Key Terms: Statistics & Probability

I. Fundamental Concepts
Part 1: The Groups (Who?)

In statistics, we usually want to learn about a massive group, but we can only afford to check a small part of it.

Population
Definition: The entire collection of people, things, or objects you want to study. It is the "whole picture."

Key Concept: In the real world, populations are often too large to check completely (e.g., "All voters in the USA" or "All items produced by a factory in 2024").

Sample
Definition: A smaller subset selected from the population.

Key Concept: The goal is to select a Representative Sample—a group that accurately reflects the characteristics of the full population. If your sample is good, the results will apply to the whole population.

Part 2: The Measurements (What?)
Once we have our sample, we need to gather information.

Variable
Definition: A characteristic of interest for each person or object in a population. Essentially it is the "question" you are studying. Variables are notated by capital letters such as X and Y.

Numerical Variable (Quantitative): Something you count or measure (e.g., Weight, Age, Amount of Money Spent). The litmus test is to ask if it makes meaningful sense to calculate an average. 

    -Average Age? Yes (Numerical)

    -Average Zip Code? No. Though a number, you can't have an "average location." (Categorical).

Categorical Variable (Qualitative): These variables place individuals into groups or categories. The answer is a label or a word.(e.g., Political Party, Hair Color, Yes/No). The litmus test is to ask if the answer 


Data
Definition: The actual values (answers) you collect for the variable. Datum is a single value

Key Distinction: The Variable is the concept (e.g., "Age"); the Data is the result (e.g., "18, 21, 19").

Part 3: The Numbers (The Results)
This is the most critical distinction in statistics. The name of the number changes depending on where the data came from.

Parameter
Definition: A number that describes the Population.

Key Concept: This is usually the "unknown truth" because we rarely have data for the entire population.

Statistic
Definition: A number that describes the Sample.

Key Concept: This is an estimate. We calculate the Statistic from our sample data to estimate the unknown Parameter.

Putting It Together: A Single Example
Let's apply all six terms to one scenario to see how they fit together.

The Study: We want to know the average amount of money first-year students at ABC College spend on school supplies.

Term              Applied to this Study

Population     All first-year students at ABC College.
Sample         100 specific students we surveyed.
Variable        The amount of money spent (excluding books).
Data             The specific dollar amounts listed: $150, $200, $225, etc.
Statistic        The average calculated from the 100 students (e.g., $191.67).
Parameter     The "true" average for all students (which remains unknown unless we ask everyone).

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https://courses.lumenlearning.com/introstats1/chapter/definitions-of-statistics-probability-and-key-terms/