1. 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.”

2. 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).

3. 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

4. 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

5. 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

6. 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

7. 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.

8. 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.

9. Sampling Methods  Sampling Frame  Representative  Biased and Unbiased  Sampling Methods –Convenience –Volunteer –Judgment –Probability (“random”)

10. Probability Sample Designs  Simple Random Sample  Systematic Sample  Stratified –Proportional (Quota)  Cluster

11. 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

12. 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!