default_max_attempts_per_step: 3 classifier_model: "MODEL_1" feedback_model: "MODEL_1" tokens_for_ai_rubric: | Evaluate the student's understanding of basic statistical concepts. Consider: - Grasp of central tendency (mean, median, mode) - Understanding of variation and spread - Ability to interpret data - Recognition of distributions - Practical application of concepts Provide clear explanations with real-world examples. sections: - section_id: introduction title: Welcome to Statistics steps: - step_id: welcome title: Why Statistics Matters content_blocks: - "# Statistics 101: Making Sense of Data 📊" - "" - "**Welcome to the world of statistics!**" - "" - "Statistics helps us:" - "- Understand patterns in data" - "- Make informed decisions" - "- Test hypotheses scientifically" - "- Predict future outcomes" - "- Avoid being fooled by randomness" - "" - "**You'll learn:**" - "✓ Measures of central tendency (mean, median, mode)" - "✓ Measures of spread (range, variance, standard deviation)" - "✓ Probability basics" - "✓ Distributions and what they mean" - "✓ How to interpret data" - "" - "**Real-world applications:**" - "- Medicine (clinical trial results)" - "- Business (sales forecasting)" - "- Sports (player performance)" - "- Science (experimental data)" - "- Everyday decisions (risk assessment)" question: Ready to learn how to understand data and make better decisions? tokens_for_ai: | Accept positive responses as 'ready'. Language preference as 'set_language'. Otherwise 'off_topic'. buckets: - ready - set_language - off_topic transitions: ready: content_blocks: - "Excellent! Let's start with the basics of describing data! 📈" next_section_and_step: central_tendency:step_1 set_language: content_blocks: - "Language preference updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: introduction:welcome off_topic: content_blocks: - "Let's learn statistics together! Are you ready to begin?" counts_as_attempt: false next_section_and_step: introduction:welcome - section_id: central_tendency title: Describing Data - Central Tendency steps: - step_id: step_1 title: The Center of Data content_blocks: - "## Central Tendency: Finding the 'Middle' 📍" - "" - "When we have a dataset, we often want to describe it with a single number that represents the 'typical' or 'central' value." - "" - "**Three measures of central tendency:**" - "" - "**1. Mean (Average)**" - "- Sum all values and divide by the count" - "- Most commonly used" - "- Sensitive to extreme values (outliers)" - "- Example: Test scores 80, 85, 90, 95 → Mean = (80+85+90+95)/4 = 87.5" - "" - "**2. Median (Middle Value)**" - "- The middle number when data is sorted" - "- Not affected by outliers" - "- Better for skewed data" - "- Example: Salaries $30k, $35k, $40k, $45k, $200k → Median = $40k" - "" - "**3. Mode (Most Frequent)**" - "- The value that appears most often" - "- Useful for categorical data" - "- Can have multiple modes or no mode" - "- Example: Shoe sizes 7, 8, 8, 8, 9, 10 → Mode = 8" - "" - "**When to use which:**" - "- Mean: Normally distributed data without outliers" - "- Median: Skewed data or data with outliers (like income)" - "- Mode: Categorical data or finding most common value" question: "You have exam scores: 60, 70, 75, 80, 85, 90, 95. What is the median score?" tokens_for_ai: | The median is the middle value when sorted. Scores: 60, 70, 75, 80, 85, 90, 95 (7 values) Middle value (4th position) = 80 Categorize as: - correct: Says 80 or "eighty" - calculated_mean: Says 79.3 or ~79 (they calculated the mean instead) - close: Says 75 or 85 (one position off) - confused: Incorrect answer showing confusion - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | If correct: - Praise them! Explain why 80 is the middle value. - Note that with odd numbers, median is straightforward. If they calculated mean: - Good effort but that's the mean! - Explain median is the MIDDLE value when sorted, not the average. If close or confused: - Show the sorted list: 60, 70, 75, [80], 85, 90, 95 - The middle position (4th out of 7) is 80. buckets: - correct - calculated_mean - close - confused - set_language - off_topic transitions: correct: ai_feedback: tokens_for_ai: | Perfect! 80 is the median - the middle value. With 7 values, the 4th position is the center. Median is great because outliers don't affect it! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: central_tendency:step_2 calculated_mean: ai_feedback: tokens_for_ai: | That's the mean (average), not the median! Median = middle value when sorted. For 60,70,75,[80],85,90,95 → median is 80. The mean would be all values summed divided by 7. metadata_add: score: "n+1" next_section_and_step: central_tendency:step_2 close: ai_feedback: tokens_for_ai: | Close! You're near the middle. Sort the values: 60, 70, 75, [80], 85, 90, 95 The exact middle (4th position out of 7) is 80. next_section_and_step: central_tendency:step_1 confused: content_blocks: - "The median is the MIDDLE value when you sort the numbers from smallest to largest." - "With 7 values, the 4th number is in the middle." next_section_and_step: central_tendency:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: central_tendency:step_1 off_topic: content_blocks: - "Let's find the median! Sort the scores and identify the middle value." next_section_and_step: central_tendency:step_1 - step_id: step_2 title: Mean vs Median with Outliers content_blocks: - "## The Power of Median: Handling Outliers 🎯" - "" - "**Why median matters: The salary example**" - "" - "Imagine a small company with 5 employees and their salaries:" - "- Employee A: $40,000" - "- Employee B: $45,000" - "- Employee C: $50,000" - "- Employee D: $55,000" - "- CEO: $500,000" - "" - "**Mean salary:** ($40k + $45k + $50k + $55k + $500k) / 5 = $138,000" - "**Median salary:** $50,000 (the middle value)" - "" - "**Which better represents the 'typical' employee salary?**" - "The median! The mean is dragged up by the CEO's outlier salary." - "" - "**This is why:**" - "- Median home prices are reported (not mean)" - "- Median household income is used (not mean)" - "- Outliers don't distort the median" - "" - "**When one extreme value can mislead, use median!**" question: "A neighborhood has 6 home prices: $200k, $210k, $220k, $230k, $240k, and $2,000k. If someone says 'the average home price is $516k,' why might that be misleading? What would better represent typical home prices?" tokens_for_ai: | They should recognize that: - The $2 million home is an outlier - Mean is misleading ($516k) - Median would be better (between $220k and $230k = $225k) Categorize as: - excellent_understanding: Mentions outlier skewing mean, median better - understands_outlier: Recognizes the expensive house is the problem - suggests_median: Says median without explaining why - partial_understanding: On the right track but incomplete - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | Validate their understanding of outliers affecting mean! Key points: - The $2M home is an outlier (way higher than others) - Mean gets pulled up to $516k (not representative) - Median would be $225k (between 220 and 230) - much more typical - This is why real estate uses median prices! Praise their critical thinking about statistics. buckets: - excellent_understanding - understands_outlier - suggests_median - partial_understanding - set_language - off_topic transitions: excellent_understanding: ai_feedback: tokens_for_ai: | Brilliant analysis! Yes - the $2M outlier drags the mean to $516k, misleading! The median ($225k) better represents typical homes. This is exactly why statistics literacy matters! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: spread:step_1 understands_outlier: ai_feedback: tokens_for_ai: | Exactly! The $2M home is an outlier. It pulls the mean to $516k, but most homes are $200-240k. The median ($225k) would be more representative. Great critical thinking! metadata_add: score: "n+1" next_section_and_step: spread:step_1 suggests_median: ai_feedback: tokens_for_ai: | Good instinct - median is better here! Why? The $2M outlier skews the mean to $516k. But the median ($225k) represents the typical home price. Outliers don't affect median - that's its power! next_section_and_step: spread:step_1 partial_understanding: ai_feedback: tokens_for_ai: | You're on the right track! The key: one $2M home among $200-240k homes. This outlier pulls mean to $516k (misleading). Median ($225k) better shows typical prices. next_section_and_step: spread:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: central_tendency:step_2 off_topic: content_blocks: - "Think about: Does $516k accurately represent what most homes in this neighborhood cost?" next_section_and_step: central_tendency:step_2 - section_id: spread title: Measuring Spread - Variability steps: - step_id: step_1 title: Understanding Variability content_blocks: - "## Spread: How Much Do Values Vary? 📏" - "" - "Central tendency tells us the 'middle,' but doesn't tell the full story." - "" - "**Consider two classes:**" - "- Class A scores: 80, 82, 78, 81, 79 (mean = 80)" - "- Class B scores: 50, 70, 80, 90, 110 (mean = 80)" - "" - "Same mean, VERY different distributions!" - "Class A is consistent. Class B is all over the place." - "" - "**Measures of Spread:**" - "" - "**1. Range**" - "- Maximum value minus minimum value" - "- Simple but sensitive to outliers" - "- Class A: 82 - 78 = 4" - "- Class B: 110 - 50 = 60" - "" - "**2. Variance**" - "- Average of squared differences from mean" - "- Measures how spread out values are" - "- Larger variance = more spread" - "" - "**3. Standard Deviation (SD)**" - "- Square root of variance" - "- Same units as original data (easier to interpret)" - "- Most commonly used measure of spread" - "" - "**Why spread matters:**" - "- Quality control (consistency in manufacturing)" - "- Risk assessment (investment volatility)" - "- Performance evaluation (consistency vs streaky)" - "- Research (reliability of measurements)" question: "Two basketball players both average 20 points per game. Player A's scores: 18, 19, 20, 21, 22. Player B's scores: 5, 10, 20, 30, 35. Which player is more consistent, and why does that matter?" tokens_for_ai: | Player A is more consistent (low spread/variance). Player B is inconsistent/volatile (high spread). Look for understanding that: - Player A has consistent performance (small variation) - Player B is unpredictable (large variation) - Consistency matters for reliability/strategy Categorize as: - excellent_answer: Identifies Player A as consistent AND explains why it matters - identifies_player_a: Correctly says Player A is more consistent - identifies_inconsistency: Recognizes the difference in variability - basic_answer: Mentions one player without explaining - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | Affirm their understanding of consistency/spread! Key points: - Player A: very consistent (range 18-22, low variation) - Player B: unpredictable (range 5-35, high variation) - Consistency matters: reliable performance, easier to plan around - Player B might have higher ceiling but less reliable Connect to real sports analysis and standard deviation concept. buckets: - excellent_answer - identifies_player_a - identifies_inconsistency - basic_answer - set_language - off_topic transitions: excellent_answer: ai_feedback: tokens_for_ai: | Perfect analysis! Player A: 18-22 (consistent, low spread). Player B: 5-35 (volatile, high spread). Consistency means reliability - you know what to expect! This is what standard deviation measures! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: probability:step_1 identifies_player_a: ai_feedback: tokens_for_ai: | Correct! Player A is much more consistent. Range: A is 18-22 (4 points), B is 5-35 (30 points!). Low spread = predictable performance. High spread = unpredictable, risky. That's what measuring spread tells us! metadata_add: score: "n+1" next_section_and_step: probability:step_1 identifies_inconsistency: ai_feedback: tokens_for_ai: | Good observation about the difference! Player A varies 18-22 (tight, consistent). Player B varies 5-35 (wild, unpredictable). Consistency = reliability. This is why we measure spread! next_section_and_step: probability:step_1 basic_answer: ai_feedback: tokens_for_ai: | Let's look at the ranges: Player A: 18, 19, 20, 21, 22 (very tight - consistent!) Player B: 5, 10, 20, 30, 35 (all over - inconsistent!) Consistency means you can rely on them. Spread measures this! next_section_and_step: probability:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: spread:step_1 off_topic: content_blocks: - "Compare the ranges: Player A (18-22) vs Player B (5-35). Who's more predictable?" next_section_and_step: spread:step_1 - section_id: probability title: Probability Basics steps: - step_id: step_1 title: Understanding Probability content_blocks: - "## Probability: Quantifying Uncertainty 🎲" - "" - "**What is probability?**" - "A measure of how likely something is to happen." - "" - "**Probability scale:**" - "- 0 = Impossible (0%)" - "- 0.5 = Even chance (50%)" - "- 1 = Certain (100%)" - "" - "**Basic probability formula:**" - "P(event) = (Number of favorable outcomes) / (Total possible outcomes)" - "" - "**Example: Fair die**" - "- P(rolling a 3) = 1/6 ≈ 0.167 (16.7%)" - "- P(rolling even) = 3/6 = 0.5 (50%)" - "- P(rolling 1-6) = 6/6 = 1 (100%)" - "" - "**Key concepts:**" - "" - "**Independent events:**" - "- One doesn't affect the other" - "- Coin flips, die rolls" - "- P(heads then heads) = 0.5 × 0.5 = 0.25" - "" - "**Dependent events:**" - "- One affects the probability of the other" - "- Drawing cards without replacement" - "" - "**Common misconceptions:**" - "- Gambler's fallacy: 'It's due!' (No - each event is independent)" - "- Hot hand fallacy: Past streaks predict future (they don't in random events)" question: "You flip a fair coin 5 times and get heads every time. What's the probability the 6th flip is heads? Why?" tokens_for_ai: | Correct answer: 50% or 0.5 or 1/2 Key understanding: Each flip is INDEPENDENT. Past flips don't affect future flips. Common wrong answer: "It's more likely to be tails" (gambler's fallacy) Categorize as: - correct_with_reasoning: Says 50% AND explains independence - correct_answer: Says 50% without full explanation - gamblers_fallacy: Says tails is more likely because "it's due" - pattern_thinking: Thinks the pattern will continue - confused: Other incorrect reasoning - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | If correct: - Excellent! Each flip is independent. - Past results don't affect future flips. - The coin has no "memory" - always 50/50. If gambler's fallacy: - Common misconception! This is the "gambler's fallacy." - Each flip is independent - past doesn't affect future. - It's still 50/50, even after 100 heads in a row! - The coin doesn't "owe" you tails. Explain independence clearly. buckets: - correct_with_reasoning - correct_answer - gamblers_fallacy - pattern_thinking - confused - set_language - off_topic transitions: correct_with_reasoning: ai_feedback: tokens_for_ai: | Perfect understanding! Each coin flip is independent - past doesn't affect future. The coin has no memory. Always 50/50! You've avoided the gambler's fallacy - great! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: distributions:step_1 correct_answer: ai_feedback: tokens_for_ai: | Correct - still 50%! Why? Each flip is INDEPENDENT. Past flips don't affect future flips. The coin doesn't "remember" or "balance out." Great job avoiding the gambler's fallacy! metadata_add: score: "n+1" next_section_and_step: distributions:step_1 gamblers_fallacy: ai_feedback: tokens_for_ai: | Common misconception! This is the "gambler's fallacy." Each flip is INDEPENDENT - the coin has no memory. Past flips don't affect future flips. It's still 50/50, even after 1000 heads! The coin doesn't "owe" you tails. next_section_and_step: probability:step_1 pattern_thinking: ai_feedback: tokens_for_ai: | The streak feels meaningful, but it's not! Each flip is independent - 50/50 every time. Past results don't predict future with fair coins. Random sequences often have "patterns" but they're meaningless. next_section_and_step: probability:step_1 confused: content_blocks: - "Key concept: INDEPENDENCE" - "Each coin flip is independent - past flips don't affect future flips." - "A fair coin always has 50% chance of heads, regardless of history." next_section_and_step: probability:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: probability:step_1 off_topic: content_blocks: - "Think: Does the coin 'remember' previous flips? Are they independent events?" next_section_and_step: probability:step_1 - section_id: distributions title: Understanding Distributions steps: - step_id: step_1 title: The Normal Distribution content_blocks: - "## The Normal Distribution: Nature's Pattern 📊" - "" - "**The bell curve (normal distribution):**" - "The most important distribution in statistics!" - "" - "**Characteristics:**" - "- Symmetric, bell-shaped" - "- Mean = Median = Mode (at the center)" - "- Most data near the mean" - "- Tails extend infinitely (but rarely reach extremes)" - "" - "**The 68-95-99.7 Rule (Empirical Rule):**" - "- 68% of data within 1 standard deviation of mean" - "- 95% of data within 2 standard deviations" - "- 99.7% of data within 3 standard deviations" - "" - "**Example: IQ scores**" - "- Mean = 100, Standard Deviation = 15" - "- 68% of people: IQ between 85-115" - "- 95% of people: IQ between 70-130" - "- 99.7% of people: IQ between 55-145" - "" - "**Why normal distribution matters:**" - "- Many natural phenomena follow it (height, measurement errors)" - "- Central Limit Theorem (averages tend toward normal)" - "- Foundation for many statistical tests" - "- Allows predictions and probability calculations" - "" - "**Real-world examples:**" - "- Test scores, heights, blood pressure, measurement errors" question: "SAT scores are normally distributed with mean 1000 and standard deviation 200. Using the 68-95-99.7 rule, approximately what percentage of students score between 800 and 1200?" tokens_for_ai: | 800 to 1200 is mean (1000) ± 1 standard deviation (200). 68% of data falls within 1 SD of the mean. Correct answer: 68% (or approximately 68%, or about 2/3) Categorize as: - correct: Says 68% or approximately 68% - close: Says 66% or 70% (reasonably close) - says_95: Says 95% (confused 1 SD with 2 SD) - unclear_reasoning: Wrong answer showing confusion - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | If correct: - Excellent! 800-1200 is 1000 ± 200 (1 SD). - 68% of data within 1 SD of mean. - You've mastered the empirical rule! If says 95%: - Close reasoning! But 95% is for 2 SDs. - 800-1200 is only 1 SD (200 points) from mean. - 1 SD = 68%, 2 SDs = 95%, 3 SDs = 99.7% Explain the calculation clearly. buckets: - correct - close - says_95 - unclear_reasoning - set_language - off_topic transitions: correct: ai_feedback: tokens_for_ai: | Perfect! 800-1200 is mean ± 1 SD. 1 SD = 68% of data. You understand the empirical rule! This is fundamental for interpreting normal distributions! metadata_add: score: "n+2" concepts_mastered: "n+1" next_section_and_step: conclusion:step_1 close: ai_feedback: tokens_for_ai: | Very close! The exact answer is 68%. 800-1200 = 1000 ± 200 (1 standard deviation). The 68-95-99.7 rule: 68% within 1 SD. Great understanding of the concept! metadata_add: score: "n+1" next_section_and_step: conclusion:step_1 says_95: ai_feedback: tokens_for_ai: | You're thinking of the right rule, but different range! 95% is for 2 standard deviations (600-1400). 800-1200 is only 1 SD (200 points) from mean. 1 SD = 68%, 2 SDs = 95%, 3 SDs = 99.7% next_section_and_step: distributions:step_1 unclear_reasoning: content_blocks: - "Use the 68-95-99.7 rule:" - "800-1200 is the mean (1000) ± 200" - "200 is 1 standard deviation" - "68% of data falls within 1 SD of the mean" next_section_and_step: distributions:step_1 set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: distributions:step_1 off_topic: content_blocks: - "Calculate: How many standard deviations is 800-1200 from the mean (1000)?" next_section_and_step: distributions:step_1 - section_id: conclusion title: Statistics Mastery steps: - step_id: step_1 title: Applying Statistical Thinking content_blocks: - "## Congratulations, Statistician! 🎓📊" - "" - "**You've mastered the fundamentals!**" - "" - "**What you've learned:**" - "✓ Central Tendency (mean, median, mode)" - "✓ When to use median vs mean (outliers!)" - "✓ Measures of spread (range, variance, standard deviation)" - "✓ Probability and independence" - "✓ The normal distribution and 68-95-99.7 rule" - "" - "**Real-world statistical thinking:**" - "" - "**Evaluating claims:**" - "- 'Average salary is $100k!' → Check for outliers, ask for median" - "- 'Significant difference!' → What's the sample size?" - "- 'This trend proves...' → Correlation ≠ causation" - "" - "**Making decisions:**" - "- Compare means AND spreads (consistency matters!)" - "- Understand probability (avoid gambler's fallacy)" - "- Consider distributions (is it normal? skewed?)" - "" - "**Critical thinking:**" - "- Always ask: What's the sample size?" - "- Question: How was data collected?" - "- Consider: What's being measured exactly?" - "- Look for: Potential biases or confounding factors" question: "How will you use statistical thinking in your daily life? Give an example of where understanding statistics could help you make better decisions." tokens_for_ai: | This is a reflection question. Look for application of concepts learned: - Evaluating claims with mean/median awareness - Understanding probability in decisions - Recognizing variability/consistency - Critical thinking about data Categorize as: - excellent_application: Specific example showing deep understanding - practical_example: Good real-world application - general_reflection: Acknowledges usefulness - brief_response: Short but relevant - set_language: Language preference - off_topic: Unrelated feedback_tokens_for_ai: | Provide encouraging, personalized feedback! Validate their example if they give one. Add suggestions for statistical thinking in daily life: - Evaluating news/research claims - Financial decisions (investments, insurance) - Health decisions (understanding medical stats) - Sports analysis - Weather forecasts (probability!) Celebrate their completion of Statistics 101! buckets: - excellent_application - practical_example - general_reflection - brief_response - set_language - off_topic transitions: excellent_application: ai_feedback: tokens_for_ai: | Fantastic example showing real understanding! Reference their specific application. Emphasize how statistical literacy empowers better decisions. Encourage continued critical thinking with data! metadata_add: activity_completed: "true" practical_example: ai_feedback: tokens_for_ai: | Great practical thinking! Acknowledge their example. Statistics helps us cut through misleading claims. You now have tools to think critically about data! metadata_add: activity_completed: "true" general_reflection: ai_feedback: tokens_for_ai: | Good reflection! Statistics is everywhere - news, health, money, sports. You can now question claims and understand probability. Keep thinking statistically! metadata_add: activity_completed: "true" brief_response: ai_feedback: tokens_for_ai: | Thank you for completing Statistics 101! You've gained powerful tools for understanding data. Use them to make informed decisions and question claims! metadata_add: activity_completed: "true" set_language: content_blocks: - "Language updated!" metadata_add: language: "the-users-response" counts_as_attempt: false next_section_and_step: conclusion:step_1 off_topic: content_blocks: - "Reflect on: How could understanding mean, median, probability, and distributions help you in everyday decisions?" next_section_and_step: conclusion:step_1