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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

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
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)
try it
Try it!
  • Pg. 9 #1-7
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