Statistics and Probability

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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

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Printed in the Philippines by EC-TEC

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

THISPROJECTWASDEVELOPEDWITHTHE 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,  

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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.

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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.

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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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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 1 o f 7 : 11 /1 2 u b je ct Tit le : Sta tis tic s a nd P roba bilit y No. of H ou rs/ S em es te r: 8 0 ho urs/ se m est er P re re q uisi te ( if n ee de d): u b je ct D es crip ti o n: At t he e nd of t he c ou rs e, th e st ude nt s m ust k now h ow t o fin d th e m ea n an d va ria nc e of a ra ndom v ari able , to apply sa m pling te ch niq ue s an d s, to est im at e populat ion m ea n an d prop ort ion , to pe rf orm h ypot he sis te st in g on populat io n m ea n an d prop o rt ion , an d to pe rf orm c orre la tion a nd re gre ssion s o n re al -lif e prob le m s. C ONT E NT C ONT E NT S TA NDA R DS P ER FO R MAN C E S TA NDA R DS LEARNING C OMP ETE NC IES C OD E om Va riab le s ro b a b ili ty b u tio ns Th e le arne r de m on st ra te s un de rst an di ng o f k ey con ce pt s of ra ndom va ria ble s a nd pr oba bilit y dist ribution s. Th e le arner is a ble t o a ppl y an a ppr opria te ra ndom va ria ble f or a give n re al -lif e prob le m (suc h a s in de cision m ak in g a nd ga m es of c ha nc e). Th e le arner … 1. illu st ra te s a ra ndom v aria bl e (d isc re te a nd co nt in uou s). M11 /12 SP -IIIa -1 2. dist in guis he s be tw ee n a dis cre te a nd a co nt in uou s ra ndom v aria ble . M11 /12 SP -IIIa -2 3. fin ds t he possible v alu es of a ra ndom v aria ble . M11 /12 SP -IIIa -3 4. illu st ra te s a prob abilit y dist ribution f or a dis cre te ra ndom v aria ble a nd it s pr ope rt ie s. M11 /12 SP -IIIa -4 5. con st ru ct s t he prob abilit y m ass f un ct io n o f a discre te ra ndom v aria ble a nd it s co rre spon din g histo gra m . M11 /12 SP -IIIa -5 6. comp ut es pr oba bilit ie s corr espon ding t o a given ra ndom v aria ble . M11 /12 SP -IIIa -6 7. illu st ra te s t he m ea n a nd va ria nc e of a di sc re te ra ndom va ria ble . M11 /12 SP -III b -1 8. ca lc ula te s t he m ea n a nd t he v aria nc e o f a discre te ra ndom v aria ble . M11 /12 SP -III b -2 9. in te rpr et s t he m ea n an d t he v aria nc e o f a discre te ra ndom v aria ble . M11 /12 SP -III b -3 10. solv es pro ble m s in volv in g m ea n a nd var ia nc e of prob abilit y dist rib ut ion s. M11 /12 SP -III b -4 al bu tio n Th e le arner de m on st ra te s un de rst an di ng o f ke y c on ce pt s of n orm al prob abilit y dist rib ut ion . Th e le arner is a ble t o ac cu ra te ly f orm ula te a nd solv e re al -lif e p roble m s in dif fe re nt di sc ipli ne s Th e le arner … 11. illu st ra te s a n orm al ra ndom v aria ble a nd it s ch ara ct erist ic s. M11 /12 SP -IIIc -1 12. c on st ru ct s a n orm al c urve. M11 /12 SP -IIIc -2

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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 2 o f 7 C ONT E NT C ONT E NT S TA NDA R DS P ER FO R MAN C E S TA NDA R DS LEARNING C OMP ETE NC IES C OD E in vol vin g norm al dist ribution . 13. ide nt ifie s re gio ns u nde r t he n orm al c urve corre spo nding to dif fe re nt s ta nda rd norm al v alu es . M11 /12 SP -IIIc -3 14. c on ve rt s a n orm al ra nd om va ria ble t o a st an da rd norm al v aria ble a nd vic e v ersa . M11 /12 SP -IIIc -4 15. c omp ut es pr oba bilit ie s a nd pe rcentile s u sin g t he st an da rd norm al t able . M11 /12 SP -IIIc -d -1 lin g an d lin g b u tio ns Th e le arner de m on st ra te s un de rst an di ng o f ke y con ce pt s of sa m pling a nd sa m pling distr ibuti on s of t he sa m ple m ea n. Th e le arner is a ble t o appl y su ita ble sa m pling a nd sa m pling distr ibuti on s of th e sa m ple m ea n t o solv e re al -lif e prob le m s i n dif fe re nt di sc ipli ne s. Th e le arner … 1. illu st ra te s ra ndom sa m pli ng . M11 /12 SP -III d -2 2. dist in guis he s be tw ee n pa ra m et er a nd st at ist ic . M11 /12 SP -III d -3 3. ide nt ifie s sa m pli ng dist rib ut ion s o f st at ist ic s (sa m ple m ea n). M11 /12 SP -III d -4 4. fin ds t he m ea n a nd va ria nc e of t he sa m pli ng dist ributi on of t he sa m ple m ea n. M11 /12 SP -III d -5 5. de fin es t he sa m pling distr ib ut ion o f t he sa m ple m ea n for norm al popula tio n w he n t he v aria nc e is : (a ) kn ow n (b ) un kn ow n M11 /12 SP -III e-1 6. illu st ra te s t he Ce nt ra l L im it Th eore m . M11 /12 SP -III e-2 7. de fin es t he sa m pling distr ib ut ion o f t he sa m ple m ea n usin g t he Ce nt ra l L im it Th eore m . M11 /12 SP -III -3 8. solv es pro ble m s in volv in g s am pling distr ibutio ns o f t he sa m ple m ea n. M11S P -IIIe -f -1 ti on of me te rs Th e le arner de m on st ra te s un de rst an di ng o f ke y con ce pt s of e st im at ion o f populat ion m ea n a nd Th e le arner is a ble t o est im at e t he popula tion m ea n a nd pop ula tio n prop ort ion t o ma ke so un d Th e le arner … 1. illu st ra te s poin t a nd in te rval e st im at ion s. M11 /12 SP -IIIf -2 2. dist in guis he s be tw ee n poi nt a nd inte rval e st im at ion . M11 /12 SP -IIIf -3

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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 3 o f 7 C ONT E NT C ONT E NT S TA NDA R DS P ER FO R MAN C E S TA NDA R DS LEARNING C OMP ETE NC IES C OD E populat ion pr oport io n. in fe re nc es in re al -li fe prob le m s in di ff ere nt disciplin es . 3. ide nt ifie s poi nt e st im at or f or t he popula tio n m ea n. M11 /12 SP -IIIf -4 4. comp ut es for t he p oin t e st im at e of t he popu la tion me an . M11 /12 SP -IIIf -5 5. ide nt ifie s t he a ppr opria te f orm of t he c on fide nc e in te rval e st im at or f or t he p opu la tion m ea n w he n: (a ) th e popula tio n v aria nc e is k now n, (b) t he popula tio n va ria nc e is un kn ow n, a nd ( c) t he Ce nt ra l L im it Th eore m is t o be u se d. M11 /12 SP -I II g -1 9. illu st ra te s t he t -dist rib ut ion . M11 /12 SP -III g -2 10. c on st ru ct s a t -di st ributio n. M11 /12 SP -III g -3 11. ide nt ifie s re gio ns u nde r t he t -dist ributio n co rre spon di ng to dif fe re nt t -v alu es . M11 /12 SP -III g -4 11. ide nt ifie s pe rce nt ile s u sin g th e t -t able . M11 /12 SP -III g -5 12. c omp ut es for t he c on fide nc e in te rval e st im at e ba se d on th e a ppr opria te f orm o f t he e st im at or f or t he populat ion m ea n. M11 /12 SP -IIIh -1 13. solv es pro ble m s in volv in g con fide nc e i nt erval est im at ion of t he popula tio n m ea n. M11 /12 SP -IIIh -2 14. dra w s c on clu si on a bo ut t he popula tion m ea n ba se d on its c on fide nc e in te rval e st im at e. M11 /12 SP -IIIh -3 15. ide nt ifie s poi nt e st im at or f or t he popula tio n prop ort ion . M11 /12 SP -IIIi -1 16. c omp ut es for t he p oin t e st im at e of t he popu la tion prop ort ion . M11 /12 SP -IIIi -2 17. ide nt ifie s t he a ppr opria te f orm of t he c on fide nc e in te rval e st im at or f or t he p opu la tion pr oport io n ba se d on t he Ce nt ra l L im it T he ore m . M11 /12 SP -IIIi -3 18. c omp ut es for t he c on fide nc e in te rval e st im at e of t he populat ion pr oport io n. M11 /12 SP -IIIi -4 19. solv es pro ble m s in volv in g con fide nc e i nt erval est im at ion of t he popula tio n prop ort io n. M11 /12 SP -IIIi -5

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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 4 o f 7 C ONT E NT C ONT E NT S TA NDA R DS P ER FO R MAN C E S TA NDA R DS LEARNING C OMP ETE NC IES C OD E 20. dra w s c on clu si on a bo ut t he popula tion pr oport io n ba se d on it s c on fide nc e in te rval e st im at e M11 /12 SP -IIIi -6 21. ide nt ifie s t he le ngt h o f a co nf ide nc e in te rv al. M11 /12 SP -IIIj -1 22. c omp ut es for t he le ngt h o f th e co nf ide nc e in te rv al. M11 /12 SP -IIIj -2 23. c omp ut es for a n a ppr opria te sa m ple size u sin g t he le ngt h o f t he in te rv al. M11 /12 SP -IIIj -3 24. solv es pro ble m s in volv in g s am ple size de te rm in at ion . M11 /12 SP -IIIj -4 of hesis Th e le arner de m on st ra te s un de rst an di ng o f ke y con ce pt s of t est s of hy pot he se s o n t he populat ion m ea n a nd populat ion pr oport io n. Th e le arner is a ble t o pe rf orm a ppr opria te t est s of h ypot he se s in volv in g t he populat ion m ea n a nd populat ion pr oport io n t o m ak e in fe re nc es i n re al -lif e prob le m s in di ff ere nt disciplin es . Th e le arner … 1. illu st ra te s: (a ) nu ll h ypot he si s (b ) a lte rnat iv e h ypot he sis (c) le ve l of signi fic an ce (d ) r ej ec tion re gi on ; a nd (e ) t ype s of e rror s in h ypot he sis t est in g. M11 /12 SP -IVa -1 2. ca lc ula te s t he pr oba bilit ie s of c omm itt in g a T ype I a nd Ty pe II e rr or. M11 /12 SP -IVa -2 3. ide nt ifie s t he pa ra m et er t o be t est ed given a re al -lif e prob le m . M11 /12 SP -IVa -3 4. form ula te s t he a ppr opria te n ull an d a lte rnat iv e hy pot he se s o n a popula tio n m ea n. M11 /12 SP -IVb -1 5. ide nt ifie s t he a ppr opria te f orm of t he t est -st at ist ic wh en : (a ) t he popula tion v aria nc e is a ssu m ed t o be k now n (b ) t he popula tion v aria nc e is a ssu m ed t o be u nk now n; an d (c) t he Ce nt ra l L im it Th eore m is t o be u se d. M11 /12 SP -IVb -2

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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 5 o f 7 C ONT E NT C ONT E NT S TA NDA R DS P ER FO R MAN C E S TA NDA R DS LEARNING C OMP ETE NC IES C OD E 6. ide nt ifie s t he a ppr opria te re je ct ion re gion f or a gi ve n le ve l of si gni fic an ce w he n: (a ) t he popula tion v aria nc e is a ssu m ed t o be k now n (b ) t he popula tion v aria nc e is a ssu m ed t o be u nk now n; an d (c) t he Ce nt ra l L im it Th eore m is t o be u se d. M11 /12 SP -IVc -1 7. comp ut es for t he t est -st at ist ic v alu e (p op ula tion m ea n) . M11 /12 SP -IVd -1 8. dra w s c on clu si on a bo ut t he popula tion m ea n ba se d on th e t est -st at ist ic v alu e a nd th e re je ct io n re gion . M11 /12 SP -IVd -2 9. solv es pro ble m s in volv in g t est of h ypot he sis o n t he populat ion m ea n. M11 /12 SP -IVe -1 10. f orm ula te s t he a ppr opria te n ull a nd a lte rnat iv e hy pot he se s o n a popula tio n prop ort ion . M11 /12 SP -IVe -2 11. ide nt ifie s t he a ppr opria te f orm of t he t est -st at ist ic w he n t he Ce nt ra l L im it T he ore m is t o be u se d. M11 /12 SP -IVe -3 12. ide nt ifie s t he a ppr opria te re je ct ion re gion f or a gi ve n le ve l of si gni fic an ce w he n t he Ce nt ra l L im it Th eore m is to be u se d. M11 /12 SP -IVe -4 13. c omp ut es for t he t est -st at ist ic v alu e (p op ula tion prop ort ion ). M11 /12 SP -IVf -1 14. dra w s c on clu si on a bo ut t he popula tion pr oport io n ba se d on t he t est -st at ist ic v alu e a nd t he re je ct ion re gion . M11 /12 SP -IVf -2 15. solv es pro ble m s in volv in g t est of h ypot he sis o n t he populat ion pr oport io n. M11 /12 SP -IVf -g -1

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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 6 o f 7 C ONT E NT C ONT E NT S TA NDA R DS P ER FO R MAN C E S TA NDA R DS LEARNING C OMP ETE NC IES C OD E H M E N T io n a n d ss io n es Th e le arner de m on st ra te s un de rst an di ng o f ke y con ce pt s of co rre la tio n a nd re gre ssion a na ly se s. Th e le arner is a ble t o pe rf orm c orre la tion a nd re gre ssion a na ly se s o n re al -lif e prob le m s i n dif fe re nt di sc ipli ne s. 1. illu st ra te s t he n at ure o f bi va ria te da ta . M11 /12 SP -IVg -2 2. con st ru ct s a s ca tt er plot . M11 /12 SP -IVg -3 3. de sc ribe s sh ape ( form ), t re nd ( dire ct io n), a nd va ria tion (st re ngt h) b ase d on a s ca tt er plot . M11 /12 SP -IVg -4 4. est im at es st re ngt h of a ssoc ia tion be tw ee n t he v aria ble s ba se d on a sc at te r plot . M11 /12 SP -IVh -1 5. ca lc ula te s t he P ea rso n’ s sa m ple co rre la tion c oe ff ic ie nt . M11 /12 SP -IVh -2 6. solv es pro ble m s in volv in g corre la tion a na ly si s. M11 /12 SP -IVh -3 7. ide nt ifie s t he in de pe nde nt a nd de pe nde nt v aria ble s. M11 /12 SP -IVi -1 8. dra w s t he be st -f it li ne on a sc at te r plot . M11 /12 SP -IVi -2 9. ca lc ula te s t he sl ope a nd y -in te rcep t of t he re gre ssio n lin e. M11 /12 SP -IVi -3 10. in te rpr et s t he calc ula te d slo pe a nd y -in te rcep t o f t he re gre ssion li ne . M11 /12 SP -IVi -4 11. pre dicts t he v al ue of t he de pe nde nt v aria ble give n t he va lu e of t he in de pe nde nt v aria ble . M11 /12 SP -IVj -1 12. solv es pro ble m s in volv in g r egre ssion a na ly sis. M11 /12 SP -IVj -2

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K t o 12 BAS IC ED U C AT ION C U R R IC U LU M S ENIOR H IGH S C H OOL – C O R E S U BJ E C T Se nio r H ig h Sc ho ol Core Curric ulum – Sta ti s ti cs a n d Pro b a b ili ty De c e m b e r 2 0 1 3 Pa ge 7 o f 7 C o de Boo k Le ge nd S amp le : M11 /12 SP -IIIa -1 LEGEND S AMP LE Fi rst En try Le arnin g A re a a nd Stra nd/ Su bj ec t or Specia liza tion Ma th em at ic s M11 /12 G ra de L ev el G ra de 1 1/1 2 U pp erca se L et te r/s D oma in /Co nt en t/ Com pon en t/ T opi c Sta tist ic s a nd P roba bilit y SP - R om a n N um era l *Z ero i f n o spe ci fic q ua rt er Qua rt er Th ird Q ua rt er III Lowe rca se L et te r/s a h yphen ( -) in be tw ee n le tt ers t o in dica te m ore t ha n a spe ci fic w ee k We ek We ek on e a - Ara b ic N um b er Com pe te nc y illu st ra te s a ra ndom v aria bl e (d isc re te a nd con tin uo us) 1

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CHAPTER 1: EXPLORING DATA

Lesson 1: Introducing Statistics

TIME FRAME: 60 minutes

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

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 2}nd_{Edition), Authored by the Faculty of the}

Institute of Statistics, UP Los Baños, College Laguna 4031

Workbooks in Statistics 1 (From 1st_{to 13}th_{Edition), Authored by the Faculty of}

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!

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? • 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,

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!

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 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 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.

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!

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.

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

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!

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.

ASSESSMENT

Note: Answers are provided inside the parentheses and italicized.

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)

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.

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!

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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CHAPTER 1: EXPLORING DATA

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}

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 2}nd_{Edition), Authored by the Faculty of the Institute of Statistics, UP}

Los Baños, College Laguna 4031

Workbooks in Statistics 1 (From 1st_{to 13}th_{Edition), Authored by the Faculty of the Institute of}

Statistics, UP Los Baños, College Laguna 4031

https://www.khanacademy.org/math/probability/statistical-studies/statistical-questions/v/statistical-questions

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DEVELOPMENT OF THE LESSON

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.

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

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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.

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

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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 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.

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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.

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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? 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.

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• 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.

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.

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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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16"

ATTACHMENT C: CLASS RECORDING SHEET (for the Teacher’s Use)

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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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)

REFERENCES

Albert, J. R. G. (2008). Basic Statistics for the Tertiary Level (ed. Roberto Padua, WelfredoPatungan, Nelia Marquez), published by Rex Bookstore.

Handbook of Statistics 1 (1st_{and 2}nd_{Edition), Authored by the Faculty of the}

Institute of Statistics, UP Los Baños, College Laguna 4031

Takahashi, S. (2009). The Manga Guide to Statistics. Trend-Pro Co. Ltd.

Workbooks in Statistics 1 (From 1st_{to 13}th_{Edition), Authored by the Faculty of the}

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DEVELOPMENT OF THE LESSON

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:

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 : : : : : : : : : : : : : : : : : : : : : : : :

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

Statistics and Probability