AP Statistics Curriculum 2007 EDA DataTypes

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General Advance-Placement (AP) Statistics Curriculum - Types of Data

Definitions

  • Population: A population is an entire group, collection or space of objects which we want to characterize.
  • Sample: A sample is a collection of observations on which we measure one or more characteristics. Frequently, we use (small) samples of (large) populations to characterize the properties and affinities within the space of objects in the population of interest. For example, if we want to characterize the US population, we can take a sample (poll or survey) and the summaries that we obtain on the sample (e.g., mean age, race, income, body-weight, etc.) may be used to study the properties of the population, in general.
  • Variable: A variable is a characteristic of an observation that can be assigned a number or a category. For instance, the year in college (variable) of a student (observational unit).

Types of Variables

There are two types of variables: categorical and quantitative these types of variables can be split further.

  • Categorical: Categorical variables are qualitative measurements of samples or populations that are classified into groups:
    • Ordinal categorical variables are qualitative descriptions that have a natural arrangement or order of the measurements -- e.g., rank in college (freshman, sophomore, junior, senior), size of soda (small, medium, large), etc.
    • Not ordinal (or nominal) variable is a categorical variable that does not have a naturally imposed (or meaningful) order of its values -- e.g., gender, race, political affiliation (democrat, republican, independent, green party, other), etc.
  • Quantitative: Quantitative variables are measurements that have a meaningful numerical value representation. There are two types of quantitative variables:
    • Continuous variables indicate numerical observations that contain intervals with infinite (uncountable) possible values - e.g., weight, height, time, speed, etc.
    • Discrete: Discrete variables are also numerical measurements, but they are sparse in space and any interval will contain at most countably many possible values -- e.g., number of students in a school, number of rational numbers in a given interval [a ; b], age, etc.

Example

Most breast cancer patients (>80%) are over the age of 50 at diagnosis. A researcher at a particular New York cancer center believes that his patients are even older than the norm, typically older than 65 years at diagnosis. To investigate, he reviews the ages of a random sample of 100 of his female patients diagnosed with breast cancer.
Identify the following:

  • Population
  • Sample
  • Sample size
  • Variable of interest
  • quantitative or qualitative?
  • Other variables
  • quantitative or qualitative?
  • Observational unit



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