[STAT 311] - Midterm Exam Guide - Everything you need to know! (36 pages long)

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STAT 311
MIDTERM EXAM
STUDY GUIDE
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January 17, 2017
Introduction to Statistics
What is Statistics?
“The science of using information discovered from collecting, analyzing, and organizing
numbers (data)”
-Cambridge Academic Dictionary
“The mathematics of the collection, organization, and interpretation of numerical data,
especially the analysis of population characteristics by inference from sampling.”
-American Heritage Dictionary
“The science that deals with the collection classification, analysis, and interpretation of
numerical facts or data, and that, by use of mathematical theories of probability, imposes order and
regularity on aggregates of more or less disparate elements.”
-Random House Dictionary
“Less dry definition: there is a thing called “reality”. It is incomprehensibly complex. It
produces observable information that we call “data”. Statistics is the process by which we use that
data to try and learn something about reality. It is imperfect and limited and our answers are always
wrong. But we do our best.
Simple example: summarizing data. This can be done visually (with graphs) or with numbers
(actual data). Both are approximations of the underlying reality.
We might want to use data to learn about a quantity that is unknown or practically
unknowable.
For instance, how many trees are there in the Rocky Mountain National Park? No one
knows, but we can gather data to approximate an answer.
Wise Words
“I believe that it would be worth trying to learn something about the world even if in trying
to do so we should merely learn that we do not know much. This state of learned ignorance might
be a help in many of our troubles. It might be well for all of us to remember that while differing
widely in the various little bits we know, in our infinite ignorance we are all equal.”
-Karl Popper, “Knowledge Without Authority,” 1960
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Uncertainty is rampant. We use statistics to answer questions about things that are unknown
(e.g., the number of trees in the Rocky Mountain National Park), but just as importantly, we use
statistics to get an idea of how sure we are of our answers.
Quantifying uncertainty is critical in statistics. We can use our data to estimate the value of
an unknown quantity; we can (and should) also use our data to estimate how wrong we think our
estimate is. And this estimate of how wrong we are about our estimate will also be wrong.
Uncertainty will be a theme of this class. “We can’t really know for sure” will underlie the
answers to all our questions. Statistical tools allow us to make the most of our limited information.
We do the best we can with what we have.
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