FRQ 6 – Investigative Task

Overview

• The Investigative Task is the final question of Section II
• 25 minutes dedicated time (after completing FRQs 1-5)
• Worth 4 points but weighted more heavily
• Makes up 12.5% of your total exam score (more than any other single FRQ)
• Calculator use is allowed and often essential
• Tests your ability to think statistically in novel situations

The Investigative Task is unique on the AP Statistics exam. Unlike FRQs 1-5 which test standard procedures, this question presents an unfamiliar context that requires creative statistical thinking. You won't have practiced this exact type of problem - that's the point. The College Board wants to see if you can apply statistical reasoning to new situations, not just execute memorized procedures.

This question often introduces a scenario you've never seen before - perhaps a new type of graph, an unusual probability situation, or a novel approach to data analysis. Success requires reading carefully, thinking flexibly, and applying fundamental statistical principles to unfamiliar territory.

Strategy Deep Dive

Unlike standard FRQs that assess procedural execution, the Investigative Task evaluates creative application of statistical thinking to unfamiliar scenarios.

Initial Assessment Phase

Unfamiliarity is intentional - the task deliberately presents novel contexts. Instead, spend 2-3 minutes carefully reading and identifying:

What statistical concept is at the core? Even in unfamiliar contexts, the question connects to fundamental ideas: variability, distribution, association, inference, or probability. Identifying this core helps you access relevant knowledge.

What information are you given? List out the facts, data, or conditions provided. Sometimes the question provides more information than you initially notice. Details that seem minor often prove crucial for later parts.

What are you asked to find or explain? Break down each part into specific tasks. The question might ask you to interpret an unusual graph, propose a method for analysis, or evaluate someone else's statistical reasoning. Understanding exactly what's requested prevents wasted effort.

Building Conceptual Bridges

The key to Investigative Tasks is connecting the unfamiliar scenario to familiar concepts. This requires flexible thinking and the ability to see past surface differences to underlying statistical structures.

Consider a question that presents data in an unusual format - perhaps temperatures recorded as deviations from average rather than actual values. While the presentation is novel, the underlying concepts are familiar: you're still dealing with distributions, center, and spread. The deviations from average are essentially already centered at zero. This recognition allows you to apply what you know about distributions to this new context.

Or imagine a probability scenario involving a game you've never seen. The specific rules might be new, but the probability concepts aren't. You still have sample spaces, events, independence, and conditional probability. Map the new scenario onto these familiar frameworks.

The Power of Examples

When stuck on an Investigative Task, creating simple examples often provides breakthrough insights. If the question involves an abstract procedure, try it with small numbers. If it describes a general scenario, create a specific instance.

Suppose the question introduces a new measure of spread that involves comparing each value to every other value. Rather than trying to understand this abstractly, create a simple dataset like {1, 3, 7} and work through the procedure. Calculate all pairwise differences: |1-3|=2, |1-7|=6, |3-7|=4. Now you can see concretely what this measure captures and how it relates to familiar measures like range or standard deviation.

Communication in Unfamiliar Territory

Clear communication becomes even more crucial when working with unfamiliar scenarios. The grader needs to follow your reasoning through uncharted territory. This means:

Define any notation you introduce. If you decide to call something X or create a formula, explain what it represents. The grader can't read your mind, especially when you're creating your own approach.

Explain your reasoning step-by-step. In standard FRQs, you might write "Checking normality condition..." and the grader knows what's coming. In Investigative Tasks, you need to explain why you're doing what you're doing: "Since we need to compare variability across groups with different scales, I'll standardize each group's values by dividing by their mean..."

Connect back to fundamental principles. Show how your approach relates to basic statistical concepts. This demonstrates that you're not just guessing but applying statistical thinking systematically.

Pattern Recognition

While each Investigative Task is unique, certain types appear more frequently. Recognizing these patterns helps you approach new problems more confidently.

Novel Graphical Displays

These questions present data in an unfamiliar visual format and ask you to interpret it. The key is identifying what aspect of the data the graph emphasizes. Does it show individual values, summaries, or relationships? What would this look like in a familiar format?

Common tasks include:

• Explaining what the graph reveals about the data
• Comparing what this shows versus standard displays
• Using the graph to answer questions about the underlying distribution
• Creating or interpreting variations of the display

Strategy: Start by identifying the axes and scale. Then look at specific examples - what does one point or element represent? Build up your understanding from concrete instances to general patterns.

Modified Inference Procedures

These questions take familiar inference scenarios but add twists that require adaptation. Perhaps you're testing whether a die is fair, but it has 8 sides instead of 6. Or you're comparing groups, but the data collection method doesn't quite fit standard assumptions.

The key insight: The logic of inference remains constant even when details change. You still have null and alternative hypotheses, test statistics that measure deviation from the null, and p-values that quantify evidence. Adapt the familiar framework to the new situation.

Common modifications:

• Non-standard parameters or hypotheses
• Unusual data collection methods requiring adjusted procedures
• Inference questions where you must design the approach
• Evaluating whether someone else's inference approach is valid

Probability with a Twist

These present probability scenarios with unfamiliar rules or structures. You might encounter a new game, a modified random process, or a complex conditional probability situation. Success requires carefully tracking what you know and systematically working through possibilities.

Effective approaches:

• List out the sample space, even if it's large
• Draw tree diagrams or tables to organize information
• Use the multiplication rule and addition rule as building blocks
• Check your answer using complementary approaches when possible

Exploring Unusual Relationships

Some tasks present relationships between variables that don't fit standard correlation/regression frameworks. Perhaps the relationship is non-linear, involves categories, or has some other complication. These questions test whether you can think beyond the standard toolkit.

Key strategies:

• Transform variables to linearize relationships
• Consider categorical summaries if continuous approaches don't work
• Think about what "association" means in this specific context
• Use graphical exploration to understand patterns

Time Management Reality

You have 25 minutes for the Investigative Task - significantly more than the ~13 minutes per standard FRQ. This extra time is necessary because you need to understand the novel context, develop an approach, and execute it. Here's how to use this time effectively:

Minutes 0-5: Deep Reading and Planning

Read the entire question twice. The first read gives you the big picture; the second helps you catch crucial details. Investigative Tasks often hide important information in seemingly casual phrases. That mention of "selected without replacement" or "measured to the nearest gram" might be critical later.

Identify all parts and their relationships. Unlike standard FRQs where parts often build linearly, Investigative Task parts might explore different aspects of the same scenario. Understanding these connections helps you see the overall story the question is telling.

Make notes about your initial thoughts. What statistical concepts seem relevant? What approaches might work? Don't commit to a strategy yet - just brainstorm possibilities.

Minutes 5-20: Working Through Parts

Start with the part that seems most accessible. Building momentum with early success helps with later, harder parts. But be prepared to revise your understanding as you work. Sometimes part (b) provides insight that changes how you think about part (a).

For each part:

• Reread what's being asked
• Develop your approach, possibly trying simple examples
• Execute your solution, showing clear work
• Check that your answer addresses the specific question

If you get stuck, try approaching from a different angle. Can you work backwards from what you need to find? Can you solve a simpler version first? Can you connect to a standard scenario you know well?

Minutes 20-25: Review and Enhance

With basic answers in place, enhance your communication. Add explanations that clarify your reasoning. If you made assumptions, state them explicitly. If you chose between multiple approaches, briefly explain why.

Check for reasonableness. Do your numerical answers make sense in context? If you calculated a probability, is it between 0 and 1? If you found a mean, is it within the range of the data? These basic checks catch calculation errors.

Add final thoughts if inspiration strikes. Sometimes the pressure-free final minutes produce insights you missed earlier. Even a sentence like "Another approach would be to..." shows broader thinking.

Common Pitfalls and How to Avoid Them

Overthinking the Novel Context

Students sometimes get so focused on understanding every detail of the unusual scenario that they miss the underlying statistical simplicity. Remember: the core concepts are ones you know. Strip away the unusual context and identify the fundamental statistical question.

Example: A question about a "fairness index" for a new game might seem completely foreign. But at its core, it's asking about expected value and variability - concepts you understand well. Don't let unfamiliar vocabulary obscure familiar ideas.

Abandoning Statistical Principles

When faced with novelty, some students abandon systematic statistical thinking and just guess. This is exactly wrong. The Investigative Task rewards applying statistical principles MORE carefully, not less. When unsure, fall back on fundamentals: What would a graph show? What summary statistics would help? How could we quantify uncertainty?

Insufficient Communication

The grader needs even more help following your reasoning in unfamiliar territory. Don't assume they'll understand jumps in logic that seem obvious to you. Explain connections, define terms, and show intermediate steps. Think of yourself as a guide leading someone through unexplored terrain.

Getting Stuck on One Approach

If your first approach isn't working after 5-7 minutes, try something different. The Investigative Task often has multiple valid approaches. Flexibility is more valuable than stubborn persistence. Keep your statistical toolkit in mind and try different tools.

Building Investigative Task Skills

While you can't practice the exact Investigative Task you'll see, you can develop the skills it tests:

Practice Statistical Translation

Take familiar scenarios and express them in unusual ways. If you know how to test whether a coin is fair, can you adapt this to test whether a 12-sided die is fair? If you can compare two means, can you compare two medians? This flexibility is exactly what Investigative Tasks require.

Develop Multiple Representations

For any statistical scenario, practice expressing it graphically, numerically, and verbally. This multi-modal thinking helps when the Investigative Task presents information in an unfamiliar format. You'll be better at extracting meaning and converting between representations.

Question Your Tools

For standard procedures, ask yourself: Why does this work? What assumptions are crucial? How could I modify this for different situations? Understanding the "why" behind procedures prepares you to adapt them to new contexts.

Embrace Uncertainty

Get comfortable working with partial understanding. In standard FRQs, you either know the procedure or you don't. In Investigative Tasks, you often work with evolving understanding. Practice staying calm and systematic even when you don't immediately see the full solution.

Final Thoughts

The Investigative Task is where AP Statistics becomes most authentic - real statistical work often involves novel situations requiring creative thinking. This question rewards deep understanding over memorization, flexibility over rigid procedure following, and clear thinking over speed.

Successful students show specific behaviors: careful reading despite unfamiliarity, connection of novel scenarios to core concepts, use of concrete examples to understand abstractions, clear communication of uncertain reasoning, and balanced trust in both intuition and systematic approaches.

Remember that the Investigative Task is worth 12.5% of your exam score - more than any other single question. This weighting reflects its importance in demonstrating true statistical thinking. But also remember that partial credit is generous. Even if you can't solve everything perfectly, showing statistical thinking earns points.

Approach this question with curiosity rather than fear. The scenario will be new, but your statistical tools aren't. Trust the thinking skills you've developed throughout the course. Read carefully, think flexibly, and explain clearly. The Investigative Task is your opportunity to show that you're not just a procedure-follower but a statistical thinker.

Effective preparation combines conceptual depth with flexible thinking practice. Understanding procedural foundations enables adaptation to novel contexts. Clear reasoning articulation makes even tentative attempts valuable. The Investigative Task mirrors authentic statistical work - applying principled analysis to unfamiliar situations. This challenge showcases genuine statistical thinking beyond rote procedures.