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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
– Nominal
– Ordinal
– Interval
– Ratio
Scales
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!