4 th QUARTER Module 7: FORMULATE STATISTICAL MINI

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1 Republic of the Philippines Department of Education Regional Office IX, Zamboanga Peninsula 10 Zest for Progress Zeal of Partnership 4 th QUARTER Module 7: FORMULATE STATISTICAL MINI-RESEARCH Name of Learner: Grade & Section: Name of School:

2 Mathematics Grade 10 Alternative Delivery Mode Quarter 4 - Module 7: Formulate Statistical Mini-Research First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalty. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio Writer: Editors: Layout Artist: Reviewers: EPS, Mathematics Principal Management Team: SDS ASDS ASDS Development Team of the Module EPS Mathematics EPS LRMS Ciara Mae P. Jamorol Rosemary B. Garcia Printed in the Philippines Department of Education Region IX, Zamboanga Peninsula Office Address: Tiguma, Airport Road, Pagadian City Telefax: (062) ; Address: [email protected] Elizabeth M. Raciles, Ed.D. Zandro G. Sepe, M.S. Vilma A. Brown, Ed.D. Zandro G. Sepe, M.S. Roy C. Tuballa, EMD, JD, CESO VI Jay S. Montealto, CESO VI Norma T. Francisco, Ed.D.,CESE Vilma A. Brown, Ed.D. Aida F. Coyme, Ed.D. 1

3 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). 2

4 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 What is the lower boundary of the class interval of the 45th percentile? A. 34 B C. 39 D 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 Organize the given data by completing the Frequency Distribution Table. a. Determine the Class Interval if the class size is 5 3

5 b. Tabulate the frequency of the data c. Determine the Lower Boundary and d. Compute for the Less than Cumulative Frequency Class Interval Frequency (f) Lower Boundary Less than Cumulative 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. Class Interval Frequency (f) Lower Less than Cumulative Boundary Frequency 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? 4

6 What is It LESSON 1 Formulating Statistical Mini-Research 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 5

7 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

8 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 5 th decile score and 95 th 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. Score Frequency Lower Boundary Less Cumulative Frequency IV. Data Analysis and Interpretation Third Quartile Score: Determine the position of the third quartile score that is: Position of Q 3 class = kn 4 = 3(30) 4 = 90 4 =

9 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 class interval, thus the 22.5th score also contained therein. kn 4 Hence, Q 3 = LB + [ cf b ] i = [ ] 5 = 63 f 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: Position of D 5 class = kn 10 = 5(30) 10 = = 15 This means we need to find a class interval where the 15th score is contained. Note that the 12th to 19th scores belong to the class interval, thus the 15th score also contained therein. kn Hence, D 5 = LB + [ 10 cf b f Dk ] i = [ ] 5 = 57 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 Ninety-fifth Percentile Score: Determine the position of the ninety-fifth percentile score that is: Position of P 95 class = kn 100 = 95(30) 100 = = 28.5 This means we need to find a class interval where the 28.5th score is contained. Note that the 29th to 30th scores belong to the class interval, thus the 28.5th score also contained therein. 8

10 kn 100 Hence, P 95 = LB + [ cf b ] i = [ ] 5 = f Pk 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. III. IV. Statement of the Problem Presentation of Data 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) 9

11 ACTIVITY: CREATE ME! What I Have Learned Directions: Create a flow chart on the steps in formulating a Statistical Mini-Research. Be creative as possible! (Use separate sheet) ACTIVITY: Directions: Write down what is asked regarding statistical mini-research. Give one reason why statistic is important 1. Give four possible statistical problems Give at least three ways of presenting data 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? 10

12 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. 11

13 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 12

14 Answer Key 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: 1. B 4. B 2. C 5. A 3. B What I Have Learned: Answers will vary What s More: Answers may vary depending on students research questions and 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) Boundary Frequency i = 10 N = 30 What I Know: 1. D 2. B 3. A 4. B 5. B 13

15 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, How to Format Your Research Paper, Science Buddies, Accessed June 26, 2020, 14

16 I AM A FILIPINO by Carlos P. Romulo I am a Filipino inheritor of a glorious past, hostage to the uncertain future. As such, I must prove equal to a two-fold task the task of meeting my responsibility to the past, and the task of performing my obligation to the future. I am sprung from a hardy race child many generations removed of ancient Malayan pioneers. Across the centuries, the memory comes rushing back to me: of brown-skinned men putting out to sea in ships that were as frail as their hearts were stout. Over the sea I see them come, borne upon the billowing wave and the whistling wind, carried upon the mighty swell of hope hope in the free abundance of the new land that was to be their home and their children s forever. This is the land they sought and found. Every inch of shore that their eyes first set upon, every hill and mountain that beckoned to them with a green and purple invitation, every mile of rolling plain that their view encompassed, every river and lake that promised a plentiful living and the fruitfulness of commerce, is a hollowed spot to me. By the strength of their hearts and hands, by every right of law, human and divine, this land and all the appurtenances thereof the black and fertile soil, the seas and lakes and rivers teeming with fish, the forests with their inexhaustible wealth in wild and timber, the mountains with their bowels swollen with minerals the whole of this rich and happy land has been for centuries without number, the land of my fathers. This land I received in trust from them, and in trust will pass it to my children, and so on until the world is no more. I am a Filipino. In my blood runs the immortal seed of heroes seed that flowered down the centuries in deeds of courage and defiance. In my veins yet pulses the same hot blood that sent Lapulapu to battle against the alien foe, that drove Diego Silang and Dagohoy into rebellion against the foreign oppressor. That seed is immortal. It is the self-same seed that flowered in the heart of Jose Rizal that morning in Bagumbayan when a volley of shots put an end to all that was mortal of him and made his spirit deathless forever; the same that flowered in the hearts of Bonifacio in Balintawak, of Gregorio del Pilar at Tirad Pass, of Antonio Luna at Calumpit, that bloomed in flowers of frustration in the sad heart of Emilio Aguinaldo at Palanan, and yet burst forth royally again in the proud heart of Manuel L. Quezon when he stood at last on the threshold of ancient Malacanang Palace, in the symbolic act of possession and racial vindication. The seed I bear within me is an immortal seed. It is the mark of my manhood, the symbol of my dignity as a human being. Like the seeds that were once buried in the tomb of Tutankhamen many thousands of years ago, it shall grow and flower and bear fruit again. It is the insigne of my race, and my generation is but a stage in the unending search of my people for freedom and happiness. I am a Filipino, child of the marriage of the East and the West. The East, with its languor and mysticism, its passivity and endurance, was my mother, and my sire was the West that came thundering across the seas with the Cross and Sword and the Machine. I am of the East, an eager participant in its struggles for liberation from the imperialist yoke. But I know also that the East must awake from its centuried sleep, shake off the lethargy that has bound its limbs, and start moving where destiny awaits. For I, too, am of the West, and the vigorous peoples of the West have destroyed forever the peace and quiet that once were ours. I can no longer live, a being apart from those whose world now trembles to the roar of bomb and cannon shot. For no man and no nation is an island, but a part of the main, and there is no longer any East and West only individuals and nations making those momentous choices that are the hinges upon which history revolves. At the vanguard of progress in this part of the world I stand a forlorn figure in the eyes of some, but not one defeated and lost. For through the thick, interlacing branches of habit and custom above me I have seen the light of the sun, and I know that it is good. I have seen the light of justice and equality and freedom, my heart has been lifted by the vision of democracy, and I shall not rest until my land and my people shall have been blessed by these, beyond the power of any man or nation to subvert or destroy. I am a Filipino, and this is my inheritance. What pledge shall I give that I may prove worthy of my inheritance? I shall give the pledge that has come ringing down the corridors of the centuries, and it shall be compounded of the joyous cries of my Malayan forebears when first they saw the contours of this land loom before their eyes, of the battle cries that have resounded in every field of combat from Mactan to Tirad Pass, of the voices of my people when they sing: I am a Filipino born to freedom, and I shall not rest until freedom shall have been added unto my inheritance for myself and my children and my children s children forever. 15