Math 1530

Unit 1 Describing Data

1.2 Data Classifications

Types of Data

Quantitative Data:

measures or counts expressed as numbers .

Discrete data result when the number of possible values is countable.
example: The number of eggs a hen lays.
Continuous data has an infinite number of possible values within a selected range.
example: The amount of milk that a cow produces. An example is $2.343115$ gallons per day

Qualitative Data

(Categorical Data): names or labels representing categories

Example: The color of a cat’s fur
Example: The number on an athletic jersey
Example: Customer satisfaction ratings

Levels of Measurement

Nominal:

Put in a category.

Qualitative data. Cannot be arranged in an ordering scheme (low to high).
No arithmetic can be carried out on the data.
Example: survey responses: yes, no, undecided

Ordinal:

Put in a category and put in order.

Qualitative or Quantitative data. Can be arranged in some order.
Differences between data values cannot be determined or are meaningless.
Example: Course grades: A, B, C, D, F

Interval:

Put in a category, put in order, and find differences between values.

Quantitative data. Can be arranged in some order.
Differences between data values can be determined and are meaningful.
There is no natural zero (does not make sense to say you have none).
Example: Years: 1000, 2014, 1776

Ratio:

Put in a category, put in order, find differences between values, and find ratios of values.

Quantitative data. Can be arranged in some order.
Differences between data values can be determined and are meaningful.
There is a natural zero (it makes sense to say you have none).
Division makes sense: You can say one is twice as much as another.
Example: Price of textbooks. $100, $25, $0

Identifying Types of Data

Identify the variable(s) if a study was conducted to answer each question, and classify the variables as qualitative (categorical) or quantitative (numerical).
1. Can eating a yogurt a day cause you to lose weight? quantitative
2. Does louder music cause people to drink more beer? quantitative
3. Are lions more likely to attack after a full moon? quantitative

Explore the Graph Below

World Health and Income Map

Coordinate plane with income on the x-axis and health on the y-axis. Income is measured in GDP per capita and health is measured in life expetency in years. The countries of the world are representd with circles on the graph.

What types of data are being shown in this graph?
- Nominal
  region (shown by color), country names
- Ordinal
  Income levels
- Interval
- Ratio
  GDP per capita, Life expectancy, population
Brainstorm for a variable in a different study that would be at the Interval level of measurement.
Which level of measurement is the number in a street address? a zip code?