Comprehensive Introduction to Statistics and Data Types

Statistics: The set of methods for obtaining, organizing, summarizing, presenting, and analyzing data.
Data Origin: Data come from characteristics measured on individuals or units.
- Individuals or units can be people, animals, places, things, etc.
Observations: The data values obtained from these individuals/units.

Population: The entire group of individuals/units about which we want information.
- This represents the target group we want to learn about.
Sample: A subset of the units in a population that we actually examine in order to gather information.

Voter Support Study:
- Scenario: $1000$ voters are asked which candidate they support in the upcoming election.
- Sample: The $1000$ voters interviewed.
- Population: All eligible voters in the election region.
Insomnia Clinical Trial:
- Scenario: $50$ insomnia patients are given a new treatment.
- Sample: The $50$ insomnia patients receiving the treatment.
- Population: All insomnia patients.
Wildlife Migration Study:
- Scenario: $200$ Canada geese are tagged to study their migration patterns.
- Sample: The $200$ tagged Canada geese.
- Population: All Canada geese.

Variable: A characteristic or property of an individual.
- A variable can be anything measurable or observable about an individual.
Examples of Variables:
- Time until a light bulb burns out
- Distance traveled by a taxi driver in one day
- Number of Heads in five tosses of a quarter
- Hair Colour
- Your Grade in this course

There are two broad classifications of data:
- Categorical Data
- Quantitative Data

Categorical Data: Data that represent values of categorical variables that place individuals into one of several groups.
Categorical data are further divided into two types: Ordinal Data and Nominal Data.

Definition: Data derived from a categorical variable where there is a logical ordering for the values.
Time-Based Ordering: Logical ordering can also be based on time (for example, month of birth).
Examples:
- Placing in a hockey tournament ( $1\text{st}$ , $2\text{nd}$ , $3\text{rd}$ , etc.)
- Service Rating at a restaurant (Good, Fair, Poor)
- Letter Grade in a course ( $\text{A+}$ , $\text{A}$ , $\text{B+}$ , $\text{...}$ , $\text{F}$ )

Definition: Data derived from a categorical variable where there is not a logical ordering for the values.
Examples:
- Gender of a newborn baby
- Reason for taking this course
- Favourite television show
- Eye Colour

Quantitative Data: Data that represent values of quantitative variables.
Definition: Variables that take numerical values for which arithmetic operations such as adding and averaging make sense.
Examples:
- Final Exam Score
- Height
- Volume of air in a balloon
- Sum of the numbers shown on two rolled dice