786 lines
32 KiB
YAML
786 lines
32 KiB
YAML
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
|