1. Variables and Types of Data
Chapter 1.2
Variables and Types of Data

2. 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

3. 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

4. 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

5. Classify each zoo themed quantitative variable as a Discrete or Continuous
Number of birds in an aviary
Age of an African elephant
Pounds of food eaten by a lion per day
Temperature in the penguin habitat
Amount of visitors during the month of September
Number of births of baby animals in 2015

6. Continuous Variables Boundaries
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 – sec
Mass
1.6 grams
1.55 – 1.65 g

7. Write the boundaries for each number:8
5.5
127
2.34

8. 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

9. 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

10. 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

11. 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°)

12. 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

13. 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)

14. 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

15. Try it!
Applying the Concepts
Pg. 9 #1-7