Chapter 1.2

Variables and Types of Data

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

Pg. 9 #1-7

Try it!