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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
Variables
1. Marital status of teachers in the school2. Time it takes to complete a test3. Weight of tiger cubs at birth in a zoo4. Colors of cars for sale at a dealership5. SAT score6. Ounces of soda in a cup
Classify each variable as Quantitative or Qualitative
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
Discrete vs. Continuous
Variable Recorded Value Boundaries
Length 15 cm 14.5 – 15.5 cm
Temperature 86 degrees Fahrenheit
85.5 – 86.5° F
Time 0.43 seconds 0.425 – 0.435 sec
Mass 1.6 grams 1.55 – 1.65 g
Continuous Variables Boundaries
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
Measurement Scales
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
Nominal 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
Ordinal 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°)
Interval 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
Ratio level of Measurement
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)
Agreement?
Classify each variable as nominal, ordinal, interval, or
ratio
Judging a costume contest (1st, 2nd, 3rd)
Time Age
Eye Color SAT score Nationality
Gender Grade (A, B, C, D, F) Temperature
Salary IQ Rating Scale (poor, fair, good, excellent)
College Major Area Code Height