AP Statistics - Unit 1 - Topic 1.1

Introducing Statistics What Can We Learn from Data?

Statistics begins with a question. A good question leads us to collect useful data, notice patterns, and make careful conclusions instead of just guessing.

Skill 1.A Determine a valid investigative question that requires a statistical investigation.
Skill 2.A Identify information needed to answer a question or solve a problem.

Start Here

Use these boxes as your quick lesson notes before practicing.

Definition: Statistics

Statistics is the study of collecting, organizing, analyzing, and using data to answer questions.

Important Idea

A question is statistical when the answer can vary. Different people or situations can give different data values.

Formula: Percent

Percent = part / whole x 100

Simple Example

Statistical: How many hours of sleep do students get on school nights? The answers will not all be the same.

How To Spot A Statistical Question

Ask these three questions. If all three answers are yes, you probably have a good statistical question.

The 3-Part Check

1 Is there a clear group?

Example: students in this class, families in a city, players on a team.

2 Is there a variable?

A variable is what you measure or record, like height, time, opinion, or score.

3 Will the answers vary?

If the answers can be different, statistics can help us learn from the data.

AP Exam Skill Builder

This is the extra layer that helps students answer AP-style prompts with confidence.

What Makes An Investigative Question Valid?

A valid investigative question is not just interesting. It must be possible to answer with data.

Clear group The question names who or what is being studied.
Measurable variable The question tells what information will be recorded.
Variability The answers are expected to be different.
Data needed The question cannot be answered well by guessing.

What Information Should You Identify?

When AP Statistics asks what information is needed, look for these parts.

Population The full group we want to learn about.
Sample The smaller group we actually collect data from.
Individuals The people, objects, or cases being measured.
Variable The characteristic recorded for each individual.

Worked Examples

Read each example like a mini AP free-response check.

Example 1: Valid Question

How many minutes do students at Lincoln High spend on homework on a typical school night?

Why it works: It has a clear group, a measurable variable, and answers will vary.

Population: all students at Lincoln High
Individuals: students
Variable: minutes spent on homework
Data needed: homework time from a sample of students
Example 2: Needs Fixing

Do students like school?

Problem: This is too vague. "Like" could mean classes, teachers, lunch, clubs, or friends.

Better question: What percent of students at our school say their classes are interesting?

Example 3: Not Statistical

What is the temperature in the classroom right now?

Why not: This asks for one fixed value at one moment. It does not study variability across individuals or situations.

Make it statistical: How does the classroom temperature change during the school day?

Example 4: Skill 2.A

Does more study time usually go with higher quiz scores?

Information needed: For each student, collect study time and quiz score. You need both variables from the same individuals.

Individuals: students
Variable 1: study time
Variable 2: quiz score
Purpose: compare two pieces of data for each student
Example 5: Avoid Bias

Why is online homework better than paper homework?

Problem: This is leading because it already suggests online homework is better.

Better question: Which type of homework do students prefer: online homework or paper homework?

Common AP Mistakes

These are small wording mistakes that can cost points.

Mistake 1: No Group

Weak: How much sleep do people get?

Better: How much sleep do students in this AP Statistics class get on school nights?

Mistake 2: No Variability

Weak: How old am I?

Better: How old are students in this class?

Mistake 3: Too Vague

Weak: Are students healthy?

Better: How many days per week do students exercise for at least 30 minutes?

Mistake 4: Leading Wording

Weak: Why is our cafeteria food bad?

Better: How do students rate the cafeteria food on a scale from 1 to 5?

Key Vocabulary

These are the words AP Statistics expects you to use clearly.

Data

Information collected to answer a question.

Individual

One person, object, or case we collect data from.

Variable

A characteristic recorded for each individual.

Population

The entire group we want to learn about.

Sample

A smaller part of the population that we actually collect data from.

Variability

Differences in data values. Statistics is useful because values often vary.

Flashcard Practice

Work through the deck. Mark cards you know, and send tricky cards back to practice again.

Card 1 of 15
Vocabulary
Click the card or press Show Answer when you are ready.

Multiple-Choice Practice

Answer one question at a time. You will get instant feedback and a review at the end.

Question 1 of 10

Final study tip: A question needs statistics when different people could give different answers and data is needed to make a fair conclusion.

FRQ-Style Practice

Prompt: A class collects data related to statistical questions and data variation. Write a free-response answer that uses the correct vocabulary and statistical reasoning.

  1. Identify the variable(s), population/sample, or study design feature requested.
  2. Choose or describe the appropriate table, graph, summary statistic, sampling method, or design decision.
  3. Write one contextual interpretation that uses statistical language rather than a vague everyday claim.

Scoring focus: Credit depends on precise vocabulary, context, and a justified choice or description.

Calculator and Technology Check

Output to read: Calculator or spreadsheet output gives n = 48, mean = 16.2, median = 15.4, IQR = 4.8, and one flagged high value.

How to interpret it: For statistical questions and data variation, connect the output to the context: compare resistant and nonresistant summaries, mention units, and decide whether the flagged value changes the story.

Source note: Aligned to AP Statistics Course and Exam Description, Effective Fall 2026.