1.1 Introducing Statistics: What Can We Learn from Data?

What statistics is about

Statistics is the science of collecting, organizing, analyzing, and interpreting data to answer questions and make decisions in the presence of variability. Data alone aren't useful — the goal is to turn data into meaningful information and conclusions about the world, while accounting for the fact that individual observations differ.

Variables and variation

A variable is any characteristic that differs from individual to individual (e.g., height, favorite color). Variability is the natural differences seen in data — no two individuals are identical. Statistics helps us describe patterns despite this variability, distinguishing genuine trends from random noise.

Types of statistical questions

Good statistical questions anticipate variability in the answer and require data to answer, unlike questions with a single fixed answer. Statisticians distinguish between descriptive questions (summarizing data) and questions aimed at making broader inferences beyond the immediate data collected.

Key terms

Statistics

The science of collecting, analyzing, and interpreting data to answer questions despite variability.

Variable

A characteristic that differs from one individual to another (e.g., age, height).

Variability

The natural differences seen among individual data values.

Good statistical question

A question that anticipates variability in its answer and requires data to answer.

Data vs. Information

Data are raw facts/numbers; information is the meaningful understanding gained by analyzing data.

Try an AP-style question

A survey of 500 randomly chosen voters finds that 52% support a measure. What is 52%?

1. A population
2. A statistic
3. A parameter
4. A variable