Stat 281: Introduction to Stat 281: Introduction to Probability and StatisticsProbability and Statistics

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

Guard: “What did you get for a sentence?”Guard: “What did you get for a sentence?”Prisoner: “I could choose life or 100 years.”Prisoner: “I could choose life or 100 years.”Guard: “And what did you choose?”Guard: “And what did you choose?”Prisoner: “Well, life, obviously. Statistically Prisoner: “Well, life, obviously. Statistically speaking, that is the shorter sentence.”speaking, that is the shorter sentence.”

Hmmm…Hmmm…

A statistician is a mathematician A statistician is a mathematician broken down by age and sex.broken down by age and sex.

Did you hear the one about the Did you hear the one about the statistician? Probably….statistician? Probably….

Statistics means never having to say Statistics means never having to say you’re certain (or wrong).you’re certain (or wrong).

Seriously, though…Seriously, though…

Definitions are crucial in stats class.Definitions are crucial in stats class.If you don’t know the precise meaning of If you don’t know the precise meaning of a word, the whole point of the a word, the whole point of the sentence/paragraph/chapter could be sentence/paragraph/chapter could be lost!lost!

Concepts are important in stats class.Concepts are important in stats class.– Lots of formulas—don’t plug in numbers Lots of formulas—don’t plug in numbers

blindly—understand whyblindly—understand why– Review and integrateReview and integrate

DefinitionsDefinitions

Data (is/are?)Data (is/are?) Population (of? Not a number)Population (of? Not a number)

Finite/Infinite/Practically InfiniteFinite/Infinite/Practically Infinite Sample (proper subset, finite)Sample (proper subset, finite) Variable (response, random)Variable (response, random) Parameter/StatisticParameter/Statistic

Greek/LatinGreek/Latin Experiment/Observational StudyExperiment/Observational Study

Probability vs. StatisticsProbability vs. Statistics

Probability: Properties of population Probability: Properties of population are known. Make predictions about are known. Make predictions about sample.sample.

Statistics: Sample is known. Guess Statistics: Sample is known. Guess (estimate) properties of population.(estimate) properties of population.

Statistics (is/are?)Statistics (is/are?)– DescriptiveDescriptive– InferentialInferential

Types of Data (Variables)Types of Data (Variables)

Categorical (Class, Attribute, Categorical (Class, Attribute, Qualitative)Qualitative)

Numeric (Quantitative)Numeric (Quantitative)– Discrete (Finite or Infinite)Discrete (Finite or Infinite)

Note: Finite/Infinite values, not populationsNote: Finite/Infinite values, not populations

– Continuous (always Infinite)Continuous (always Infinite) Measurement ScalesMeasurement Scales

– NominalNominal– OrdinalOrdinal– IntervalInterval– RatioRatio

Identify the Data TypesIdentify the Data Types

1.1. The daily high temperature (°F) in Brookings.The daily high temperature (°F) in Brookings.2.2. The make of automobile driven by each student.The make of automobile driven by each student.3.3. The defect status of 9 volt batteries being tested.The defect status of 9 volt batteries being tested.4.4. The weight of a lead pencil.The weight of a lead pencil.5.5. The length of time billed for a long distance call.The length of time billed for a long distance call.6.6. Which brand of cereal children eat for breakfast.Which brand of cereal children eat for breakfast.7.7. The genre of a book checked out of the library.The genre of a book checked out of the library.8.8. The time until a pain reliever begins to work.The time until a pain reliever begins to work.

VariationVariation

No matter what the response No matter what the response variable: there will always be variable: there will always be variabilityvariability in the data. in the data.

One of the primary objectives of One of the primary objectives of statistics: measuring and statistics: measuring and characterizing variability.characterizing variability.

Controlling (or reducing) variability in Controlling (or reducing) variability in a manufacturing process: statistical a manufacturing process: statistical process control.process control.

Sampling MethodsSampling Methods

Sampling FrameSampling Frame RepresentativeRepresentative Biased and UnbiasedBiased and Unbiased Sampling MethodsSampling Methods

– ConvenienceConvenience– VolunteerVolunteer– JudgmentJudgment– Probability (“random”)Probability (“random”)

Probability Sample DesignsProbability Sample Designs

Simple Random SampleSimple Random Sample Systematic SampleSystematic Sample StratifiedStratified

– Proportional (Quota)Proportional (Quota) ClusterCluster

The Role of StatisticsThe Role of Statistics Central to scienceCentral to science

– Observation and experimentation must Observation and experimentation must culminate with dataculminate with data

– Hypotheses are evaluated based on results Hypotheses are evaluated based on results (data)(data)

– Correct conclusions are only possible if data Correct conclusions are only possible if data are collected correctly and analyzed correctlyare collected correctly and analyzed correctly

Central to many business, industry, and Central to many business, industry, and government activities.government activities.

Anybody who has to make objective Anybody who has to make objective decisions needs statistics.decisions needs statistics.

Statistical thinking trains us to distinguish Statistical thinking trains us to distinguish coincidences from meaningful patternscoincidences from meaningful patterns

Are you above average?Are you above average?

The vast majority of people have The vast majority of people have more than the average number of more than the average number of legs.legs.

““When she told me I was average, When she told me I was average, she was just being mean.”she was just being mean.”

You know how dumb the average You know how dumb the average person is? Well, half the population person is? Well, half the population is dumber than that!is dumber than that!