variables we need to observe or measure to verify the validity of the statement. You may ask
the students to participate in the discussion by asking them to identify a question to get the
needed data. The following are some possible suggested queries:
1. Do you usually have a breakfast before going to school?
(Note: This is answerable by Yes or No)
2. What do you usually have for breakfast?
(Note: Possible responses for this question are rice, bread, banana, oatmeal, cereal, etc)
The responses in Questions Numbers 1 and 2 could lead us to identify whether a student in
the class had a healthy breakfast, an unhealthy breakfast or no breakfast at all.
Furthermore, there is a need to determine the performance of the student in a quiz on that
day. The score in the quiz could be used to identify the student’s performance as best,
average or worst.
As we describe the data collection process to verify the validity of the statement, there is also
a need to include the levels of measurement for the variables of interest.
B. Main Lesson:
1. Levels of Measurement
Inform students that there are four levels of measurement of variables: nominal, ordinal,
interval and ratio. These are hierarchical in nature and are described as follows:
Nominal level of measurement arises when we have variables that are categorical and non-
numeric or where the numbers have no sense of ordering. As an example, consider the
numbers on the uniforms of basketball players. Is the player wearing a number 7 a worse
player than the player wearing number 10? Maybe, or maybe not, but the number on the
uniform does not have anything to do with their performance. The numbers on the uniform
merely help identify the basketball player. Other examples of the variables measured at the
nominal level include sex, marital status, religious affiliation. For the study on the validity of
the statement regarding effect of breakfast on school performance, students who responded
Yes to Question Number 1 can be coded 1 while those who responded No, code 0 can be
assigned. The numbers used are simply for numerical codes, and cannot be used for ordering
and any mathematical computation.
Ordinal level also deals with categorical variables like the nominal level, but in this level
ordering is important, that is the values of the variable could be ranked. For the study on the
validity of the statement regarding effect of breakfast on school performance, students who
had healthy breakfast can be coded 1, those who had unhealthy breakfast as 2 while those
who had no breakfast at all as 3. Using the codes the responses could be ranked. Thus, the
students who had a healthy breakfast are ranked first while those who had no breakfast at all
are ranked last in terms of having a healthy breakfast. The numerical codes here have a
meaningful sense of ordering, unlike basketball player uniforms, the numerical codes suggest
that one student is having a healthier breakfast than another student. Other examples of the
ordinal scale include socio economic status (A to E, where A is wealthy, E is poor), difficulty

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of questions in an exam (easy, medium difficult), rank in a contest (first place, second place,
etc.), and perceptions in Likert scales.
Note to Teacher: Let us also emphasize to the students that while there is a sense or ordering,
there is no zero point in an ordinal scale. In addition, there is no way to find out how much
“distance” there is between one category and another. In a scale from 1 to 10, the difference
between 7 and 8 may not be the same difference between 1 and 2.
Interval level tells us that one unit differs by a certain amount of degree from another unit.
Knowing how much one unit differs from another is an additional property of the interval
level on top of having the properties posses by the ordinal level. When measuring
temperature in Celsius, a 10 degree difference has the same meaning anywhere along the
scale – the difference between 10 and 20 degree Celsius is the same as between 80 and 90
centigrade. But, we cannot say that 80 degrees Celsius is twice as hot as 40 degrees Celsius
since there is no true zero, but only an arbitrary zero point. A measurement of 0 degrees
Celsius does not reflect a true "lack of temperature." Thus, Celsius scale is in interval level.
Other example of a variable measure at the interval is the Intelligence Quotient (IQ) of a
person. We can tell not only which person ranks higher in IQ but also how much higher he or
she ranks with another, but zero IQ does not mean no intelligence. The students could also be
classified or categorized according to their IQ level. Hence, the IQ as measured in the
interval level has also the properties of those measured in the ordinal as well as those in the
nominal level.
Special Note: Inform also the students that the interval level allows addition and subtraction
operations, but it does not possess an absolute zero. Zero is arbitrary as it does not mean the
value does not exist. Zero only represents an additional measurement point.
Ratio level also tells us that one unit has so many times as much of the property as does
another unit. The ratio level possesses a meaningful (unique and non-arbitrary) absolute,
fixed zero point and allows all arithmetic operations. The existence of the zero point is the
only difference between ratio and interval level of measurement. Examples of the ratio scale
include mass, heights, weights, energy and electric charge. With mass as an example, the
difference between 120 grams and 135 grams is 15 grams, and this is the same difference
between 380 grams and 395 grams. The level at any given point is constant, and a
measurement of 0 reflects a complete lack of mass. Amount of money is also at the ratio
level. We can say that 2000 pesos is twice more than 1,000 pesos. In addition, money has a
true zero point: if you have zero money, this implies the absence of money. For the study on
the validity of the statement regarding effect of breakfast on school performance, the
student’s score in the quiz is measured at the ratio level. A score of zero implies that the
student did not get a correct answer at all.
In summary, we have the following levels of measurement:
Level Property Basic Empirical Operation
Nominal No order, distance, or origin Determination of equivalence
Ordinal
Has order but no distance or
unique origin
Determination of greater or lesser values
Interval
Both with order and distance but
no unique origin
Determination of equality of intervals or
difference
Ratio
Has order, distance and unique
origin
Determination of equality of ratios or
means

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The levels of measurement depend mainly on the method of measurement, not on the
property measured. The weight of primary school students measured in kilograms has a ratio
level, but the students can be categorized into overweight, normal, underweight, and in which
case, the weight is then measured in an ordinal level. Also, many levels are only interval
because their zero point is arbitrarily chosen.
To assess the students understanding of the lesson, you may go back to the set of variables in
the data gathering activity done in Lesson 2. You could ask the students to identify the level
of measurement for each of the variable. If they did it right, you have the following:
VARIABLE LEVEL OF MEASUREMENT
Class Student Number Nominal
Sex Nominal
Number of Siblings Ratio
Weight (in kilograms) Ratio
Height (in centimeters) Ratio
Age of Mother Ratio
Usual Daily Allowance in School (in pesos) Ratio
Usual Daily Food Expenditure in School (in pesos) Ratio
Usual Number of Text Messages Sent in a Day Ratio
Usual Sleeping Time Nominal
Most Preferred Color Nominal
Happiness Index for the Day Ordinal
2. Methods of Data Collection
Variables were observed or measured using any of the three methods of data collection,
namely: objective, subjective and use of existing records. The objective and subjective
methods obtained the data directly from the source. The former uses any or combination of
the five senses (sense of sight, touch, hearing, taste and smell) to measure the variable while
the latter obtains data by getting responses through a questionnaire. The resulting data from
these two methods of data collection is referred to as primary data. The data gathered in
Lesson 2 are primary data and were obtained using the subjective method.
On the other hand, secondary data are obtained through the use of existing records or data
collected by other entities for certain purposes. For example, when we use data gathered by
the Philippine Statistics Authority, we are using secondary data and the method we employ to
get the data is the use of existing records. Other data sources include administrative records,
news articles, internet, and the like. However, we must emphasize to the students that when
we use existing data we must be confident of the quality of the data we are using by knowing
how the data were gathered. Also, we must remember to request permission and acknowledge
the source of the data when using data gathered by other agency or people.

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KEY POINTS
• Four levels of measurement: Nominal, Ordinal, Interval and Ratio
• Knowing what level the variable was measured or observed will guide us to know the
type of analysis to apply.
• Three methods of data collection include objective, subjective and use of existing records.
• Using the data collection method as basis, data can be classified as either primary or
secondary data.
REFERENCES
and 2nd
to 13th

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ASSESSMENT
1. Using the data of the teachers in a particular school gathered by a market researcher
company, identify the level of measurement for each of the following variable.
• highest educational attainment (ordinal)
• predominant hair color (nominal)
• body temperature (interval)
• civil status (nominal)
• brand of laundry soap being used (nominal)
• total household expenditures last month in pesos (ratio)
• number of children in a household (ratio)
• number of hours standing in queue while waiting to be served by a bank teller (ratio)
• amount spent on rice last week by a household (ratio)
• distance travelled by the teacher in going to school (ratio)
• time (in hours) consumed on Facebook on a particular day (ratio)
2. The following variables are included in a survey conducted among students in a certain
school. Identify the level of measurement for each of the variables.
a. number of family members who are working (ratio);
b. ownership of a cell phone among family members (nominal);
c. length (in minutes) of longest call made on each cell phone owned per month (ratio);
d. ownership/rental of dwelling (nominal);
e. amount spent in pesos on food in one week (ratio);
f. occupation of household head (nominal);
g. total family income (ratio);
h. number of years of schooling of each family member (ratio);
i. access of family members to social media (nominal);
j. amount of time last week spent by each family member using the internet (ratio)
3. In the following, identify the data collection method used and the type of resulting data.
a. The website of Philippine Airlines provides a questionnaire instrument that can be
answered electronically. (subjective method, primary data)
b. The latest series of the Consumer Price Index (CPI) generated by the Philippine
Statistics Authority was downloaded from PSA website. (use of existing record,
secondary data)
c. A reporter recorded the number of minutes to travel from one end to another of the
Metro Manila Rail Transit (MRT) during peak and off-peak hours. (objective
method, primary data)
d. Students getting the height of the plants using a meter stick. (objective method,
primary data)
e. PSA enumerator conducting the Labor Force Survey goes around the country to
interview household head on employment-related variables. (subjective method,
primary data)

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Lesson 5: Data Presentation
OVERVIEW OF LESSON
In this lesson we enrich what the students have already learned from Grade 1 to 10 about
presenting data. Additional concepts could help the students to appropriately describe further
the data set.
LEARNING OUTCOME(S): At the end of the lesson, the learner is able to identify and
use the appropriate method of presenting information from a data set effectively.
LESSON OUTLINE:
1. Review of Lessons in Data Presentation taken up from Grade 1 to 10.
2. Methods of Data Presentation
3. The Frequency Distribution Table and Histogram
A. Review of Lessons in Data Presentation taken up from Grade 1 to 10.
You could assist the students to recall what they have learned in Grade 1 to 10 regarding data
presentation by asking them to participate in an activity. The activity is called ‘Toss the Ball’.
This is actually a review and wake-up exercise. Toss a ball to a student and he/she will give
the most important concept he/she learned about data presentation.
You may list on the board their responses. You could summarize their responses to be able to
establish what they already know about data presentation techniques and from this you could
build other concepts on the topic. A suggestion is to classify their answers according to the
three methods of data presentation, i.e. textual, tabular and graphical. A possible listing will
be something like this:
Textual or Narrative Presentation:
• Detailed information are given in textual presentation
• Narrative report is a way to present data.
Tabular Presentation:
• Numerical values are presented using tables.
• Information are lost in tabular presentation of data.
• Frequency distribution table is also applicable for qualitative variables

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Graphical Presentation:
• Trends are easily seen in graphs compared to tables.
• It is good to present data using pictures or figures like the pictograph.
• Pie charts are used to present data as part of one whole.
• Line graphs are for time-series data.
• It is better to present data using graphs than tables as they are much better to look at.
B. Main Lesson
1. Methods of Data Presentation
You could inform the students that in general there are three methods to present data. Two or
all of these three methods could be used at the same time to present appropriately the
information from the data set. These methods include the (1) textual or narrative; (2) tabular;
and (3) graphical method of presentation.
In presenting the data in textual or paragraph or narrative form, one describes the data by
enumerating some of the highlights of the data set like giving the highest, lowest or the
average values. In case there are only few observations, say less than ten observations, the
values could be enumerated if there is a need to do so. An example of which is shown below:
The country’s poverty incidence among families as reported by the Philippine
Statistics Authority (PSA), the agency mandated to release official poverty
statistics, decreases from 21% in 2006 down to 19.7% in 2012. For 2012, the
regional estimates released by PSA indicate that the Autonomous Region of Muslim
Mindanao (ARMM) is the poorest region with poverty incidence among families
estimated at 48.7%. The region with the smallest estimated poverty incidence
among families at 2.6% is the National Capital Region (NCR).
Data could also be summarized or presented using tables. The tabular method of presentation
is applicable for large data sets. Trends could easily be seen in this kind of presentation.
However, there is a loss of information when using such kind of presentation. The frequency
distribution table is the usual tabular form of presenting the distribution of the data. The
following are the common parts of a statistical table:
a. Table title includes the number and a short description of what is found inside the table.
b. Column header provides the label of what is being presented in a column.
c. Row header provides the label of what is being presented in a row.
d. Body are the information in the cell intersecting the row and the column.
In general, a table should have at least three rows and/or three columns. However, too many
information to convey in a table is also not advisable. Tables are usually used in written
technical reports and in oral presentation. Table 5.1 is an example of presenting data in
tabular form. This example was taken from 2015 Philippine Statistics in Brief, a regular
publication of the PSA which is also the basis for the example of the textual presentation
given above.

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Table 5.1 Regional estimates of poverty incidence among families based on
the Family Income and Expenditures Survey conducted on the
same year of reporting.
Region 2006 2009 2012
NCR 2.9 2.4 2.6
CAR 21.1 19.2 17.5
I 19.9 16.8 14.0
II 21.7 20.2 17.0
III 10.3 10.7 10.1
IV A 7.8 8.8 8.3
IV B 32.4 27.2 23.6
V 35.4 35.3 32.3
VI 22.7 23.6 22.8
VII 30.7 26.0 25.7
VIII 33.7 34.5 37.4
IX 40.0 39.5 33.7
X 32.1 33.3 32.8
XI 25.4 25.5 25.0
XII 31.2 30.8 37.1
Caraga 41.7 46.0 31.9
ARMM 40.5 39.9 48.7
Graphical presentation on the other hand, is a visual presentation of the data. Graphs are
commonly used in oral presentation. There are several forms of graphs to use like the pie
chart, pictograph, bar graph, line graph, histogram and box-plot. Which form to use depends
on what information is to be relayed. For example, trends across time are easily seen using a
line graph. However, values of variables in nominal or ordinal levels of measurement should
not be presented using line graph. Rather a bar graph is more appropriate to use. A graphical
presentation in the form of vertical bar graph of the 2012 regional estimates of poverty
incidence among families is shown below:
Figure 5.1 2012 Regional poverty incidence among families (2012 FIES).
0!
10!
20!
30!
40!
50!
60!
NCR!
CAR!
I!
II!
III!
IV!A!
IV!B!
V!
VI!
VII!
VIII!
IX!
X!
XI!
XII!
Caraga!
ARMM!
Poverty"Incidence"Among"
Families"in"Percent"

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Other examples of graphical presentations that are shown below are lifted from the Handbook
of Statistics 1 (listed in the reference section at the end of this Teaching Guide).
Figure 5.2. Percentage distribution of dogs according to groupings identified in a dog show.
Figure 5.3. Distribution of fruits sales of a store for two days.
Figure 5.4 Weapons arrest rate from 1965 to 1992 by age of offender.

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Figure 5.5. Height and weight of STAT 1 students registered during the previous term.
2. The Frequency Distribution Table and Histogram
A special type of tabular and graphical presentation is the frequency distribution table (FDT)
and its corresponding histogram. Specifically, these are used to depict the distribution of the
data. Most of the time, these are used in technical reports. An FDT is a presentation
containing non-overlapping categories or classes of a variable and the frequencies or counts
of the observations falling into the categories or classes. There are two types of FDT
according to the type of data being organized: a qualitative FDT or a quantitative FDT. For a
qualitative FDT, the non-overlapping categories of the variable are identified, and
frequencies, as well as the percentages of observations falling into the categories, are
computed. On the other hand, for a quantitative FDT, there are also of two types: ungrouped
and grouped. Ungrouped FDT is constructed when there are only a few observations or if the
data set contains only few possible values. On the other hand, grouped FDT is constructed
when there is a large number of observations and when the data set involves many possible
values. The distinct values are grouped into class intervals. The creation of columns for a
grouped FDT follows a set of guidelines. One such procedure is described in the following
steps, which is lifted from the Workbook in Statistics 1 (listed in the reference section at the
end of this Teaching Guide)
Steps in the construction of a grouped FDT
1. Identify the largest data value or the maximum (MAX) and smallest data value or the minimum
(MIN) from the data set and compute the range, R. The range is the difference between the largest
and smallest value, i.e. R = MAX – MIN.
2. Determine the number of classes, k using k N= , where N is the total number of observations in
the data set. Round-off k to the nearest whole number. It should be noted that the computed k
might not be equal to the actual number of classes constructed in an FDT.
3. Calculate the class size, c, using c = R/k. Round off c to the nearest value with precision the same
as that with the raw data.
30
40
50
60
70
80
110 130 150 170 190
weightinkg
height in cm

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4. Construct the classes or the class intervals. A class interval is defined by a lower limit (LL) and an
upper limit (UL). The LL of the lowest class is usually the MIN of the data set. The LL’s of the
succeeding classes are then obtained by adding c to the LL of the preceding classes. The UL of the
lowest class is obtained by subtracting one unit of measure
1
10x
! "
# $
% &
, where x is the maximum
number of decimal places observed from the raw data) from the LL of the next class. The UL’s of
the succeeding classes are then obtained by adding c to the UL of the preceding classes. The
lowest class should contain the MIN, while the highest class should contain the MAX.
5. Tally the data into the classes constructed in Step 4 to obtain the frequency of each class. Each
observation must fall in one and only one class.
!
6. Add (if needed) the following distributional characteristics:
a. True Class Boundaries (TCB). The TCBs reflect the continuous property of a continuous data.
It is defined by a lower TCB (LTCB) and an upper TCB (UTCB). These are obtained by taking
the midpoints of the gaps between classes or by using the following formulas: LTCB = LL –
0.5(one unit of measure) and UTCB = UL + 0.5(one unit of measure).
b. Class Mark (CM). The CM is the midpoint of a class and is obtained by taking the average of
the lower and upper TCB’s, i.e. CM = (LTCB + UTCB)/2.
c. Relative Frequency (RF). The RF refers to the frequency of the class as a fraction of the total
frequency, i.e. RF = frequency/N. RF can be computed for both qualitative and quantitative
data. RF can also be expressed in percent.
d. Cumulative Frequency (CF). The CF refers to the total number of observations greater than or
equal to the LL of the class (>CF) or the total number of observations less than or equal to the
UL of the class (<CF).
e. Relative Cumulative Frequency (RCF). RCF refers to the fraction of the total number of
observations greater than or equal to the LL of the class (>RCF) or the fraction of the total
number of observations less than or equal to the UL of the class (<RCF). Both the <RCF and
>RCF can also be expressed in percent.
The histogram is a graphical presentation of the frequency distribution table in the form of a
vertical bar graph. There are several forms of the histogram and the most common form has
the frequency on its vertical axis while the true class boundaries in the horizontal axis.
As an example, the FDT and its corresponding histogram of the 2012 estimated poverty
incidences of 144 municipalities and cities of Region VIII are shown below.
Poverty Incidence
(%)
Frequency
00.000 - 20.015 3
20.015 - 40.015 59
40.015 - 60.015 78
60.015 - 80.015 4
80.015 - 100.00 0 0!
20!
40!
60!
80!
3!
59!
78!
4! 0!
Frequency"
True"Class"Boundaries"

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KEY POINTS
• Three methods of data presentation: textual, tabular and graphical
• Two or all the methods could be combined to fully describe the data at hand.
• Distribution of data is presented using frequency distribution table and histogram.
REFERENCES
and 2nd
to 13th

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ASSESSMENT
Note: This exercise and its corresponding possible answers were lifted from Workbook in
Statistics 1 (listed in the reference section)
A. You are to describe the data on the following table. Perform what is being asked for in the
questions found after the table.
!!!!Table!5.2!!Characteristics!of!the!30!members!of!the!Batong!Malake!Senior!Citizens!Association!
(BMSCA)!who!participated!in!their!2009!LakbayFAral.!
No. Gender
Age as of Last
Birthday
Receiving
Monthly
Pension?
(Y/N)
Gross Monthly
Family Income
(in thousand pesos)
Number of Years as
Member
1 Female 61 Yes 45.0 1
3 Male 74 No 33.5 10
4 Male 80 No 50.0 12
7 Female 75 No 41.0 2
8 Male 64 No 10.1 3
9 Male 65 No 46.5 5
10 Female 68 Yes 18.0 3
11 Female 71 Yes 34.2 6
12 Female 63 Yes 73.1 2
13 Female 72 Yes 15.6 11
14 Male 76 Yes 17.4 11
15 Female 69 No 33.8 8
16 Male 70 Yes 35.1 9
17 Male 74 Yes 18.6 6
18 Female 68 Yes 65.7 8
19 Female 70 No 19.6 3
20 Male 65 Yes 53.0 2
21 Male 64 Yes 18.4 1
22 Female 62 Yes 27.8 1
23 Female 63 No 33.4 2
24 Male 68 No 38.0 5
25 Male 67 Yes 37.6 5
26 Male 69 No 50.4 7
27 Female 68 Yes 44.3 4
28 Female 66 No 36.7 3
29 Female 63 No 18.0 2
30 Male 64 Yes 63.2 2
!

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1. Choose a QUANTITATIVE variable from the given data set. Construct a quantitative
grouped FDT for this variable. Show preliminary computations (R, k, and c). Also,
construct a histogram for the data. Use appropriate labels and titles for the table and
graph. Describe the characteristics of the units in the data set using a brief narrative
report. Refer to the FDT and histogram constructed.
R = ____________________ k = ____________________ c = ________________
Table ______________________________________________________________________
Classes Frequency
(F)
RF
(%)
CF RCF (%)
CM
TCB
LL UL < CF > CF < RCF > RCF LTCB UTCB
Histogram:
Textual presentation:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Which of the three methods of data presentation do you think is most appropriate to use
for the variable chosen in Number 1? Justify your answer.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________

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2. Choose a QUALITATIVE variable from Table 5.2 Construct an appropriate graph. Use
labels and a title for the graph.
Give a brief report describing the variable:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Possible Answers:
1. For the quantitative variable gross monthly family income:
R = 73.1 – 10.1 = 63 k = 30 5.477 ~ 5= c = 63/5 = 12.6
Table 1. Distribution of the gross monthly family income (in thousand pesos) of the 30
Batong Malake Senior Citizens Association members who joined the Lakbay-Aral.
Classes Frequency
(F)
RF
(%)
CF RCF (%)
CM
TCB
LL UL < CF > CF < RCF > RCF LTCB UTCB
10.1 22.6 9 30.00 9 30 30.00 100.00 16.35 10.05 22.65
22.7 35.2 8 26.67 17 21 56.67 70.00 28.95 22.65 35.25
35.3 47.8 7 23.33 24 13 80.00 43.33 41.55 35.25 47.85
47.9 60.4 3 10.00 27 6 90.00 20.00 54.15 47.85 60.45
60.5 73.0 2 6.67 29 3 96.67 10.00 66.75 60.45 73.05
73.1 85.6 1 3.33 30 1 100.00 3.33 79.35 73.05 85.65
Histogram:
!
Figure 1. Monthly gross family income (in thousand pesos) of the 30 BMSCA members.
0!
2!
4!
6!
8!
10!
1! 2! 3! 4! 5! 6!
Frequency"
TCB"
10.05!!!!!!!!!!!!!!!22.65!!!!!!!!!!!!!!!!35.25!!!!!!!!!!!!!!!!47.85!!!!!!!!!!!!!!!!!60.45!!!!!!!!!!!!!!!!73.05!!!!!!!!!!!!!!!!!
85.65!

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Textual presentation:
(Sample) The monthly gross family income of the 30 BMSCA members range from 10.1 to
73.1 thousand pesos. More than half of them have income of at most 35,250 pesos. Only three
of them, or 10%, have monthly family income of at least 60,450 pesos.
Which of the three methods of data presentation do you think is most appropriate to use for
the variable chosen in Number 1? Justify your answer.
(Sample)
Textual presentation: It is most appropriate to use a textual presentation since the highlights
of the family income of the BMSCA members can be presented.
Tabular presentation: It is most appropriate to use a tabular presentation since a lot of the
numerical information can be presented and trends in the monthly income of the members
can be seen.
Graphical presentation: A graphical presentation is most appropriate so that trends in the
monthly income of the BMSCA are easily visible.
2. For the qualitative variable: gender
!
! Figure 2. Distribution of the 30 BMSCA members by gender.
! !
Brief Description: Majority of the 30 BMSCA who joined the Lakbay-Aral are males.
Only 43% are females.
For the qualitative variable: whether member is receiving monthly pension or not
!
Figure 2. Distribution of the 30 BMSCA members as to whether
they are receiving monthly pension or not.
Brief Description: More than half of the 30 BMSCA members receive monthly pension.
Forty percent are not receiving monthly pension.

STATISTICS AND PROBABILITY (TEACHING GUIDE)

STATISTICS AND PROBABILITY (TEACHING GUIDE)

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