Mode of Group and Ungroup Data

Grouped vs. Ungrouped Data
Grouped Data – Data that has been organized into groups (into a frequency distribution).
If you see a table similar to the one below, you will know that you are
dealing with grouped data:

Ungrouped Data – Data that has not been organized into groups.
Ungrouped data looks like a big ol’ list of numbers

How to Group Data
On your exam, you may have to construct a frequency distribution. Constructing a
frequency distribution is the same thing as grouping data.
The first step in grouping data is deciding how large of a class interval to use.
(Class interval = Class size)
There are 2 formulas for determining the appropriate class interval. You must be able to
choose which one would be appropriate for any given problem.

**Don’t forget to always round up to the nearest whole number when dealing with

class interval.**

Mode of Group Data Example:

The size of shirts manufactured by a tailor are as follows
32, 33, 35, 39, 33, 37, 42, 33, 36.
Find the mode of the above data.
Solution:
Let us construct a frequency table for the given data

Here, the frequency of 33 is maximum. Thus, the mode of the data is 33.

You have seen that by just observing the given ungrouped data carefully its mode

can be obtained. However, for grouped data it is not possible to find the mode just

by observation.

For finding the mode of grouped data, first of all we have to determine the modal

class. The class interval whose frequency is maximum is known by this name. the

mode lies in between this class. Then the mode is calculated by the following

formula.

Here,

l = lower limit of modal class

f1 = frequency of modal class

fo = frequency of class preceding the modal class.

f2 = frequency of class succeeding the modal class

h = size of class interval.

Let us understand this method more clearly with the help of an example.

Example:

Find the mode of following data

Solution:

Here frequency of class interval 15 - 20 is maximum.

So, it is the modal class

Now

l = the lower limit of modal class = 15

f1 = frequency of modal class = 7

fo = frequency of class preceding the modal class = 5

f2 = frequency of class succeeding the modal class = 2

h = size of class intervals = 5

So,

Mode = 15 + [(7 - 5) / (2 x 7 - 5 - 2)] x 5

Mode = 15 + [2 / (14 - 7)] x 5

Mode = 15 + (2 / 7) x 5

Mode = 15 + (10 / 7)

Mode = 15 + 1.42

Mode = 16.42

Mode of Ungroup Data Example:

Ungroped Data

Mean of ungrouped data:
Let x₁, x₂, x₃, ..., x_n be n observations then mean is obtained by dividing the sum of n observations by n. It is denoted by
X' = ^åXi/_n
For Eg: Find the mean of 4,6,8,6,7,8
Sol:
Mean X' = ^åXi/_n
= ^{(4 + 6 + 8 + 6 + 7 + 8)}/₆
= ³⁹/₆
= 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
4,6,8,6,7,8,8

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 median of the following observations
4,6,8,6,7,8,8Sol:
In the given data, the observation 8 occurs maximum
number of times (3)
\ Mode(Z) = 8

References:
http://web.grcc.edu/Pr/tutoring/BA254TEST1OUTLINE.PDF
http://www.atozmath.com/Help/HStats.htm
http://www.2classnotes.com/images/uploads/epaper/admin_200912305643.pdf

CRISENCIO M. PANER

CP : 0915-1429675 Email : panercris@gmail.com

EDUCATION

• 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

PUBLICATIONS

Book:

Co-author in LET Reviewer in Biology, 2006-2010 eds. Published by MET Inc.

ISBN # 97193249-6-1, sold in National Bookstores

Articles:

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 20^th 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

RESEARCH WORK

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

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WORK EXPERIENCE

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

OTHER PROFESSIONAL EXPERIENCE

· 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.

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Beato Angelico Service Award
10^th 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 4^th 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

TRAINING /SEMINAR WORKSHOPS

Seminar on Test and Measurement Evaluation

Seminar on Principles/Philosophy of Education

· Faculty Development Seminar

Traditional Filipino Art

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Certificate on Adobe Photoshop
Certificate on PC Troubleshooting and Networking
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Principles and Methods of Humane Educators
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· Research Colloquia on Indoor Air and Water Quality in Relation to Building Design

· Convention of Philippine Association of Academic Biochemists,

16^th Annual Convention of Philippine Biochemical Society
Script Writing Workshop
Basic Business and Financial Management

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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

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English, Filipino, Italian, Japanese

OTHER SPECIAL SKILLS/TALENTS

Thesis Editing/Research Assistance
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Website/Blog Construction
Photography
Swimming
Playing Banduria
Singing
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Mode of Group and Ungroup Data

Saturday, March 24, 2012

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