overview and nature of data

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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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



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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



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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



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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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overview and nature of data

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