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TYPES OF DATA - Full of my life with mathematics only · PDF fileTYPES OF DATA 4 Quantitative Data ... a “countable” number. ... EXAMPLE: the number of bedrooms in a house, or

May 03, 2018

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  • TYPES OF DATA

  • IS STATISTICS 100% CORRECT?

    2

  • Secondary Data Compilation

    Observation

    Experimentation

    Print or Electronic

    Survey

    Primary

    Data Collection

    DATA SOURSES

    3

    3

  • Data

    Categorical

    Numerical

    Discrete Continuous

    Examples:

    Marital Status

    Political Party

    Eye Color

    (Defined categories) Examples:

    Number of Children

    Defects per hour

    (Counted items)

    Examples:

    Weight

    Voltage

    (Measured characteristics)

    TYPES OF DATA

    4

  • Quantitative Data (Numerical) consists of

    numbers representing counts or

    measurements.

    Qualitative Data (Categorical) can be

    separated into different categories that are

    distinguished by some nonnumeric

    characteristic.

    DEFINITIONS

    5

  • Discrete Data result when the number of

    possible values is either a finite number or

    a countable number.

    Continuous Data result from infinitely

    many possible values that correspond to

    some continuous scale that covers a range

    of values without gaps.

    DEFINITIONS

    6

  • A variable - a characteristic of a population or a sample, e.g.

    Examination marks

    Stock price

    The waiting time for medical services

    Data - Observed values of variables

    WHAT IS A VARIABLE?

    7

  • EXAMPLE

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    Data - Observed values of variables

    46 49 46 48 45 49 46 45 47 43

    45 46 44 47 44 45 49 46 42 47

    46 44 42 45 46 46 42 45 41 47

    48 43 43 49 40 44 46 43 45 44

    41 47 43 47 48 42 44 48 48 45

    Scores on a Test

  • TYPES OF VARIABLES

    A. Qualitative or Attribute variable - the characteristic being studied is nonnumeric.

    EXAMPLES: Gender, religious affiliation, type of automobile owned, state of birth, eye color are examples.

    B. Quantitative variable - information is reported numerically.

    EXAMPLES: balance in your checking account, minutes remaining in class, or number of children in a family.

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  • QUANTITAIVE VARIABLES

    Classifications

    Quantitative variables can be classified as either discrete or continuous.

    A. Discrete variables: can only assume certain values and there are usually gaps between values.

    EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local

    Home Depot (1,2,3,,etc).

    B. Continuous variable can assume any value within a specified range.

    EXAMPLE: The pressure in a tire, the weight of a pork chop, or the height of students in a

    class.

    10

  • SUMMARY: TYPES OF VARIABLES

    11

  • Scales of Measurement

    1. Nominal Scale

    Categorical/qualitative observations

    Use number to represent the categories.

    Example: Single=1, Married=2

    2. Ordinal Scale

    Ordered categorical observations

    Value are in order

    Example: Poor-1 Fair-2 Good-3

    3. Interval Scale

    Numerical/quantitative observations

    Numerical bring the meaning of value.

    Example: marks, temperature, IQ

    4. Ratio Scale

    Numerical/quantitative observations

    Have absolute zero value

    Example: weight, height, income

    SCALES OF MEASUREMENT

    12

  • SCALES OF MEASUREMENT

    Nominal level data that is classified into categories and cannot be arranged in any particular order.

    EXAMPLES: eye color, gender, religious affiliation.

    Ordinal level involves data arranged in some order, but the differences between data values cannot be determined or are meaningless.

    EXAMPLE: During a taste test of 4 soft drinks, Mellow Yellow was ranked number 1, Sprite number 2, Seven-up number 3, and Orange Crush number 4.

    Interval level similar to the ordinal level, with the additional property that meaningful amounts of differences between data values can be determined. There is no natural zero point.

    EXAMPLE: Temperature on the Fahrenheit scale.

    Ratio level the interval level with an inherent zero starting point. Differences and ratios are meaningful for this level of measurement.

    EXAMPLES: Monthly income of surgeons, or distance traveled by manufacturers representatives per month.

    13

  • Nominal Scale is characterized by data

    that consists of names, labels, or

    categories only.

    Ordinal Scale data can be arranged in

    some order, but differences between data

    values either cannot be determined or are

    meaningless.

    DEFINITIONS

    14

  • Interval Scale is like the ordinal scale, with additional property that the difference between any two data values is meaningful. However, data at this level do not have a natural zero starting point.

    Ratio Scale is similar to the interval scale with additional property that there is an absolute zero (where zero indicates that none of the quantity is present). In this scale ratios are meaningful.

    DEFINITIONS

    15

  • SUMMARY: SCALES OF

    MEASUREMENT

    16

  • Ratio/Interval data

    Age - income 55 75000

    42 68000

    . .

    . . Weight gain +10

    +5 . .

    Nominal

    Person Marital status Ahmad married

    Siva single

    Ah Keong single . . . . Computer Brand

    1 IBM

    2 Dell

    3 IBM . . . .

    EXAMPLES

    17

  • Ratio/Interval data

    Age - income 55 75000

    42 68000

    . .

    . . Weight gain +10

    +5 . .

    Nominal

    With nominal data,

    all we can do is,

    calculate the proportion

    of data that falls into

    each category.

    IBM Dell Compaq Other Total

    25 11 8 6 50

    50% 22% 16% 12%

    EXAMPLES

    18

  • Knowing the type of data is necessary to properly select the

    suitable technique to be used when analyzing data.

    Type of analysis allowed for each type of data

    Ratio/Interval data arithmetic calculations/Average

    67,74,71,83,93,55,48,82,68,62

    Average=70.3

    Nominal data counting the number of observation/

    frequency in each category

    Single:1 ,Married:2 Divorced:3, Widowed:4

    Data record: 1,2,2,2,4,1,2,2,1,3

    Average=2.0; Does this mean average person is

    married????

    TYPES of DATA TYPES of

    ANALYSIS

    19

  • Solution of Nominal data Category Code Frequency

    Single 1 3

    Married 2 5

    Divorced 3 2

    Widowed 4 4

    Ordinal data - computations based on an ordering process

    TYPES of DATA TYPES of

    ANALYSIS

    20

  • Ratio/Interval*

    Values are real numbers

    All calculations are valid

    Data may be treated as ordinal or nominal

    Example : Examination Marks

    Ordinal

    Value must represent the ranked order of the data

    Calculation based on an ordering process are valid

    Data may be treated as nominal but not as interval

    Nominal

    Value are the arbitrary numbers that represent categories.

    Only calculation based on the frequencies of occurrence are valid.

    Data may not be treated as ordinal or interval

    *Higher-level data type may be treated as lower-level ones.

    HIERARCHY OF DATA

    21

  • This is often a preferred source of data due to low cost and convenience.

    Published data is found as printed material, tapes, disks, and on the Internet.

    Data published by the organization that has collected it is called PRIMARY DATA

    For example: Data published by the US

    Bureau of Census.

    Data published by an organization different than the

    organization that has collected it is called

    SECONDARY DATA.

    For example: The Statistical abstracts of the United States,

    compiles data from primary sources

    Compustat, sells variety of financial data tapes

    compiled from primary sources

    PUBLISHED DATA

    22

  • Observational study is one in which measurements

    representing a variable of interest are observed and

    recorded, without controlling any factor that might

    influence their values.

    Experimental study is one in which measurements

    representing a variable of interest are observed and

    recorded, while controlling factors that might influence

    their values.

    When published data is unavailable, one

    needs to conduct a study to generate the

    data.

    OBSERVATIONAL or

    EXPERIMENTAL

    23

  • Statistical

    Studies

    Do you

    make observations

    only, or do you modify the

    subjects?

    Experiment Observational

    When

    observations

    are made?

    Retrospective

    study

    Prospective

    study

    Cross-sectional

    study

    Past

    At

    one

    point

    Future Design:

    1. Control effects of variables

    2. Use replication

    3. Use randomization

    STATISTICAL STUDIES

    24

  • IS STATISTICS 100% CORRECT?

    25

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