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Stat 281: Introduction to Probability and Statistics

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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

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.”

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…
• 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
• 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: 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)
• 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

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
• 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 Frame
• Representative
• Biased and Unbiased
• Sampling Methods
• Convenience
• Volunteer
• Judgment
• Probability (“random”)
Probability Sample Designs
• Simple Random Sample
• Systematic Sample
• Stratified
• Proportional (Quota)
• Cluster
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?
• 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!