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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.”


Stat 281 introduction to probability and statistics
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!