Mean, Median and Mode

Mean, Median and Mode

Ungrouped Data (Raw Data): The information collected systematically regarding a population or a sample survey is called an ungrouped data. It is also called raw data.

Mean of ungrouped data:

Let x1, x2, x3, ..., xn be n observations then mean is obtained by dividing the sum of n observations by n. It is denoted by X' = For Eg: Find the mean of 4,6,8,6,7,8

Sol:Mean X' = (4 + 6 + 8 + 6 + 7 + 8)/639/6= 6.5

Median of ungrouped data:

If the observations of an ungrouped data are arranged in increasing or decreasing order of their magnitude, a value which divides these ordered observations into two equal parts is called the median of the data. It is denoted by M.

If the number of observations (n) is an odd integer, then
M = Value of (n+1)/2 th observation in the arrangement of observations in increaseing order.

If the number of observations (n) is an even integer, then
M = (Value of n/2 th observation + Value of (n/2 + 1) th observation)/2

For Eg: 
Find the median of the following observations

Sol: Observations in the ascending order are :
4, 6, 6, 7, 8, 8, 8 
Here, n = 7 is odd.
Median :
M = Value of (n+1)/2 th observation
= Value of (7+1)/2 th observation 
= Value of 4 th observation 
= 7

Mode of ungrouped data:

An observation occurring most frequently in the data is called mode of the data. It is denoted by Z.

For Eg:
Find the mode of the following observations

In the given data, the observation 8 occurs maximum
number of times (3)
Mode(Z) = 8


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Curriculum Vitae of Crisencio Paner


CP : 0915-1429675                                                             Email :                                                                                                         


        Ph.D. in Biological Science (candidate)
University of Santo Tomas, Graduate School
  • M.S. Microbiology
University of Santo Tomas
      Thesis: “Chemical Control of Fungi Infesting Easel Oil Paintings at
                   University of Santo Tomas Museum of Arts and Sciences”
  • Italian Scholarship Grant
Restoration and Conservation of Artworks Attacked by Biological Agents
Istituto Centrale Per Il Restauro, Rome, Italy (January 1-June 30, 2004)

  • B.S. Biochemistry
University of Santo Tomas

  • Professional Teaching Certification Program (Major in Biological Science)
Caloocan City Polytechnic College


  Co-author in LET Reviewer in Biology, 2006-2010 eds. Published by MET Inc.
                          ISBN # 97193249-6-1, sold in National Bookstores                                                                                                                 
  • Understanding Museum Pests: The Molds. CFAD Atelier Journal, University of  Santo Tomas, Vol. 2 No. 1, 2003-2004, pp. 80-83
  • On the Conservation of 20th Century Color Photographs Attacked by Molds. CFAD Atelier Journal, UST., Vol. 2 No. 1, 2003-2004, pp. 106-113
  • Witnessing the Glory of Italy in Its Art History and Ancient Spaces. CFAD Atelier Journal, UST, Vol. 3 No. 1, 2004-2005, pp. 55-72 
  • _______________. Panorama Magazine, November 13, 2005, pp. 12, 13, & 21.
  • Deterioration of Paintings and Painting Components Caused by Microorganisms. CFAD Atelier Journal, UST., Vol. 3 No. 1, 2004-2005, pp. 91-94
  • Microbial Deterioration of Painting Materials. CFAD Atelier Journal, UST., Vol. 3 No. 1, 2004-2005, pp. 94-97.
  • Conservation of Paintings Attacked by Molds. In College Freshman English Book II. Agalabia, U., Aranda, R., et. al., pp. 124-125, UST Publishing House, 2004
  • Today’s Restoration Establishments.  CFAD Atelier Journal, UST., Vol. 4 & 5 No. 1, 2005-2006 & 2006-2007, pp. 95-99


·        Indoor Air Quality of Beato Angelico Building of the University of Santo Tomas -Commissioned by UST (Nov. 2009-May 2010)


1. (Money-Making Secrets)
2.   (Internet Marketing Secrets)
3.  (The Painting Doctor-“Restorer/Conservator”)
4.  (Research assistance/Thesis Assistance/Thesis Editing)
5. (LET Review by a LET Topnotcher and Veteran Reviewer)
6. (Lotto Secrets Revealed!)
7. (Muscle Building Cookbook)
8. (Wedding Photography Secrets)
9. (Food Cart Franchise Business)
10. (St. Peter Life Plan and Memorial Chapels)
11. ( Art and Craft Materials for Sale At Low Price!)
12. (Cleaning and Restoration of Paintings)
13.  (Natracare Food Supplements)
14. (LET Reviewer Books)
15. (How to Lose Weight Fast!)
16. ( How to Stop Hair Loss and Regrow It the Natural Way)
17.  (How to Get Pregnant Fast!)
18.  (Condo for Rent at 39K Infinity Tower, Global City, Taguig)


  • Instructor 5, CFAD, IPEA, Pharmacy, CTHM, University of Santo Tomas
SY 1995-Present
Subjects taught: Organic Chemistry lab., Statistics, College Algebra,
                           Algebra with Trigonometry, Business Math, Physics,
                          Plane & Solid Geometry, Environmental Science, Biology
  • Part Time Instructor, Our Lady of Perpetual Help College, Manila
Subjects taught: Food Microbiology (Lecture and Laboratory)                                                                                                         
  • Part Time Instructor, St. Paul’s College, Quezon City
Subjects taught: Lec. & Lab: General Microbiology, Biochemistry, Microtechnique

  • Part Time Instructor, Unciano Colleges and General Hospital, Inc., Manila
Subjects taught: Lec. & Lab: General Microbiology and Parasitology, Inorganic Chemistry,
                          Comparative Anatomy, Botany, Organic Chemistry, General Zoology,
                          Biology, Biochemistry


·         Editor and Professional Consultant, MET Publishing House, Manila
·         Microbiologist, Silver Swan Manufacturing Inc.,Panghulo, Malabon
·         Biochemist, Watercare Philippines, Inc., Valenzuela City
·         Food Production Researcher(Mushroom Culture), TWH, Inc., Cainta Rizal
·         Review Director for LET, Center for Educational Excellence, Inc.
·         Project Consultant on “Biodeterioration of Artworks”, Paper Conservation Laboratory, Archives Dept., Arzobispado de Manila
Projects: Conservation of paintings by Fernando Amorsolo, Botong Francisco,
               Ben Cab, Cezar Legaspi, Simon Flores, Betsy Westerndorp
·         Licensure Exams For Teachers (LET) Reviewer at:
- Malabon City University,MET Review Center, UST-College of Education, Caloocan   Polytechnic College, Trinity College, & Center for Educational Excellence Inc.


  • Beato  Angelico Service Award
  • 10th Placer (85.60%), Licensure Examinations for Teachers (LET)
  • Full College Scholarship by Lourdes Reyes Foundation
  • Professional Civil Service Examinations, weighted ave: 86.49%
  • Valedictorian, High School
  • Salutatorian, Elementary
  • Certificate of Appreciation as resource speaker on the topic “Visual Arts and Restorations”, Faculty-Student Art Forum, Beato Angelico Bldg.,UST.
  • Recognition Award for invaluable support and committed service to HARIBON UST as adviser from 2002-2004
  • Honored as 4th Degree(highest degree) member of the Knights of Columbus
 Given by Philippine District IV-NCR
·            Loyalty and Faithful Award for 13 years of Service
 Knights of Columbus UST- Faculty Council 4321
·            Dedicated and Competent Service Award as LET Reviewer
 Malabon City University                                                                                           
·            Champion, Pautakan Quiz Bee for Coaches, UST                                                          
·            Family of the Year Award
            Knights of Columbus UST Faculty Council 4321
·         UST Graduate School Thesis Writing Grant
  UST Graduate School Alumni Association
·         Certificate of Recognition for invaluable Contribution as Lecturer/Reviewer
 Pilot Project on Review Classes for Licensure Examinations for Teachers
 College of Education, UST                                                   
·      Certificate of Appreciation as guest speaker on the topic “Products that Cause Cancer”, given by NEWAYS International (Phils.), Makati City



  • Seminar on Test and Measurement Evaluation
  • Seminar on Principles/Philosophy of Education
·        Faculty Development Seminar
  • Traditional Filipino Art
  • Curriculum Development                                                
  • Rubrics Development Across Disciplines                                         
  • Certificate on Adobe Photoshop
  • Certificate on PC Troubleshooting and Networking
  • The Ethics of Teaching
  • Rights and Responsibilities of the Faculty Members, Academic and Administrative Officials and Office Staff Seminar                                                   
  • UST-CFAD Planning and Development Seminar
  • Shepherding the Shepherds
  • Workshop on Syllabus Construction                                                                        
  • Textbook and Learning Materials Development
  • Computer Literacy on Adobe Illustrator, Photoshop, & MS Excel
  • Symposium on Waste Management
  • Ecological Symposium
  • Bringing Out the Best in Me and the Best in You
  • Integrating Media in Classroom Instruction( Design, Production, and Utilization of Media)
  • Principles and Methods of Humane Educators
  • Certificate on Basic Industrial Electronics
  • Certificate on Information Technology
  • Symposium on the Preservation of our Environment
·         Research Colloquia on Indoor Air and Water Quality in Relation to Building Design
·         Convention of Philippine Association of Academic Biochemists,          
  • 16th Annual Convention of Philippine Biochemical Society
  • Script Writing Workshop
  • Basic Business and Financial Management                                                             


  • Member, CFAD- Adhoc Committee on Math Department
  • Member, CFAD-Committee on Environmental Advocacy
  • Member, CFAD-Adhoc Committee on Value Formation
  • Board of Director
Philippine Association  for the Scientific Conservation of Cultural Properties   
  • Deputy Grand Knight, Knights of Columbus UST Faculty Council No. 4321
  • Auditor
College of Fine Arts & Design Faculty Association
  • Adviser, HARIBON UST
  • Business Manager, NOH-SCC Alumni Association
  • Member, Outreach Program Committee
College of Architecture and Fine Arts


English, Filipino, Italian, Japanese


  • Thesis Editing/Research Assistance
  • Computer operation using MS Word, Excel, Powerpoint, Adobe Photoshop, Internet
  • Computer Hardware repair and Software installations
  • Website/Blog Construction
  • Photography
  • Swimming
  • Playing Banduria
  • Singing
  • Riding ATV

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