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Stat 281: Introduction to Probability and Statistics. A prisoner had just been sentenced for a heinous crime and was returned to his cell. An inquisitive guard could not wait to ask him about the outcome. Guard: “What did you get for a sentence?” Prisoner: “I could choose life or 100 years.”

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stat 281 introduction to probability and statistics

Stat 281: Introduction to Probability and Statistics

A prisoner had just been sentenced for a heinous crime and was returned to his cell. An inquisitive guard could not wait to ask him about the outcome.

Guard: “What did you get for a sentence?”

Prisoner: “I could choose life or 100 years.”

Guard: “And what did you choose?”

Prisoner: “Well, life, obviously. Statistically speaking, that is the shorter sentence.”

slide2
Hmmm…
  • A statistician is a mathematician broken down by age and sex.
  • Did you hear the one about the statistician? Probably….
  • Statistics means never having to say you’re certain (or wrong).
seriously though
Seriously, though…
  • Definitions are crucial in stats class.

If you don’t know the precise meaning of a word, the whole point of the sentence/paragraph/chapter could be lost!

  • Concepts are important in stats class.
    • Lots of formulas—don’t plug in numbers blindly—understand why
    • Review and integrate
definitions
Definitions
  • Data (is/are?)
  • Population (of? Not a number)

Finite/Infinite/Practically Infinite

  • Sample (proper subset, finite)
  • Variable (response, random)
  • Parameter/Statistic

Greek/Latin

  • Experiment/Observational Study
probability vs statistics
Probability vs. Statistics
  • Probability: Properties of population are known. Make predictions about sample.
  • Statistics: Sample is known. Guess (estimate) properties of population.
  • Statistics (is/are?)
    • Descriptive
    • Inferential
types of data variables
Types of Data (Variables)
  • Categorical (Class, Attribute, Qualitative)
  • Numeric (Quantitative)
    • Discrete (Finite or Infinite)
      • Note: Finite/Infinite values, not populations
    • Continuous (always Infinite)
  • Measurement Scales
    • Nominal
    • Ordinal
    • Interval
    • Ratio
identify the data types
Identify the Data Types

1. The daily high temperature (°F) in Brookings.

2. The make of automobile driven by each student.

3. The defect status of 9 volt batteries being tested.

4. The weight of a lead pencil.

5. The length of time billed for a long distance call.

6. Which brand of cereal children eat for breakfast.

7. The genre of a book checked out of the library.

8. The time until a pain reliever begins to work.

variation
Variation
  • No matter what the response variable: there will always be variability in the data.
  • One of the primary objectives of statistics: measuring and characterizing variability.
  • Controlling (or reducing) variability in a manufacturing process: statistical process control.
sampling methods
Sampling Methods
  • Sampling Frame
  • Representative
  • Biased and Unbiased
  • Sampling Methods
    • Convenience
    • Volunteer
    • Judgment
    • Probability (“random”)
probability sample designs
Probability Sample Designs
  • Simple Random Sample
  • Systematic Sample
  • Stratified
    • Proportional (Quota)
  • Cluster
the role of statistics
The Role of Statistics
  • Central to science
    • Observation and experimentation must culminate with data
    • Hypotheses are evaluated based on results (data)
    • Correct conclusions are only possible if data are collected correctly and analyzed correctly
  • Central to many business, industry, and government activities.
  • Anybody who has to make objective decisions needs statistics.
  • Statistical thinking trains us to distinguish coincidences from meaningful patterns
are you above average
Are you above average?
  • The vast majority of people have more than the average number of legs.
  • “When she told me I was average, she was just being mean.”
  • You know how dumb the average person is? Well, half the population is dumber than that!
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