Math 225 Course Notes

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Chapter 1


The Big Picture

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.

An Example to Illustrate Basic Concepts

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,