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Chapter 1.2. Variables and Types of Data. Variables. Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. Example: gender Quantitative variables are numerical and can be ordered or ranked. Example: age.

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Chapter 1.2

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Chapter 1 2

Chapter 1.2

Variables and Types of Data


Variables

Variables

  • Qualitative variables are variables that can be placed into distinct categories, according to some characteristic or attribute. Example: gender

  • Quantitative variables are numerical and can be ordered or ranked. Example: age


Classify each variable as quantitative or qualitative

Classify each variable as Quantitative or Qualitative

  • Marital status of teachers in the school

  • Time it takes to complete a test

  • Weight of tiger cubs at birth in a zoo

  • Colors of cars for sale at a dealership

  • SAT score

  • Ounces of soda in a cup


Discrete vs continuous

Discrete vs. Continuous

Quantitative variables can be classified into two groups: discrete and continuous.

  • Discrete variables assume values that can be counted. Example: number of students in a class

  • Continuous variables can assume an infinite number of values between any two specific values. They are obtained by measuring. Often including fractions and decimals. Example: temperature


Continuous v ariables boundaries

Continuous Variables Boundaries


Measurement scales

Measurement Scales

  • Measurement scales classify variables by how they are categorized, counted, or measured. Example: area of residence, height

  • The four common types of scales that are used are:

    nominal, ordinal, interval, and ratio


Nominal level of measurement

Nominal Level of Measurement

  • Classifies data into mutually exclusive (nonoverlapping) categories in which no order or ranking can be imposed on the data

    Examples:

  • Gender

  • Zip code

  • Political party

  • Religion

  • Marital status


Ordinal level of measurement

Ordinal level of Measurement

  • Classifies data into categories that can be ranked, however, precise differences between the ranks do not exist

    Examples:

  • First, second, third place

  • Superior, average, or poor

  • Small, medium, or large


Interval level of measurement

Interval level of Measurement

  • Ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero

  • Different from ordinal because precise differences do exist between units

    Examples:

  • IQ (no zero because it does not measure people without intelligence)

  • Temperature (no zero because temperature exists even at 0°)


Ratio level of measurement

Ratio level of Measurement

  • Possesses all the characteristics of interval measurement, and there exists a true zero. In addition, true ratios exist when the same variable is measured on two different members of the population

    Examples:

  • Height

  • Weight

  • Area


Agreement

Agreement?

There is not complete agreement among statisticians about classification of data. And data can be altered so that they fit into different categories.

Examples:

  • Income: low, medium high (ordinal) or $100,00,

    $45, 000, etc. (ratio)

  • Grade: A, B, C, D, F (ordinal) or 100, 90, 80, etc. (interval)


Classify each variable as nominal ordinal interval or ratio

Classify each variable as nominal, ordinal, interval, or ratio


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Try it!

  • Pg. 9 #1-7


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