Republic of the Philippines

Department of Education
Regional Office IX, Zamboanga Peninsula

10 Zest for Progress

Z Peal of artnership

4th QUARTER – Module 7:

FORMULATE STATISTICAL MINI-RESEARCH

Name of Learner: ___________________________

Grade & Section: ___________________________
Name of School: ___________________________
Mathematics – Grade 10
Alternative Delivery Mode
Quarter 4 - Module 7: Formulate Statistical Mini-Research
First Edition, 2020
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Published by the Department of Education

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Undersecretary: Diosdado M. San Antonio

Development Team of the Module

Writer: Ciara Mae P. Jamorol
Editors: Rosemary B. Garcia
Elizabeth M. Raciles, Ed.D.
Layout Artist: Zandro G. Sepe, M.S.
Reviewers: EPS, Mathematics Vilma A. Brown, Ed.D.
Principal Zandro G. Sepe, M.S.
Management Team: SDS Roy C. Tuballa, EMD, JD, CESO VI
ASDS Jay S. Montealto, CESO VI
ASDS Norma T. Francisco, Ed.D.,CESE
EPS Mathematics Vilma A. Brown, Ed.D.
EPS LRMS Aida F. Coyme, Ed.D.

Printed in the Philippines

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Office Address: Tiguma, Airport Road, Pagadian City
Telefax: (062) – 215 – 3751; 991 – 5975
E-mail Address: region9@deped.gov.ph

1
Introductory Message
This Self – Learning Module (SLM) is prepared so that you, our dear learners, can continue
your studies and learn while at home. Activities, questions, directions, exercises, and
discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you
discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell
you if you can proceed on completing this module or if you need to ask your facilitator or your
teacher’s assistance for better understanding of the lesson. At the end of each module, you
need to answer the post-test to self-check your learning. Answer keys are provided for each
activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our
facilitators and parents for strategies and reminders on how they can best help you on your
home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use
a separate sheet of paper in answering the exercises and tests. Read the instructions carefully
before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this
module, do not hesitate to consult your teacher or facilitator.
Thank you.

What I Need to Know

While measures of central tendency, dispersion, and skewness are used often
in statistics and statistical research, there are other methods of characterizing or
describing data distributions or portions that are commonly used as well – these are
called the measures of position.

Measures of position are a method by which the position that a particular data
value has within a given data set can be identified. With this, data analysis for
statistical mini-research and other statistical application relative to the position of
certain values (e.g. academic ranking) can be achieved.

After going through the module, you are expected to:

• Formulate statistical mini- research (M10SP-Iv-f-g-1).

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 What I Know
Directions: Choose the letter that corresponds to your answer. Write your answer
on a separate sheet.

1. Which of the following is not an example of statistical methods?

A. Range B. Class Size C. Frequency Table D. Introduction
2. All, EXCEPT one, are parts of statistical mini research.
A. Introduction B. Data Analysis C. Publishing D. Conclusion
3. Which among the choices is used to present an organized and summarized data?
A. Frequency Distribution Table C. Questionnaire
B. Interview D. Observation

For item number 4-5. Refer to the table below.

Score Frequency Less Cumulative Frequency

40-45 6 18
35-39 5 12
30-34 3 7
25-29 4 4
4. What is the lower boundary of the class interval of the 45th percentile?
A. 34 B. 34.5 C. 39 D. 39.5
5. What cumulative frequency should be used in solving for the 30th percentile?
A. 4 B. 7 C.12 D. 18

What’s In

Let us review on how to construct a Frequency Distribution Table.

Below is the daily allowance data collected from 30 randomly selected students of
Mercedes National High School.
Daily allowance in peso

20 20 25 25 25 30 35 40 40 40
42 43 45 45 50 50 50 55 58 60
63 65 68 70 72 72 75 76 78 79

Organize the given data by completing the Frequency Distribution Table.

a. Determine the Class Interval if the class size is 5

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 b. Tabulate the frequency of the data
c. Determine the Lower Boundary and
d. Compute for the Less than Cumulative Frequency

Less than
Lower
Class Interval Frequency (𝒇) Cumulative
Boundary Frequency

𝑖=5 𝑁 = 30

What’s New
Directions: Study the given frequency distribution table and answer the questions that
follow.

The table below shows the electricity bill of forty (40) randomly selected households
of barangay Baliwasan for the month of December.

Lower Less than Cumulative

Class Interval Frequency (𝒇) Frequency
Boundary
1235 – 1401 3 1234.5 40
1068 – 1234 5 1067.5 37
901 – 1067 4 900.5 32
734 – 900 10 733.5 28
567 – 733 12 566.5 18
400 – 566 6 399.5 6
𝑖 = 167 𝑁 = 40

Questions:
a. What type of data is collected to construct this table?
b. Why do we need to organize data?
c. What statistical method/s should be used to analyze these data?
d. If you are to create a statistical mini-research about the given data, what
possible statement of the problem can you draw from these?

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 What is It

LESSON
Formulating Statistical Mini-Research
1

A What is Statistics?

STATISTICS
Statistics is a branch of science that deals with the collection,
organization, analysis of data and drawing of inferences from the samples to
the whole population.

What is a Statistical Mini-Research?

Statistical mini-research uses appropriate measures of position and other

statistical methods in analyzing and interpreting research data. There are
three (3) parts of a mini-research namely: Introduction, Supporting paragraphs
and Conclusion.
• Introduction is the part of the mini-research where the researcher will
discuss the purpose of the study, the target respondents, the statistical
methods and measures of position that will be used in analyzing the data
and interpreting the results in order to give solution to the research problem.

• The second part of the study is supporting paragraphs. Here, the researcher
will show the data collected in a table form, graphs, frequency table,
compute data using statistical methods such as the range, class size or
width, and measures of position which include the quartile, decile, and
percentile for ungrouped and grouped data.

• The last part is the conclusion where the researcher interprets the results
and provides answer to the research problem or question

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B STEPS IN FORMULATING A STATISTICAL MINI-RESEARCH

1. INTRODUCTION: The introduction should be designed to attract the reader's

attention and explain the focus of the research. You will introduce your overview of
the topic, your main points of information.

2. STATEMENT OF THE PROBLEM: This is used in research work as a claim that

outlines the problem addressed by a study. The statement of the problem briefly
addresses the question: What is the problem that the research will address?

3. PRESENTATION OF DATA: This refers to the organization of data into tables,

graphs or charts, so that logical and statistical conclusions can be derived from the
collected measurements. Data may be presented in 3 Methods: (a) Textual, (b)
Tabular or (c) Graphical.

4. DATA ANALYSIS AND INTERPRETATION: Data analysis is a process that

involves examining, and molding collected data for interpretation to discover
relevant information, draw or propose conclusions and support decision-making to
solve a research problem. This involves interpreting data to answer research
questions.

5. CONCLUSION: The conclusion is the last part of a research paper which

summarizes the whole paper and explains its main purpose.

EXAMPLE:
I. Introduction

This mini-research will investigate the results of the Summative Examination in Basic

Calculus given to the G10 STEM class during the fourth quarter period. Furthermore, the

analysis will include the measures of position for grouped data.

II. Statement of the Problem

The study will investigate the results of the Summative Examination in Basic Calculus

given to the G10 STEM class during the fourth quarter period. This will be conducted in

Ayala National High School of the Division of Zamboanga City during the school year

2019-2020.

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 Specifically, the study will answer the following:

a. What is the frequency distribution of the scores of the Grade 10 STEM students in

their summative examination on Basic Calculus?

b. How many students passed the summative examination if the passing score belongs

to the third quartile?

c. What is the 5th decile score and 95th percentile score of the results in the summative

examination of G10 STEM class?

II. Presentation of Data

Table 1: Frequency Distribution Table on the scores of G10 STEM class in their

Summative Exam on Basic Calculus.

Less Cumulative
Score Frequency Lower Boundary
Frequency
70 – 74 2 69.5 30
65 – 69 4 64.5 28
60 – 64 5 59.5 24
55 – 59 8 54.5 19
50 – 54 5 49.5 11
45 – 49 4 44.5 6
40 – 44 2 39.5 2

IV. Data Analysis and Interpretation

Third Quartile Score:

Determine the position of the third quartile score that is:

kN 3(30) 90
Position of Q 3 class = = = = 22.5
4 4 4

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 This means we need to find a class interval where the 22.5th score is contained. Note

that the 20th to 24th scores belong to the 60 - 64 class interval, thus the 22.5th score also

contained therein.
𝑘𝑁
−𝑐𝑓𝑏 22.5−19
Hence, 𝑄3 = 𝐿𝐵 + [ 4 𝑓 ] 𝑖 = 59.5 + [ ] 5 = 63
𝑄𝑘 5

This means that 75% of the G10 STEM students obtained a score less than or equal

to 63. Moreover, this also implies that only 25% of the class passed the exam with scores

greater than 63.

Fifth Decile Score:

Determine the position of the fifth decile score that is:

kN 5(30) 150
Position of D5 class = = = = 15
10 10 10

This means we need to find a class interval where the 15 th score is contained. Note

that the 12th to 19th scores belong to the 55 - 59 class interval, thus the 15th score also

contained therein.
𝑘𝑁
−𝑐𝑓𝑏 15−11
Hence, 𝐷5 = 𝐿𝐵 + [ 10 ] 𝑖 = 54.5 + [ ] 5 = 57
𝑓 𝐷𝑘 8

This means that half of the class obtained a score less than or equal to 57 while the

other half got a score greater than or equal to 57.

Ninety-fifth Percentile Score:

Determine the position of the ninety-fifth percentile score that is:

kN 95(30) 2850
Position of P95 class = = = = 28.5
100 100 100

This means we need to find a class interval where the 28.5 th score is contained. Note

that the 29th to 30th scores belong to the 70 - 74 class interval, thus the 28.5th score also

contained therein.

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 𝑘𝑁
−𝑐𝑓𝑏 28.5−28
100
Hence, 𝑃95 = 𝐿𝐵 + [ ] 𝑖 = 69.5 + [ ] 5 = 70.75 ≈ 71
𝑓𝑃𝑘 2

This means that 95% of the class obtained a score less than or equal to 71 while the

remaining 5% obtained a score higher than 71.

IV. Conclusion

Analysis of the data obtained in this mini-research shows that the minimum score

needed to pass the summative higher than 71 is 63. Hence, 75% of the class failed while the

upper 25% passed the summative higher than 71. It can also be noted that the median score

is 57. This means that 50% of the class got scores below or equal to 57 and the other 50%

got scores higher than 57. Moreover, students who got scores higher than 71 are part of the

upper 5% of the class.

What’s More
Directions: Formulate a statistical mini-research based on a thought problem that can
be easily conducted in a school environment.

Elements that should be included in your mini-research:

I. Introduction
II. Statement of the Problem
III. Presentation of Data
IV. Data analysis and interpretation
V. Conclusion

Guidelines to be followed:
1. Paper – Standard size (8.5 x 11”)
2. Page Margins – 1” on top, bottom and left while 1.5” on right side. 1” all
side for the cover page.
3. Font – size 12 and use Times New Roman.
4. Spacing – Double-spaced throughout.
5. Paragraph Indention – ½” (or 5 spaces)

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 What I Have Learned
ACTIVITY: CREATE ME!

Directions: Create a flow chart on the steps in formulating a Statistical Mini-Research.

Be creative as possible! (Use separate sheet)

ACTIVITY: 1-4-3

Directions: Write down what is asked regarding statistical mini-research.

Give one reason why statistic is important

1.
Give four possible statistical problems
1.
2.
3.
4.
Give at least three ways of presenting data
1.
2.
3.

What I Can Do
ACTIVITY: PONDER ON ME!

Directions: Read each question carefully and write your answer on a separate sheet.

1. How do we formulate a statistical mini-research?

__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
2. Are statistical researches important? Why or why not?

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 ______________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________

Assessment
Directions: Read each item carefully and write only the letter which corresponds to
the correct answer on a separate sheet of paper.

1. What part of a mini research summarizes the whole paper and explains its main
purpose?
a. Supporting paragraphs c. Presentation of data
b. Conclusion d. Introduction

2. Which study uses appropriate measures of position and other statistical method to
interpret research data?
a. Reflection paper c. Statistical mini-research
b. Action plan d. Feasibility study

3. Zamboanga City, specifically Barangay Bolong is experiencing blackout every now

and then. If you are a researcher, what is the best mini-research title would you
suggest for this problem?
a. The number of times the blackout occurs in Zamboanga City.
b. The number of hours of blackout in a week in Bolong, Zamboanga City.
c. The number of times of blackout in a week in Zamboanga City.
d. The number of hours of blackout in a week in Zamboanga City.

4. Which of the following describes the title and brief description of the mini-research?
a. Title of the mini research c. Conclusion
b. Mini-research proposal d. Introduction

5. What is the purpose of interpreting data?

a. To provide answers to research problem or question.
b. To show the statistical methods used in computing the data.
c. To show the measures of position used in the study.
d. To be able to make future research.

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 Additional Activities
Directions: Search up the words in the grid described / defined by the given hints.
Each word can be found in different directions (horizontally, vertically,
diagonally or backwards).

HINTS:
1. This is designed to attract the reader's attention and explain the focus of the
research.
2. It is a process that involves examining, and molding collected data for interpretation
to discover relevant information, propose or draw conclusions and support
decision-making to solve a research problem.
3. It is the last part of a research paper which summarizes the whole paper and
explains its main purpose.
4. This refers the collection, organization, analysis of data and drawing of inferences
from the samples of the whole population.
5. This is a statistical method where data are divided into 100 equal parts

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 13
Additional Activities: (Optional) What I Can Do:
Some answers may vary
1. To formulate a statistical mini-research, one
must have an approved title proposal first.
Afterwards, you may proceed to the
construction of your paper. Make sure the
following parts are followed: (a) Introduction,
(b) Statement of the problem, (c) Presentation
of data, (d) Data analysis and interpretation,
and (e) Conclusion.
2. YES, mainly because it is used in different
fields of application such as in science,
business and education.
Assessment: What I Have What’s More:
1. B 4. B Learned: Answers may vary depending on
2. C 5. A Answers will vary students research questions and
3. B respondents.
What’s New: Some answers may vary
a. Quantitative data or primary/raw data
b. Organizing data into frequency table is important because it will make the process of
analysis easier.
c. Measures of Position for Grouped Data
d. One possible answer is: How much does a household under the 25 th percentile score
pay for their electric bill?
What’s In:
Lower Less than Cumulative
Class Interval Frequency (𝒇) Frequency
Boundary
70 – 79 7 69.5 30
60 – 69 4 59.5 23
50 – 59 5 49.5 19
40 – 49 7 39.5 14
30 – 39 2 29.5 7
20 – 29 5 19.5 5
𝑖 = 10 𝑁 = 30
What I Know:
1. D 2. B 3. A 4. B 5. B
Answer Key
References:
Edsel A. Dagalea, Mathematics 10 Exemplar: Formulate Statistical Mini-Research,
Department of Education 2019

Mohammad Sharief S. Eldani, Mathematics 10 Exemplar: Analyzing Data, Department of

Education 2019

“A Mini Research for Math Grade 10(1),” Raffy Saga, Accessed June 26, 2020,
www.scribd.com/document/395813964/A-Mini-Research-for-Math-Grade-10-1#

“How to Format Your Research Paper,” Science Buddies, Accessed June 26, 2020,
www.sciencebuddies.org/science-fair-projects/scince-fair/how-to-format-a-research-paper

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 I AM A FILIPINO
by Carlos P. Romulo
I am a Filipino – inheritor of a glorious past, hostage to the It is the mark of my manhood, the symbol of my dignity as
uncertain future. As such, I must prove equal to a two-fold a human being. Like the seeds that were once buried in the
task – the task of meeting my responsibility to the past, and tomb of Tutankhamen many thousands of years ago, it shall
the task of performing my obligation to the future. grow and flower and bear fruit again. It is the insigne of my
I am sprung from a hardy race – child many generations race, and my generation is but a stage in the unending
removed of ancient Malayan pioneers. Across the centuries, search of my people for freedom and happiness.
the memory comes rushing back to me: of brown-skinned I am a Filipino, child of the marriage of the East and the
men putting out to sea in ships that were as frail as their hearts West. The East, with its languor and mysticism, its passivity
were stout. Over the sea I see them come, borne upon the and endurance, was my mother, and my sire was the West
billowing wave and the whistling wind, carried upon the that came thundering across the seas with the Cross and
mighty swell of hope – hope in the free abundance of the new Sword and the Machine. I am of the East, an eager
land that was to be their home and their children’s forever. participant in its struggles for liberation from the imperialist
This is the land they sought and found. Every inch of shore yoke. But I know also that the East must awake from its
that their eyes first set upon, every hill and mountain that centuried sleep, shake off the lethargy that has bound its
beckoned to them with a green and purple invitation, every limbs, and start moving where destiny awaits.
mile of rolling plain that their view encompassed, every river For I, too, am of the West, and the vigorous peoples of the
and lake that promised a plentiful living and the fruitfulness West have destroyed forever the peace and quiet that once
of commerce, is a hollowed spot to me. were ours. I can no longer live, a being apart from those
By the strength of their hearts and hands, by every right of whose world now trembles to the roar of bomb and cannon
law, human and divine, this land and all the appurtenances shot. For no man and no nation is an island, but a part of the
thereof – the black and fertile soil, the seas and lakes and main, and there is no longer any East and West – only
rivers teeming with fish, the forests with their inexhaustible individuals and nations making those momentous choices
wealth in wild and timber, the mountains with their bowels that are the hinges upon which history revolves. At the
swollen with minerals – the whole of this rich and happy land vanguard of progress in this part of the world I stand – a
has been for centuries without number, the land of my forlorn figure in the eyes of some, but not one defeated and
fathers. This land I received in trust from them, and in trust lost. For through the thick, interlacing branches of habit and
will pass it to my children, and so on until the world is no custom above me I have seen the light of the sun, and I
more. know that it is good. I have seen the light of justice and
I am a Filipino. In my blood runs the immortal seed of heroes equality and freedom, my heart has been lifted by the vision
– seed that flowered down the centuries in deeds of courage of democracy, and I shall not rest until my land and my
and defiance. In my veins yet pulses the same hot blood that people shall have been blessed by these, beyond the power
sent Lapulapu to battle against the alien foe, that drove Diego of any man or nation to subvert or destroy.
Silang and Dagohoy into rebellion against the foreign I am a Filipino, and this is my inheritance. What pledge
oppressor. shall I give that I may prove worthy of my inheritance? I
That seed is immortal. It is the self-same seed that flowered shall give the pledge that has come ringing down the
in the heart of Jose Rizal that morning in Bagumbayan when corridors of the centuries, and it shall be compounded of the
a volley of shots put an end to all that was mortal of him and joyous cries of my Malayan forebears when first they saw
made his spirit deathless forever; the same that flowered in the contours of this land loom before their eyes, of the battle
the hearts of Bonifacio in Balintawak, of Gregorio del Pilar cries that have resounded in every field of combat from
at Tirad Pass, of Antonio Luna at Calumpit, that bloomed in Mactan to Tirad Pass, of the voices of my people when they
flowers of frustration in the sad heart of Emilio Aguinaldo at sing:
Palanan, and yet burst forth royally again in the proud heart “I am a Filipino born to freedom, and I shall not rest until
of Manuel L. Quezon when he stood at last on the threshold freedom shall have been added unto my inheritance—for
of ancient Malacanang Palace, in the symbolic act of myself and my children and my children’s children—
possession and racial vindication. The seed I bear within me forever.”
is an immortal seed.

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