Unit 1: COLLECTING DATA AND DRAWING CONCLUSIONS

Topic 1: Data and Variables

What is statistics? Statistics is the science of collecting, analyzing, summa-

rizing, and presenting data. The data are numbers or characteristics with

some specific meaning. As an example, suppose I gave you the list of num-

bers: 7.2, 9.3, 8.5, 8.3, 9.7. As given, this is just a list of 5 numbers with no

meaning. These could be the birth weights in pounds of 5 newborn babies

at the local hospital, or the average number of dandelions per square foot in

the yards of 5 houses on a local street. It is important to clearly state what

your data represent, not just give the values.

Definition: A variable is a characteristic of a subject that can be assigned a

number or category.

So data are the values taken on by some variable. There are two basic types

of variables:

1. Quantitative (Measurement) - takes numerical values for which arith-

metic comparisons make sense. (ex: height, weight, concentration, etc.)

2. Categorical (Qualitative) - records into which of several categories a

subject falls. (ex: sex, political affiliation, etc.)

A categorical variable with exactly two categories (such as sex) is said to be

a binary variable.

Definitions: Observational units or cases are the actual subjects assigned

the variable values. (Ex: If we collect the heights of the students

in this class, the students are the observational units.)

The notion that variables take on different values or categories

from different observational units is known as variability.

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Ch1 NotesTerms and concepts:statistics is based upon variability—concrete decisions are based upon variable data

data (singular is datum) are not numbers but rather are numbers with context

in a statistical study, there are 2 main things you must distinguish, the observational unit and the variable(s)--the observational units are the subjects (people, places or things) of the study and variables are characteristics of the observational units

there are 2 kinds of variables, categorical variables and quantitative variables

quantitative variables are numbers with attached unit (like 7.6 mph). You must always state the unit along with the number when listing the quantitative variable quantity

discrete quantitative variables only have specific values possible for the variable, whereas continuous quantitative variables can take on any value within an interval

categorical variables do not have units (like quantities do) and can either be ordered (where one level or category is higher/lower than another—like grades A, B, etc.), or they can have no order (like eye color)

a binary variable is a categorical variable with only 2 categories (like gender, male/female)

Study Emphasis:get much practice taking word problems and being able to distinguish the observational units and variables from the word problem—only practice can make you good at doing this

picture a study as a spread sheet—the rows will be the observational units and the column titles are variables

realize that quantitative variables always are ordered (one value is either less than, same as, or greater than another value)

realize that sometimes categorical variables are numbers, but they are not quantitative (like zip codes), and that they are sometimes ordered and sometimes not ordered

realize that summary numbers (like mean, standard deviation, median, etc) of a

variable is NOT a variable—the “watch out” on page 6 of the text is worth rereading and remembering