LEADER: MIRASOL, Jester T. MEMBERS: MARIÑAS, Carl Lester D. MENDOZA, Rico D. PEDRANO, John Mark R. SOTTO, Mark Anthony A. PROFESSOR: Mr. Mark Ronoele Gonzalvo THE GROUP 3 PRESENTERS CARL LESTER D. MARIÑAS RICO D. MENDOZA JOHN MARK R. PEDRANO JESTER T. MIRASOL MARK ANTHONY A. SOTTO Republic of the Philippines EULOGIO “Amang” RODRIGUEZ INSTITUTE OF SCIENCE AND TECHNOLOGY Nagtahan, Sampaloc, Manila COLLEGE OF ENGINEERING SURVEY ON CIVIL ENGINEERING STUDENTS OF EULOGIO AMANG RODRIGUEZ INSTITUTE OF SCIENCE AND TECHNOLOGY – MANILA CAMPUS ABOUT THEIR FAVORITE DATE OF THE MONTH (1-31) OVERVIEW DATA COLLECTION DATA PRESENTATION GRAPHICAL REPRESENTATION MEASURE OF CENTRAL TENDENCY MEASURE OF POSITION MEASURE OF VARIABILITY GROUP 3 DATA COLLECTION GROUP 3 DATA COLLECTION 1ST YEAR CE STUDENTS 2ND YEAR CE STUDENTS 3RD YEAR CE STUDENTS 4TH YEAR CE STUDENTS GROUP 3 DATA COLLECTION Snowball Sampling was employed as the group reached out few students from each year level and let those students relay the google form to their classmates via their respective Group Chats. SNOWBALL SAMPLING is a sampling method used by researchers to generate a pool of participants for a research study through referrals made by individuals who share a particular characteristic of research interest with the target population (Frey, 2018). GROUP 3 DATA COLLECTION The survey targets 25 respondents each from 1st year to 3rd year and 15 respondents from 4th year. QUOTA SAMPLING is defined as a non-probability sampling method in which researchers create a sample involving individuals that represent a population (QuestionPro Survey Software, 2022). GROUP 3 DATA COLLECTION To finally obtain the target number of respondents, simple random sampling technique was used through ‘Wheel of Names' method which was done per year level. SIMPLE RANDOM SAMPLING is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected (Thomas, 2020). GROUP 3 DATA COLLECTION FINAL TABULATED LISTS FAVORITE DATE OF THE MONTH 1 13. Castillo, Monica E. 13 14. Tamosa, Reynante R. 7 15. Zabat, Ulysses Xandrex L. 29 2. Lacanilao, Lizel G. 30 16. Yumang, Vincent L. 26 3. Dela Cruz, James R. 7 17. Galang, Ronalyn S. 3 4. Abejero, Welmor A. 17 18. Manaloto, Jonard M. 1 5. Varias, Gerielle Louisee DG. 26 19. Mendeja, Christelle L. 29 6. Justo, Princess Anne I. 17 20. Sarmiento, Khalia 4 7. Escarro, Caryll Joy C. 17 21. Arevalo, Aila Marie P. 28 8. Estrada, Aldrin Daniel L. 26 22. Introlizo, Jeffrey 25 9. Bonot, Jedraleen D. 31 23. Rodrigo, Andrei 17 10. Kempiz, Alwayne 26 24. Mabugay, Ricky A Jr. 17 11. Villaceran, Franz-Yari S. 27 25. Acuña, Kurt Daniel 25 12. Barbosa, John Steven D. 15 NAME 1. Netrua, Glyza Mae DC. 13. Priego, Jeffrey L. 3 14. Balasbas, Stefany Mary Joy P. 9 1. Ambon, Hannah Marie L. FAVORITE DATE OF THE MONTH 7 15. Velasquez, Andrea 31 2. Delos Reyes, Carl Bryan Y. 3 16. Manalo, Cedric D. 14 3. Bicar, Denver 5 17. Pena, Reign Marie L. 17 4. Yamamoto, Kazayuki G. 21 18. Caampued, Annie C. 13 5. Geuvarra, Drey Matthew F. 15 19. Buntalan, Jecell 26 6. Santos, Criselda Joy N. 8 20. Balolot, Mark Genesis L. 29 7. Gepollo, Missy S. 14 21. Mopal, Gethel M. 28 8. Acibar, Cherrie Mae B. 7 22. Selda, Ydel Mae R. 22 9. Lorenzo, Igi Mark R. 7 23. Lumugdang, Ralfh Robert P. 24 10. Abello, Andrea Joyce S. 17 24. Buensalida, Jovell P. 4 11. Esteras, Fevonica Reign S. 19 25. Anaviso, Daniel F. 9 12. Panaligan, Jherlyn May D. 12 NAME NAME 1. Gabilan, Joey Albert FAVORITE DATE OF THE MONTH 6 13. Manrique, Jessel C. 7 14. Orellana, Karla Mikaela M. 9 15. Arizobal, Emmanuel A. 18 2. Serrato, Mary Chris A. 10 16. Alcober, Jay-Ar C. 28 3. Arcueno, Jeruz V. 18 17. Jocson, Lorraine Ann N. 28 4. Tulaylay, Hannah Rica DS. 12 18. Agot, Romeo Tito S. 16 5. Serrano, John Angelo P. 17 19. Callanta, Ara Mae F. 17 6. Telan, Ian Migelle G. 21 20. Diaz, Janelle R. 6 7. Gomez, John Anthony I. 14 21. Pacinos II, Edwin R. 12 8. Velasco, Kin Oliver P. 28 22. De Jesus, Carla Angelica C. 16 9. Dacca, Gilbert A. 13 23. Calturan, Lady Ann G. 22 10. Fadriquela, Ilver M. 5 24. De Jesus, Aldren E. 26 11. Brin, Raymond L. 21 25. Razos, Billy James C. 4 12. Perez, Jerome J. 1 NAME 1. Biscocho, Royell Cris P. 2. Sedaba, Mae Joy U. 3. Bueno, Apple C. 4. Catapia, Alyssa Joy M. 5. Aliodin, Sittie Ainie L. 6. Biñas, Lester 7. Cuevas, Jayson 8. Cabali, John Leonard M. 9. Montañez, John Paul B. 10. Ordiales, Joe Angelica C. 11. Galero, Marvin Zandro R. 12. Buynay, Marven B. 13. Pascua, Raymond A. 14. Baleta, Andrea Nicole R. 15. Dinaguit, Jamia Mae A. FAVORITE DATE OF THE MONTH 30 11 12 31 10 19 4 12 1 1 9 7 19 30 28 1 27 30 15 7 13 17 7 26 29 17 26 17 3 26 1 31 29 26 4 28 8 14 25 14 17 17 7 13 17 7 26 25 17 29 7 19 28 3 12 22 5 3 24 21 9 4 15 31 9 6 21 12 10 1 16 18 7 22 12 9 26 17 18 4 21 28 30 14 28 11 28 16 12 13 17 31 5 6 10 19 4 12 1 1 9 7 19 30 28 ARRAY (Largest to Smallest) The favorite date of the month (1-31) of EARIST - Manila CE students arranged from largest to smallest. 31 31 31 30 30 30 29 29 29 28 28 28 28 28 28 27 26 26 26 26 26 26 25 25 24 22 22 21 21 21 19 19 19 18 18 17 17 17 17 17 17 17 17 17 16 16 15 15 14 14 14 13 13 13 12 12 12 12 12 11 10 10 9 9 9 9 8 7 7 7 7 7 7 7 6 6 5 5 4 4 4 4 3 3 3 1 1 1 1 1 ARRAY (Smallest to Largest) The favorite date of the month (1-31) of EARIST - Manila CE students arranged from smallest to largest. 1 1 1 1 1 3 3 3 4 4 4 4 5 5 6 6 7 7 7 7 7 7 7 8 9 9 9 9 10 10 11 12 12 12 12 12 13 13 13 14 14 14 15 15 16 16 17 17 17 17 17 17 17 17 17 18 18 19 19 19 21 21 21 22 22 24 25 25 26 26 26 26 26 26 27 28 28 28 28 28 28 29 29 29 30 30 30 31 31 31 Stem – and – Leaf Diagram STEM LEAVES 0 1 1 1 1 1 3 3 3 4 4 4 4 5 5 6 6 7 7 7 7 7 7 7 8 9 9 9 9 1 0 0 1 2 2 2 2 2 3 3 3 4 4 4 5 5 6 6 7 7 7 7 7 7 7 7 7 8 8 9 9 9 2 1 1 1 2 2 4 5 5 6 6 6 6 6 6 7 8 8 8 8 8 8 9 9 9 3 1 1 1 Frequency Distribution Table CLASSES TALLY CLASS FREQUENCY MARK (X) LIMIT BOUNDARY Lower Upper Lower Upper RELATIVE FREQUENCY CUMULATIVE FREQUENCY <cf >cf 1–5 IIIII IIIII IIII 14 3 1 5 0.5 5.5 0.156 14 90 6 – 10 IIIII IIIII IIIII I 16 8 6 10 5.5 10.5 0.178 30 76 11 – 15 IIIII IIIII IIII 14 13 11 15 10.5 15.5 0.156 44 60 16 – 20 IIIII IIIII IIIII I 16 18 16 20 15.5 20.5 0.178 60 46 21 – 25 IIIII III 8 23 21 25 20.5 25.5 0.089 68 30 26 – 30 IIIII IIIII IIIII IIII 19 28 26 30 25.5 30.5 0.211 87 22 31 – 35 III 3 33 31 35 30.5 35.5 0.033 90 3 TOTAL 90 1.001 HISTOGRAM CLASS BOUNDARY CLASSES LOWER UPPER CLASS MARK (x) FREQUENCY 1–5 14 0.5 5.5 3 6 – 10 16 5.5 10.5 8 11 – 15 14 10.5 15.5 13 16 – 20 16 15.5 20.5 18 21 – 25 8 20.5 25.5 23 26 – 30 19 25.5 30.5 28 31 – 35 13 30.5 35.5 33 TOTAL 90 FREQUENCY POLYGON CLASSES FREQUENCY 20 CLASS MARK (x) 19 18 16 14 3 6 – 10 16 8 11 – 15 14 13 16 – 20 16 18 14 FREQUENCY 1–5 16 14 16 14 12 10 8 8 6 4 21 – 25 8 23 26 – 30 19 28 31 – 35 13 TOTAL 90 33 3 2 0 0 0 3 8 13 18 CLASS MARK 23 28 33 0 38 OGIVE (Less than Cumulative Frequency) 1–5 14 14 CLASS BOUNDARY 90 LOWER UPPER 80 0.5 5.5 6 – 10 16 30 5.5 10.5 11 – 15 14 44 10.5 15.5 16 – 20 16 60 15.5 20.5 21 – 25 8 68 20.5 25.5 26 – 30 19 87 25.5 30.5 CUMULATIVE FREQUENCY CUMULATIVE CLASSES FREQUENCY FREQUENCY > cf 100 87 90 68 70 60 60 50 44 40 30 30 20 10 14 0 0 31 – 35 13 TOTAL 90 90 30.5 35.5 0,5 5,5 10,5 15,5 20,5 CLASS BOUNDARY 25,5 30,5 35,5 OGIVE (Greater than Cumulative Frequency) 1–5 14 90 CLASS BOUNDARY 90 LOWER UPPER 80 0.5 5.5 6 – 10 16 76 5.5 10.5 11 – 15 14 60 10.5 15.5 16 – 20 16 46 15.5 20.5 21 – 25 8 30 20.5 25.5 26 – 30 19 22 25.5 30.5 CUMULATIVE FREQUENCY CUMULATIVE CLASSES FREQUENCY FREQUENCY > cf 100 90 76 70 60 60 46 50 40 30 30 22 20 10 3 0 0 31 – 35 13 TOTAL 90 3 30.5 35.5 0,5 5,5 10,5 15,5 20,5 CLASS BOUNDARY 25,5 30,5 35,5 Pie Chart SECTOR OCCUPIED IN THE PIE CHART CLASSES FREQUENCY RELATIVE FREQUENCY 1–5 14 0.156 56⁰ 6 – 10 16 0.178 64⁰ 11 – 15 14 0.156 56⁰ 16 – 20 16 0.178 64⁰ 21 – 25 8 0.089 32⁰ 26 – 30 19 0.211 76⁰ 31 – 35 3 0.033 12⁰ TOTAL 90 1.001 360⁰ MEAN CLASSES TALLY FREQUENCY (f) 1–5 IIIII IIIII IIII 14 6 – 10 11 – 15 16 – 20 21 – 25 26 – 30 31 – 35 TOTAL IIIII IIIII IIIII I IIIII IIIII IIII IIIII IIIII IIIII I IIIII III IIIII IIIII IIIII IIII III CLASS MARK (x) fx 3 42 16 8 128 14 13 182 16 18 288 8 23 184 19 28 532 3 33 99 90 1,455 𝑓𝑥 𝑥= 𝑛 𝑥= 𝑥 𝑥 14 3 +16 8 +14 13 +16 18 +8 23 +19 28 +3(33) 90 42+128+182+288+184+532+99 = 90 1455 = 90 𝒙 = 𝟏𝟔. 𝟏𝟕 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑴𝒆𝒂𝒏 𝒊𝒔 𝟏𝟔. 𝟏𝟕. MEDIAN c=5 CLASSES FREQUENCY (f) CUMULATIVE FREQUENCY (<cf) 1–5 14 14 6 – 10 16 30 11 – 15 14 44 𝑪𝑭< 16 𝒇𝒎 = 𝟏𝟔 𝑴𝒆𝒅𝒊𝒂𝒏 60 𝑪𝒍𝒂𝒔𝒔 21 – 25 8 68 𝑇ℎ𝑒 45𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 4𝑡ℎ class. 26 – 30 19 87 ∴ 𝑻𝒉𝒆 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟒𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 31 – 35 TOTAL 3 90 90 𝑳𝒎 = 𝟏𝟓. 𝟓 16 – 20 𝒏 = 𝟗𝟎 𝑛 𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 = 2 90 𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 = 2 𝑀𝑒𝑑𝑖𝑎𝑛 𝐶𝑙𝑎𝑠𝑠 = 𝟒𝟓 (45𝑡ℎ 𝑑𝑎𝑡𝑎 𝑜𝑟 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛) (16 – 20). MEDIAN 𝑥 = 𝐿𝑚 + 𝑳𝒐𝒘𝒆𝒓 𝑩𝒐𝒖𝒏𝒅𝒂𝒓𝒚 𝒐𝒇 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔 (𝑳𝒎 ) = 𝟏𝟓. 𝟓 𝑥 = 15.5 + 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔 (𝒇𝒎 ) = 𝟏𝟔 𝑪𝒖𝒎𝒖𝒍𝒂𝒕𝒊𝒗𝒆 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒕𝒉𝒆 𝑪𝒍𝒂𝒔𝒔 𝒑𝒓𝒆𝒄𝒆𝒅𝒊𝒏𝒈 𝒕𝒉𝒆 𝑴𝒆𝒅𝒊𝒂𝒏 𝑪𝒍𝒂𝒔𝒔(𝑪𝑭< ) = 𝟒𝟒 𝑓𝑚 90 −44 2 16 ∙𝑐 𝑥 = 15.5 + 1 16 ∙5 𝑥 = 15.5 + 5 16 𝑥 = 15.5 + 45 −44 ∙ 16 𝑥 = 15.5 + 1 16 𝑻𝒐𝒕𝒂𝒍 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 (𝒏) = 𝟗𝟎 𝑪𝒍𝒂𝒔𝒔 𝑺𝒊𝒛𝒆 (𝒄) = 𝟓 𝑛 2 ( ) −𝐶𝐹< ∙5 5 ∙5 𝑥 = 15.5 + 0.31 𝒙 = 𝟏𝟓. 𝟖𝟏 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑴𝒆𝒅𝒊𝒂𝒏 𝒊𝒔 𝟏𝟓. 𝟖𝟏. MODE 𝒄=𝟓 𝑳𝒎𝒐 = 𝟐𝟓. 𝟓 CLASSES FREQUENCY (f) 1–5 14 6 – 10 16 11 – 15 14 16 – 20 16 21 – 25 8 𝒇𝟏 = 𝟖 19 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 3 𝒇𝟐 = 𝟑 26 – 30 𝒇𝒎𝒐 = 𝟏𝟗 31 – 35 TOTAL 𝒏 = 𝟗𝟎 90 𝐓𝐡𝐞 𝐦𝐚𝐱𝐢𝐦𝐮𝐦 𝐟𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲 𝐢𝐬 𝟏𝟗 𝐚𝐧𝐝 𝐢𝐭 𝐚𝐩𝐩𝐞𝐚𝐫𝐬 𝐰𝐢𝐭𝐡𝐢𝐧 𝐭𝐡𝐞 𝟔𝐭𝐡 𝐜𝐥𝐚𝐬𝐬. ∴ 𝑻𝒉𝒆 𝒎𝒐𝒅𝒂𝒍 𝒄𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 (26 – 30). MODE 𝑥 = 𝐿𝑚𝑜 + 𝑳𝒐𝒘𝒆𝒓 𝑩𝒐𝒖𝒏𝒅𝒂𝒓𝒚 𝒐𝒇 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 (𝑳𝒎𝒐 ) = 𝟐𝟓. 𝟓 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 (𝒇𝒎𝒐 ) = 𝟏𝟗 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒍𝒂𝒔𝒔 𝒑𝒓𝒆𝒄𝒆𝒅𝒊𝒏𝒈 𝒕𝒉𝒆 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔 (𝒇𝟏 ) = 𝟖 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝒐𝒇 𝒕𝒉𝒆 𝒄𝒍𝒂𝒔𝒔 𝒂𝒇𝒕𝒆𝒓 𝒕𝒉𝒆 𝑴𝒐𝒅𝒂𝒍 𝑪𝒍𝒂𝒔𝒔(𝒇𝟐 ) = 𝟑 𝑓𝑚𝑜 −𝑓1 2(𝑓𝑚𝑜 )−𝑓1 −𝑓2 𝑥 = 25.5 + 19−8 ∙ 2(19)−8−3 𝑥 = 25.5 + 11 ∙ 27 5 55 27 ∙𝑐 𝑥 = 25.5 + 5 𝑥 = 25.5 + 2.04 𝒙 = 𝟐𝟕. 𝟓𝟒 𝑻𝒐𝒕𝒂𝒍 𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 (𝒏) = 𝟗𝟎 𝑪𝒍𝒂𝒔𝒔 𝑺𝒊𝒛𝒆 (𝒄) = 𝟓 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑴𝒐𝒅𝒆 𝒊𝒔 𝟐𝟕. 𝟓𝟒. 𝐐𝟏 Quartile 1 CLASSES FREQUENCY 1-5 14 Lq=5.5 6-10 fq = 16 16 30 11-15 14 44 16-20 16 60 21-25 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 C=5 CF< CF< = 14 𝑛𝑘 𝑞= 4 90 ∙ 1 𝑞= 4 90 𝑞= 4 𝒒 = 𝟐𝟐. 𝟓 14 Quartile Class 𝑇ℎ𝑒 22.5𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 2𝑛𝑑 class. ∴ 𝑻𝒉𝒆 𝑸𝒖𝒂𝒓𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟐𝒏𝒅 𝒄𝒍𝒂𝒔𝒔 (6 – 10). 𝐐𝟏 Quartile 1 Lower Boundary of Quartile Class (Lq) = 5.5 𝑄1 = 𝐿𝑞 + Frequency of Quartile Class (fq ) = 16 𝑄1 = 5.5 + Cumulative Frequency of the Class immediately preceding the Quartile Class (CF< ) = 14 Total Frequency (n) = 90 Class Size (c) = 5 𝑄1 = 5.5 + kn 4 − CF < f𝑞 8.5 𝑄1 = 5.5 + ∙5 16 .𝑐 1 ∙ 90 4 − 14 16 𝑄1 = 5.5 + 0.53125 5 .5 22.5 − 14 .5 16 𝑄1 = 5.5 + 2.66 𝑸𝟏 = 𝟖. 𝟏𝟔 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑸𝟏 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟖. 𝟏𝟔. 𝐐𝟑 C=5 Quartile 3 CLASSES FREQUENCY CF< 1-5 14 14 6-10 16 30 11-15 14 44 16-20 16 Lq= 20.5 21-25 fq = 8 CF< = 60 𝑛𝑘 𝑞= 4 90 ∙ 3 𝑞= 4 270 𝑞= 4 𝒒 = 𝟔𝟕. 𝟓 60 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 Quartile Class 𝑇ℎ𝑒 67.5𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 5𝑡ℎ class. ∴ 𝑻𝒉𝒆 𝑸𝒖𝒂𝒓𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟓𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 (21 – 25). 𝐐𝟑 Quartile 3 Lower Boundary of Quartile Class (Lq) = 20.5 𝑄3 = 𝐿𝑞 + Frequency of Quartile Class (fq ) = 8 𝑄3 = 20.5 + Cumulative Frequency of the Class immediately preceding the Quartile Class (CF< ) = 60 Total Frequency (n) = 90 Class Size (c) = 5 𝑄3 = 20.5 + kn 4 − CF < f𝑞 7.5 𝑄3 = 20.5 + ∙5 16 .𝑐 3 ∙ 90 4 − 14 16 𝑄3 = 20.5 + 0.9375 5 .5 67.5 − 14 .5 16 𝑄3 = 20.5 + 4.69 𝑸𝟑 = 𝟐𝟓. 𝟏𝟗 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑸𝟑 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟓. 𝟏𝟗. 𝐃𝟏 C=5 Ld = 0.5 Decile 1 CLASSES FREQUENCY CF< = 0 CF< 𝑛𝑘 𝑑= 10 90 ∙ 1 𝑑= 10 90 𝑑= 10 𝒅=𝟗 14 Decile Class 1-5 fd = 14 14 6-10 16 30 11-15 14 44 16-20 16 60 21-25 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 𝑇ℎ𝑒 9𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 1𝑠𝑡 class. ∴ 𝑻𝒉𝒆 𝑫𝒆𝒄𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟏𝒔𝒕 𝒄𝒍𝒂𝒔𝒔 (1 – 5). 𝐃𝟏 Decile 1 Lower Boundary of Decile Class (Ld) = 0.5 𝐷1 = 𝐿𝑑 + Frequency of Decile Class (fq ) = 14 𝐷1 = 0.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 0 Total Frequency (n) = 90 Class Size (c) = 5 𝐷1 = 0.5 + kn 10 − CF < f𝑑 1 ∙ 90 10 − 0 14 9−0 .5 14 .𝑐 𝐷1 = 0.5 + 9 ∙5 14 𝐷1 = 0.5 + 0.64 5 .5 𝐷1 = 0.5 + 3.21 𝑫𝟏 = 𝟑. 𝟕𝟏 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑫𝟏 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟑. 𝟕𝟏. 𝐃𝟒 C=5 Decile 4 CLASSES FREQUENCY CF< 1-5 14 14 6-10 16 Ld = 10.5 11-15 fd = 14 CF< = 30 𝑛𝑘 𝑑= 10 90 ∙ 4 𝑑= 10 360 𝑑= 10 𝒅 = 𝟑𝟔 30 14 44 Decile Class 16-20 16 60 21-25 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 𝑇ℎ𝑒 36𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 3𝑟𝑑 class. ∴ 𝑻𝒉𝒆 𝑫𝒆𝒄𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟑𝒓𝒅 𝒄𝒍𝒂𝒔𝒔 (11 – 15). 𝐃𝟒 Decile 4 Lower Boundary of Decile Class (Ld) = 10.5 𝐷4 = 𝐿𝑑 + Frequency of Decile Class (fq ) = 14 𝐷4 = 10.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 30 Total Frequency (n) = 90 Class Size (c) = 5 𝐷4 = 10.5 + kn 10 − CF < f𝑑 𝐷4 = 10.5 + .𝑐 4 ∙ 90 10 − 30 14 36 − 30 .5 14 6 ∙5 14 𝐷4 = 10.5 + 0.4286 5 .5 𝐷4 = 10.5 + 2.14 𝑫𝟒 = 𝟏𝟐. 𝟔𝟒 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑫𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟏𝟐. 𝟔𝟒. 𝐃𝟖 C=5 Decile 8 CLASSES FREQUENCY CF< 1-5 14 14 6-10 16 30 11-15 14 44 16-20 16 60 21-25 8 Ld = 25.5 26-30 fd = 19 CF< = 68 𝑛𝑘 𝑑= 10 90 ∙ 24 𝑑= 10 720 𝑑= 10 𝒅 = 𝟕𝟐 68 19 87 Decile Class 31-35 3 90 TOTAL n = 90 90 𝑇ℎ𝑒 72𝑛𝑑 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 6𝑡ℎ class. ∴ 𝑻𝒉𝒆 𝑫𝒆𝒄𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 (26 – 30). 𝐃𝟖 Decile 8 Lower Boundary of Decile Class (Ld) = 25.5 𝐷8 = 𝐿𝑑 + Frequency of Decile Class (fq ) = 19 𝐷8 = 25.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 68 Total Frequency (n) = 90 Class Size (c) = 5 𝐷8 = 25.5 + kn 10 − CF < f𝑑 𝐷8 = 25.5 + .𝑐 8 ∙ 90 10 − 68 19 72 − 68 .5 19 4 ∙5 14 𝐷8 = 25.5 + 0.21 5 .5 𝐷8 = 25.5 + 1.05 𝑫𝟖 = 𝟐𝟔. 𝟓𝟓 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑫𝟖 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟔. 𝟓𝟓. 𝐏𝟐𝟒 Percentile 24 CLASSES FREQUENCY 1-5 14 Lp = 5.5 6-10 fp = 16 16 30 11-15 14 44 16-20 16 60 21-25 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 C=5 CF< CF< = 14 𝑛𝑘 𝑝= 100 90 ∙ 24 𝑝= 100 2160 𝑝= 100 𝒑 = 𝟐𝟏. 𝟔 14 Percentile Class 𝑇ℎ𝑒 21.6𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 2𝑛𝑑 class. ∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟐𝒏𝒅 𝒄𝒍𝒂𝒔𝒔 (6 – 10). 𝐏𝟐𝟒 Percentile 24 Lower Boundary of Percentile Class (Lp) = 5.5 𝑃24 = 𝐿𝑝 + Frequency of Percentile Class (fp ) = 16 𝑃24 = 5.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 14 Total Frequency (n) = 90 Class Size (c) = 5 𝑃24 = 5.5 + kn 100 − CF < f𝑝 𝑃24 = 5.5 + .𝑐 24 ∙ 90 100 − 14 16 21.6 − 14 .5 16 7.6 ∙5 16 𝑃24 = 5.5 + 0. 475 5 .5 𝑃24 = 5.5 + 3.38 𝑷𝟐𝟒 = 𝟕. 𝟖𝟖 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟐𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟕. 𝟖𝟖. 𝐏𝟑𝟏 Percentile 31 CLASSES FREQUENCY 1-5 14 Lp = 5.5 6-10 fp = 16 16 30 11-15 14 44 16-20 16 60 21-25 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 C=5 CF< CF< = 14 𝑛𝑘 𝑝= 100 90 ∙ 24 𝑝= 100 2790 𝑝= 100 𝒑 = 𝟐𝟕. 𝟗 14 Percentile Class 𝑇ℎ𝑒 27.9𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 2𝑛𝑑 class. ∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟐𝒏𝒅 𝒄𝒍𝒂𝒔𝒔 (6 – 10). 𝐏𝟑𝟏 Percentile 31 Lower Boundary of Percentile Class (Lp) = 5.5 𝑃31 = 𝐿𝑝 + Frequency of Percentile Class (fp ) = 16 𝑃31 = 5.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 14 Total Frequency (n) = 90 Class Size (c) = 5 𝑃31 = 5.5 + kn 100 − CF < f𝑝 𝑃31 = 5.5 + .𝑐 31 ∙ 90 100 − 14 16 27.9 − 14 .5 16 13.9 ∙5 16 𝑃31 = 5.5 + 0. 8688 5 .5 𝑃31 = 5.5 + 4.34 𝑷𝟑𝟏 = 𝟗. 𝟖𝟒 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟑𝟏 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟗. 𝟖𝟒. 𝐏𝟒𝟒 Percentile 44 CLASSES FREQUENCY CF< 1-5 14 14 6-10 16 Lp = 10.5 11-15 fp = 14 14 44 16-20 16 60 21-25 8 68 26-30 19 87 31-35 3 90 TOTAL n = 90 90 C=5 CF< = 30 𝑛𝑘 𝑝= 100 90 ∙ 44 𝑝= 100 3960 𝑝= 100 𝒑 = 𝟑𝟗. 𝟔 30 Percentile Class 𝑇ℎ𝑒 39.6𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 3𝑟𝑑 class. ∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟑𝒓𝒅 𝒄𝒍𝒂𝒔𝒔 (11 – 15). 𝐏𝟒𝟒 Percentile 44 Lower Boundary of Percentile Class (Lp) = 10.5 𝑃44 = 𝐿𝑝 + Frequency of Percentile Class (fp ) = 14 𝑃44 = 10.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 30 Total Frequency (n) = 90 Class Size (c) = 5 𝑃44 = 10.5 + kn 100 − CF < f𝑝 𝑃44 = 10.5 + .𝑐 44 ∙ 90 100 − 30 14 39.6 − 30 .5 14 9.6 ∙5 14 𝑃44 = 10.5 + 0. 6857 5 .5 𝑃44 = 10.5 + 3.43 𝑷𝟒𝟒 = 𝟏𝟑. 𝟗𝟑 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟒𝟒 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟏𝟑. 𝟗𝟑. 𝐏𝟖𝟖 Percentile 88 CLASSES FREQUENCY CF< 1-5 14 14 6-10 16 30 11-15 14 44 16-20 16 60 21-25 8 Lp = 25.5 26-30 fp = 19 19 87 31-35 3 90 TOTAL n = 90 90 C=5 CF< = 68 𝑛𝑘 𝑝= 100 90 ∙ 88 𝑝= 100 7920 𝑝= 100 𝒑 = 𝟕𝟗. 𝟐 68 Percentile Class 𝑇ℎ𝑒 79.2𝑛𝑑 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 6𝑡ℎ class. ∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 (26 – 30). 𝐏𝟖𝟖 Percentile 88 Lower Boundary of Percentile Class (Lp) = 25.5 𝑃88 = 𝐿𝑝 + Frequency of Percentile Class (fp ) = 19 𝑃88 = 25.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 68 Total Frequency (n) = 90 Class Size (c) = 5 𝑃88 = 25.5 + kn 100 − CF < f𝑝 𝑃88 = 25.5 + .𝑐 88 ∙ 90 100 − 68 19 79.2 − 68 .5 19 11.2 ∙5 19 𝑃88 = 25.5 + 0.589 5 .5 𝑃88 = 25.5 + 2.95 𝑷𝟖𝟖 = 𝟐𝟖. 𝟒𝟓 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟖𝟖 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟖. 𝟒𝟓. 𝐏𝟗𝟑 Percentile 93 CLASSES FREQUENCY CF< 1-5 14 14 6-10 16 30 11-15 14 44 16-20 16 60 21-25 8 Lp = 25.5 26-30 fp = 19 19 87 31-35 3 90 TOTAL n = 90 90 C=5 CF< = 68 𝑛𝑘 𝑝= 100 93 ∙ 88 𝑝= 100 8370 𝑝= 100 𝒑 = 𝟖𝟑. 𝟕 68 Percentile Class 𝑇ℎ𝑒 83.7𝑡ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑒𝑠 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 6𝑡ℎ class. ∴ 𝑻𝒉𝒆 𝑷𝒆𝒓𝒄𝒆𝒏𝒕𝒊𝒍𝒆 𝑪𝒍𝒂𝒔𝒔 𝒊𝒔 𝒕𝒉𝒆 𝟔𝒕𝒉 𝒄𝒍𝒂𝒔𝒔 (26 – 30). 𝐏𝟗𝟑 Percentile 93 Lower Boundary of Percentile Class (Lp) = 25.5 𝑃93 = 𝐿𝑝 + Frequency of Percentile Class (fp ) = 19 𝑃93 = 25.5 + Cumulative Frequency of the Class immediately preceding the Decile Class (CF< ) = 68 Total Frequency (n) = 90 Class Size (c) = 5 𝑃93 = 25.5 + kn 100 − CF < f𝑝 .𝑐 93 ∙ 90 100 − 68 19 83.7 − 68 .5 19 𝑃93 15.7 = 25.5 + ∙5 19 𝑃93 = 25.5 + 0.826 5 .5 𝑃93 = 25.5 + 4.13 𝑷𝟗𝟑 = 𝟐𝟗. 𝟔𝟑 ∴ 𝑻𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝑷𝟗𝟑 𝒊𝒔 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 𝟐𝟗. 𝟔𝟑. QUARTILE DECILE PERCENTILE 𝑸𝟑 = 𝟐𝟓. 𝟏𝟗 𝑸𝟏 = 𝟖. 𝟏𝟔 𝑫𝟏 = 𝟑. 𝟕𝟏 𝑫𝟒 = 𝟏𝟐. 𝟔𝟒 𝑷𝟐𝟒 = 𝟕. 𝟖𝟖 𝑷𝟑𝟏 = 𝟗. 𝟖𝟒 𝑷𝟒𝟒 = 𝟏𝟑. 𝟗𝟑 𝑫𝟖 = 𝟐𝟔. 𝟓𝟓 𝑷𝟖𝟖 = 𝟐𝟖. 𝟒𝟓 𝑷𝟗𝟑 = 𝟐𝟗. 𝟔𝟑 𝟏 First Formula FREQUENCY (f) CLASS MARK (x) fx 1-5 14 3 42 -13.16667 173.36120 2427.0568 6-10 16 8 128 -8.16667 66.69450 1067.112 11-15 14 13 182 -3.16667 10.02780 140.3892 16-20 16 18 288 1.83333 3.36110 53.7776 21-25 8 23 184 6.83333 46.69440 373.5552 26-30 19 28 532 11.83333 140.02770 2660.5263 CLASSES 𝒙−𝒙 𝒙−𝒙 𝟐 𝒇 𝒙−𝒙 𝟐 𝟐 𝒔𝟐 = 𝒇 𝒙−𝒙 𝒏−𝟏 𝟐 𝒔= 𝒇 𝒙−𝒙 𝒏−𝟏 𝑓𝑥 𝑛 1455 𝑥= 90 𝒙 = 𝟏𝟔. 𝟏𝟔𝟔𝟔𝟕 𝑥= 31-35 TOTAL 3 90 33 99 𝑓𝑥 = 1455 16.83333 283.36100 850.083 𝒇 𝒙−𝒙 𝟐 7772.5001 = 𝒔𝟐 = 𝑛 = 90 𝒇 𝒙−𝒙 𝒏−𝟏 𝟐 7572.5001 𝑠 = 90 − 1 2 𝑓𝑥 = 1455 𝒇 𝒙−𝒙 𝟐 = 7772.5001 𝑠2 7572.5001 = 89 𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕 𝒔= 𝒇 𝒙−𝒙 𝒏−𝟏 𝑠 = 85.08427 𝒔 = 𝟗. 𝟐𝟐 𝟐 𝟐 Second Formula CLASS FREQUENCY (f) CLASS MARK (x) fx x2 fx2 1-5 14 3 42 9 126 6-10 16 8 128 64 1024 11-15 14 13 182 169 2366 16-20 16 18 288 324 5184 21-25 8 23 184 529 4232 26-30 19 28 532 784 14896 31-35 3 33 99 1089 3267 n=90 𝑓𝑥 = 1455 2 𝑓𝑥 = 31095 𝒔𝟐 = 𝒔= 𝒏 𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐 𝒏 𝒏−𝟏 𝒏 𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐 𝒏 𝒏−𝟏 𝑛 = 90 𝑓𝑥 = 1455 𝑓𝑥 2 = 31095 𝒏 𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐 𝒏 𝒏−𝟏 𝒔𝟐 = 𝑠2 90 31095 − (1455)2 = 90 89 2798550 − 2117025 𝑠 = 8010 681525 2 𝑠 = 8010 𝒔= 𝒏 𝒇𝒙𝟐 − ( 𝒇𝒙)𝟐 𝒏 𝒏−𝟏 𝑠 = 85.08427 2 𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕 𝒔 = 𝟗. 𝟐𝟐 𝟑 Third Formula CLASS f d 𝑓. 𝑑 𝑑2 𝑓. 𝑑2 1-5 14 -3 -42 9 126 6-10 16 -2 -32 4 64 11-15 14 -1 -14 1 14 16-20 16 0 0 0 0 21-25 8 1 8 1 8 26-30 19 2 38 4 76 31-35 3 3 9 9 27 TOTAL 90 𝑓. 𝑑= -33 𝑓. 𝑑 2 = 315 𝒔𝟐 = 𝒔= 𝒄𝟐 ∗ 𝒄𝟐 ∗ 𝒏 𝒇. 𝒅𝟐 − 𝒇. 𝒅 𝒏 𝒏−𝟏 𝟐 𝒏 𝒇. 𝒅𝟐 − 𝒇. 𝒅 𝒏 𝒏−𝟏 𝟐 𝒔𝟐 = 𝒄𝟐 ∗ 𝑠2 𝑛 = 90 𝑓. 𝑑 = −33 𝑓. 𝑑 2 = 315 = 52 𝒏 𝒇. 𝒅𝟐 − 𝒇. 𝒅 𝒏 𝒏−𝟏 90 315 − (−33)2 ∗ 90(90 − 1) 28350 − 1089 𝑠 = 25 ∗ 8010 𝟐 𝒔= 𝒄𝟐 ∗ 27261 = 25 ∗ 8010 𝑠 2 = 25 ∗ 3.403370787 𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕 𝒇. 𝒅𝟐 − 𝒇. 𝒅 𝒏 𝒏−𝟏 𝑠 = 85.08427 2 𝑠2 𝒏 𝒔 = 𝟗. 𝟐𝟐 𝟐 𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕 𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕 𝒔𝟐 = 𝟖𝟓. 𝟎𝟖𝟒𝟐𝟕 𝒔 = 𝟗. 𝟐𝟐 𝒔 = 𝟗. 𝟐𝟐 𝒔 = 𝟗. 𝟐𝟐 Republic of the Philippines EULOGIO “Amang” RODRIGUEZ INSTITUTE OF SCIENCE AND TECHNOLOGY Nagtahan, Sampaloc, Manila COLLEGE OF ENGINEERING SURVEY ON CIVIL ENGINEERING STUDENTS OF EULOGIO AMANG RODRIGUEZ INSTITUTE OF SCIENCE AND TECHNOLOGY – MANILA CAMPUS ABOUT THEIR FAVORITE DATE OF THE MONTH (1-31) THE GROUP 3 PRESENTERS CARL LESTER D. MARIÑAS RICO D. MENDOZA JOHN MARK R. PEDRANO JESTER T. MIRASOL MARK ANTHONY A. SOTTO PRESENTED TO: MR. MARK RONOELE GONZALVO It’s audiences like you that make presentations awesome. Thank you very much for your unwavering attention throughout this presentation. PADAYON! From our Group, to Everyone: