S ECTION 1.1A Introduction; Displaying Distributions with Graphs

S TATISTICS IS.. The science of data. We begin our study of statistics by mastering the art of examining data Any set of data contains information about some group of individuals, organized by variables.

I NDIVIDUALS AND VARIABLES The individuals are the objects described by a set of data. Individuals may be people but they may also be animals or things. Often they are referred to as subjects. A variable is a characteristic which varies from one individual to another. Example of variables for humans are height, weight, number of siblings, marital status, and eye color. When you meet a new set of data, ask yourself the following questions: Who? -Who are the individuals being described? What?- What variables are being measured, and in what units? Why?- Why is the information being gathered?

T YPES OF V ARIABLES A categorical variable is non- numerically valued variable, also sometimes called a qualitative variable. A quantitative variable is a numerically valued variable.

E XAMPLE : Consider the research question: “How many licks does it take to get to the center of a Tootsie Roll Pop?” Who are the individuals in this case? Tootsie Roll Pops What is the variable being measured? Number of licks What type of variable is this? Quantitative

E XAMPLE : Consider runners in the Boston Marathon. There are a variety of variables we could measure, depending on our research question, and therefore different types of information which could be recorded. For instance: The place/finish of each participant Categorical The running time of each finisher Quantitative The gender of each runner Categorical The age of each runner Quantitative

Q UESTION : Are there variables that take on numerical values but are not quantitative? Yes, place/finish/rank, ID or serial number, zip code

D ISTRIBUTION The distribution of a variable tells us what values the variable takes and how often it takes these values.

D ATA Data is information obtained by observing values of a variable for one or more people/things. It will be described using the same type as the variable observed/measured. It is possible, then, to observe either categorical or quantitative data. We will begin to examine our data (a process called exploratory data analysis ) with graphs.

D ISPLAYING CATEGORICAL VARIABLES The values of a categorical variable are labels for the categories The distribution of a categorical variable lists the categories and gives either the count or the percent of individuals who fall in each category. Whichever type of graph is used, it should help the reader quickly grasp the distribution.

QUESTION What is your place in the birth order of your family? FIRSTMIDDLELASTONLY

HOMEWORK Pg. 7 #1.1, 1.2, 1.4 Pg #1.5, 1.6