### Math 225 Course Notes

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### Chapter 1

#### Contents

Statistics is the science of analyzing data to gain useful information.
We will study two main branches of statistics:

*Descriptive Statistics* includes the techniques of graphical
and numerical summary of data.

*Inferential Statistics* includes methods for reaching decisions
and making estimates about a large group of individuals
on the basis of data from a small sample of the group.

The methods of inferential statistics depend on the assumption
that the observed data is randomly sampled,
so we will learn a little about
the *probability* of random sampling.

Conclusions drawn from the analysis of data can only be as good as the data
itself.
We will allude briefly to the important statistical branch
of the *design of experiments*,
which gives methods for generating data that worthy of analysis.

Here is a small portion of data collected from hundreds of patients
who were admitted to the burn center of a university hospital
over a period of several years.

Age Gender Race Temp Degree %Burned Survive
===================================================
29 Male White 99.7 2nd 15% yes
46 Female White 101.3 3rd 50% no
37 Male Black 98.9 1st 5% yes
===================================================

A *variable* is a characteristic that might take on different values
among different individuals.
In this example, the values of seven variables
have been recorded for each individual.
A *quantitative variable* is measured as a number.
Age, temperature, and percent burned are examples
of quantitative variables.

A *qualitative variable* (or *categorical variable*)
is a characteristic that is measured by categorizing an individual.
Gender, race, highest degree of burn, and survival are examples
of categorical variables.

A *population* comprises all individuals in which we are interested.
In this example,
the population may be all hypothetical patients who might come to this
burn center,
or perhaps all hypothetical burn patients who might arrive at any hospital's
burn center.

A *sample* is the part of the population for which we have data.
In this example,
the sample would be the hundreds of individuals who arrived at the burn
center during the study period.

Last modified: Jan 15, 1996

Bret Larget,
larget@mathcs.duq.edu