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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

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

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 Variables Boundaries

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

- 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

- 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

- 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

- 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?

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! ratio

- Pg. 9 #1-7

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