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8/13/2019 Overview and Nature of Data
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STATISTICS AND
MEASUREMENTSOVERVIEW: NATURE OF DATA
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OVERVIEW
Statistics
Two Meanings
Specific numbers
Method of analysis
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STATISTICS
SPECIFIC NUMBERS
measurement determ
of data
METHOD OF ANALYSIS
of methods for p
experiments, obtaininthen then organizing, s
presenting, analyzing,
and drawing conclusio
the data
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STATISTICS
Specific number - numericalmeasurement determined by of data
Example: Twenty-three percenpeople surveyed believed thatlearning statistics is difficult.
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STATISTICS
Specific number
Example:Her vital statistics are: 34-24-
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STATISTICS
Method of analysis : a collection of method
(1) planning experiments,(2) obtaining data, and then
(3) organizing,
(4) summarizing,
(5) presenting,
(6) analyzing,
(7) interpreting, and
(8) drawing conclusions based on the data
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Two Broad Areas
STATISTICS
(Collection,Organization, Summary,
Presentation, Analysis
and
Interpretation of Data)
DESCRIPTIVE
-deals with processing data without atteany inferences/conclusions from them. representation of data in the form of tabto the description of some characteristi
such as averages and deviati
INFERENTIAL
-is a scientific discipline concerned witand using mathematical tools to make f
inferences. Basic to the developmunderstanding of inferential/inductive st
concepts of probability theor
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THE NATURE OF DA(LEVELS OF)MEASUREME
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DEFINITIONS
DATA
QUALITATIVE
(CATEGORICAL)
OR
(ATTRIBUTE)
consist of attribor non-numer
QUANTITATIVE
(NUMERICAL)
consist of nmeasurement
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Classifying Data by Type
The suggested retail prices of several Ford vehicles are shotable. Which data are qualitative data and which are quant
Model Suggested RetailPrice
Focus SedanFusion
MustangEdgeFlexEscape HybridExpeditionF-450
$15,995$19,270
$20,995$26,920$28,495$32,260$35,085$44,145
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Classifying Data by Type
The populations of
several regions inPhilippines are shown inthe table. Which dataare qualitative data andwhich are quantitativedata? Identifythe two
data sets. Decidewhether each data setconsists of numericalornon-numericalentries.Specify the qualitativedata and the
quantitativedata.
A B C D
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Levels of Measurements Another common way of classifying data is to u
levels of measurement: nominal, ordinal, interv
ratio. In applying statistics to real problems, thmeasurement of the data is an important factordetermining which procedure to use. Never docomputations and never use statistical methodsthat are NOT appropriate.
For example, it would not make sense to compuaverage of social security numbers, because thnumbers are data that are used for identificatiodont represent measurements or counts of any
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TYPES OF DATA
Qualitative
Categorical or Attribute data
can be separated into different categories that aredistinguished by some nonnumeric characteristic
NOMINAL
ORDINAL
QuantitatConsist of numbers rep
or measurem
INTERVA
RATIO
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DEFINITIONS
nominal level of measurement characterized
that consist of names, labels, or categories data cannot be arranged in an ordering scheas low to high)
Data at the nominal level of measurementaqualitative only. Data at this level are categ
using names, labels, or qualities. No mathecomputations can be made at this level.
Example: survey responses yes, no, undecid
Gender (male or female)
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DEFINITIONS
ordinal level of measurement involves da
may be arranged in some order, but diffebetween data values either cannot be deor are meaningless
Data at the ordinal level of measuremen
qualitative or quantitative. Data at this lebe arranged in order, or ranked, but diffebetween data entries are not meaningfu
Example: Course grades A, B, C, D, or F
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Two data sets are shown. Which data set consists of data at level? Which data set consists of data at the ordinal level?
Data 2
VHF Philippine Televisio
1. ABS-CBN TV-22. Peoples Television Netw3. ABC Development Corp
4. GMA Network Inc. TV-75. Radio Philippine Netwo
Entertainment TV-96. Intercontinental Broadc
Corporation TV-13
Data 1
Top 5 Grossing Movies of 2012
1. Marvels The Avengers2. The Dark Knight Rises
3. The Hunger Games4. Skyfall5. The Twilight Saga: Breaking
Dawn Part 2
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Example: In 2012, Business Insider chose the 50 best businethe world. Business Insider based it on an extensive survey thousand professionals (n > 1000) of which 87 percent had abusiness school and 71 percent had hiring experience.
What is the level of measurement?
Business Insider Worlds Top 5 Business Scho
1. Stanford University2. Harvard University3. University of Pennsylvania (Wharton)
4. Massachusetts Institute of Technology (Sloan5. London Business School
Example: Mathematics students can take elective courses that r
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Example: Mathematics students can take elective courses that rlinear algebra to math structures for computer science. Graduat
jobs in statistics, teaching, and many other professional fields. Tworld's best universities for mathematics
What is the level of measurement?
US News Worlds Best Mathematics Universitie
Massachusetts Institute of Technology (MIT)Harvard UniversityStanford UniversityPrinceton UniversityUniversity of California Los Angeles (UCLA)
University of California Berkeley (UCB)New York UniversityYale UniversityUniversity of CambridgeUniversity of Oxford
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DEFINITIONS: The two highest levels of meaconsist of quantitative data only.
Data at the interval level of measurembe ordered, and meaningful differencebetween data entries can be calculateinterval level, a zero entry simply rep
position on a scale; the entry is not a or inherent zero.
Example: Years 1000, 2000, 1776, an
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interval level of measurement
Years 1000, 2000, 1776, and 1492
1. Category: [11th, 21st, 18th, 15thCentu
2. Rank/Order: [1000, 1492, 1776, 2000]
3. Difference between two values can becalculated: 1000 1492 = 492
(year 1000 is 492 years earlier than year 1
2000 1776 = 224
(year 2000 is 224 years later than year 17
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Interval Data
1. Category2. Rank
3. Difference bvalues can
4. No inherentis not a sta
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DEFINITIONS: Ratio
Data at the ratio level of measuremen
similar to data at the interval level, wadded property that a zero entry is aninherent or natural zero. A ratio of twvalues can be formed so that one datcan be meaningfully expressed as a mof another.
Example: Prices of college textbooks
DEFINITIONS R ti
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DEFINITIONS: Ratio Example: Prices of college textbooks in Pesos: 100, 400, 6
1. Category: [Php100, Php400, Php600 and Php800 Books
2. Rank/Order: Cheapest to Most expensive3. Difference between two values:
400 100 = 300 (a 400-peso book is 300 pesos more expen100-peso book)
400 650 = 250 (a 400-peso book is 250 pesos cheaper thpeso Book
4. Inherent Zero (Zero as starting point)
400 100 = 4 (A 400-peso book is 4 times more expensive tpeso book
100 400 = 0.25 (Less than 1)
(A 100-peso book is 4 times cheaper than a 400-peso book)
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DEFINITIONS: Ratio
Examples: (ratio data)
Height: A person whose height of 66 incis twice as tall than a child whose heiginches tall.
Weight: A person who weighs 60 kilos itimes as heavy as a child who weighs
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The two highest levels of measurement coquantitative data only.
An inherent or natural zero is a zero thatnone. For instance, the amount of monhave in a savings account could be zero this case, the zero represents no moneyinherent or natural zero.
On the other hand, a temperature of 0oCrepresent a condition in which no heat isThe temperature is simply a position on Celsius scale; it is not an inherent or nat
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DEFINITIONS: The two highest levels of meaconsist of quantitative data only.
To distinguish between data at the intlevel and at the ratio level, determinethe expression twice as much has ameaning in the context of the data. Fo
example, 2 pesos is twice as much asso these data are at the ratio level. Oother hand, 20oC is not twice as warmso these data are at the interval level
The following tables summarize which operatio
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The following tables summarize which operatiomeaningful at each of the four levels of measuWhen identifying a data sets level of measurethe highest level that applies.
Level ofMeasurement
Put data inCategories
Arrangedata inorder
Subtractdata values
NominalOrdinalIntervalRatio
YESYESYESYES
NOYESYESYES
NONOYESYES
Summary of Four Levels of Measurement
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Summary of Four Levels of Measurement
Level Example of a Data Set Meaningf
Nominal Level(Qualitative)
Types of Shows Televised bya Network
Comedy,Documentaries,Drama,Cooking,
Reality Shows,Sports,Soap Operas,Talk Shows
Put in a ca
A show tenetwork cinto one ocategories
Summary of Four Levels of Measurement
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Summary of Four Levels of Measurement
Level Example of a Data Set MCa
Ordinal Level(Qualitative or
Quantitative)
Motion Picture Association ofAmerican Ratings Description
G General AudiencesPG Parental Guidance
SuggestedPG-13 Parents Strongly CautionedR RestrictedNC-17 No One Under 17 Admitted
Put in and pu
A PG rstrong
than aLikewhas a restricPG rat
Summary of Four Levels of Measurement
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Summary of Four Levels of Measurement
Level Example of a Data Set MCa
Interval Level
(Quantitative)
Average Monthly Temperatures (indegrees Fahrenheit) for DenverColorado
January 29.2 July 73.4February 33.1 August 71.7March 39.6 September 62.4April 47.6 October 51.0May 57.2 November 37.5June 67.6 December 30.3
Put in aput it infind difbetwee
57.2
May is than Ap
30.3 Decemcolder t
Novem
Summary of Four Levels of Measurement
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Summary of Four Levels of Measurement
Level Example of a Data Set Meaningf
Ratio Level(Quantitative)
Average Monthly Gross Income
(millions) for McDonalds
January 2.4 July 7.2February 2.4 August 6.3March 3.5 September 5.8
April 2.4 October 2.7May 3.7 November 2.3June 7.4 December 2.3
Put in a cate
order, find dbetween varatios of val
7.4 3.7 = June has 3.more gross
May
(7.4)/(3.7) There is twigross incomMay
DEFINITIONS
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DEFINITIONS
Population (N): the completecollection of all elements (scopeople, measurements, and sto be studied. The collection icomplete that it includes allsubjects to be studied.
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Population
Study Unit
Target Population
The whole group of study units w
interested in applying our infeconclusions
Study Population (Samp
The group of study units to whlegitimately apply our infereconclusions
DEFINITIONS
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DEFINITIONS
A population can be finite(Countable)) o(Cannot be Counted) and is made up of s
units
Unfortunately the target population is noreadily accessible, and we can study onlypart of it that is available.
There are many ways to collect informatithe study population. One way is to condsample. A sample(n)is a sub-collection omembers selected from a population.
DEFINITIONS
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DEFINITIONS
DEFINITIONS
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DEFINITIONS
The
reprePOPU
The
pizzaSAMPopu
DEFINITIONS
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DEFINITIONS
The
reprPOP
The
pizzSAMPop
DEFINITIONS
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DEFINITIONS Example: A fisheries researcher is interested in the b
pattern of a crab along the coast of the Lingayen Gulfbe unthinkable and impossible to investigate every cr
individually. The only way to make any kind of educaabout their behaviour would be by examining a smallcollection, that is, a sample.
Example: Suppose a machine has produced 10,000 e
and we are interested in getting some idea about howbulbs will last. It would not be practical to test all thebecause the bulbs that are tested will never reach theSo we might pick 50 of these bulbs to test. Our interelearning about the 10,000 bulbs and we study 50. Thbulbs constitute the population and the 50 bulbs a sa
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