Introduction to Statistics

Study Notes

Statistics is the science of collecting, organizing, summarizing, and analyzing data to draw conclusions or answer questions. Data are factual information used for reasoning.
Research objective: A researcher defines the question(s) to be answered, detailing the population to be studied and the questions.
Population/Universe: The entire group of individuals or objects under study.
Sample: A subset of the population, used when studying the whole population is too large or expensive.
Descriptive statistics: Organizing and summarizing data using numerical measurements, charts, and graphs to provide an overview of the collected information.
Inferential statistics: Extending results from a sample to the entire population and assessing the reliability of the results.

Qualitative variables: Yield categorical responses (e.g., color, categories).
Quantitative variables: Numerical values representing an amount or quantity.
- Discrete variables: Finite or countable number of possible values (e.g., number of children).
- Continuous variables: Infinite number of possible values that are not countable (e.g., height).

Nominal: Classifies objects or events without a natural ordering (e.g., eye color).
Ordinal: Classifies objects or events with a natural order (e.g., rank in a competition).
Interval: Identifies, orders, and has equal intervals between values, but no true zero point (e.g., temperature in Celsius).
Ratio: Identifies, orders, has equal intervals, and has a true zero point (e.g., height).

Raw Data: Unorganized data collected in their original form.
Frequency distribution: Organizing raw data into classes and frequencies in table form.
Categorical frequency distribution: For data in categories (e.g., blood type).
Ungrouped frequency distribution: Data is arranged without grouping into classes (e.g number of hours traveled to campus)
Grouped frequency distribution: Data is grouped into classes for large datasets (e.g. lifetimes of batteries).
Frequency polygons and histograms: Visual representations of frequency distributions.
Ogive: Represents cumulative frequencies.

Probability experiments: Actions with specific outcomes (e.g., rolling a die).
Outcomes: Result of a single probability experiment.
Sample space: Set of all possible outcomes.
Events: Subsets of the sample space.
Simple events: Events consisting of a single outcome.
Classical probability: Each outcome in the sample space is equally likely.
Empirical probability: Based on observations from probability experiments.
Subjective probability: Based on intuition, educated guesses, and estimates.
Complementary events: Outcomes not in an event.
Independent/Dependent events: Occurrence of one event doesn't/does affect the probability of the other.
Mutually exclusive events: Cannot occur at the same time.
Addition Rule/Multiplication Rule: Used to calculate probabilities of events.