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Statistics

Fundamental Elements of Statistics

Statistical methods are particularly useful for studying, analyzing, and learning about populations of experimental units.

An experimental (or observationalunit is an object (e.g., person, thing, transaction, or event) about which we collect data
population is a set of all units (usually people, objects, transactions, or events) that we are interested in studying.

Examples of populations: 

  1. All students at Centennial
  2. Everybody in Ontario
  3. Every flight leaving Pearson Airport
  4. Every grain of sand on a beach.
variable is a characteristic or property of an individual experimental unit in the population.

Examples of variables:

  1. The student number, program of study, and year of study of Centennial students
  2. The age, current occupation, and number of people in current household of someone in Ontario 
  3. The departure time and destination of flights leaving Pearson.
  4. The size and weight of each grain of sand on a beach.

It is nearly impossible to measure each grain of sand on a bench, so instead of collecting the population, we can estimate using a sample.

sample is a subset of the units of a population.
statistical inference is an estimate, prediction, or some other generalization about a population based on information contained in a sample.

Examples of statistical inferences:

  1. Using the average age of a student of one class to estimate the average age of Centennial students.
  2. The tallest or shortest person of the first 100 people you encounter to estimate the tallest or shortest in Ontario.

However, the accuracy of the statistical inference depends on how reliable it is.

measure of reliability is a statement (usually quantitative) about the degree of uncertainty associated with a statistical inference.
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