Feline Frenzy Teacher GuideTeacher Guide Lesson: Feline Frenzy Statistics Grades 9-10 Learning Objectives Calculate mean, median, mode, and range from raw datasets. Construct and interpret dot plots and histograms. Use frequency tables to calculate experimental and theoretical probability. Discussion Prompts "Why might the range of Jerry's cheese sizes be more important to him than the mean?" "Looking at the chase histogram, does Tom's performance improve or worsen over time?" "How does an outlier (like a super-fast chase) affect the mean versus the median?" Teaching Tips The Outlier Hook: Use Tom's "extreme" failures to explain how outliers skew the mean but have less impact on the median. Visualization: Remind students that histograms represent intervals, while dot plots represent individual data points. Probability: Connect the frequency table directly to the concept of "Relative Frequency" as a predictor for future "cat-tastrophes." Pacing (60 min) Warm-up (10m) Central Tendency review. Worksheet (40m) Guided practice in pairs. Review (10m) Class-wide data analysis.
Cartoon Chaos Stats PacketCartoon Chaos MISSION 1: The Mouse Hole Measurements NAME: DATE: The Great Cheese Heist Jerry has stolen the following cheese weights (in grams) over 10 days: 12, 15, 8, 12, 20, 15, 12, 18, 10, 28 1. Find the MEAN (Average): 2. Find the MODE (Most Frequent): 3. Find the MEDIAN (Middle): (Show ordered list) 4. Find the RANGE: Tom's Trap Troubles Number of traps set per room: 5, 7, 2, 5, 8, 5, 10, 6 5. Calculate Mean, Median, and Mode. Which one best represents "typical" trap numbers? Why? 6. Day 11: Jerry steals a huge 50g wedge! Which measure (Mean or Median) is most "sensitive" to this outlier? Explain. Cartoon Chaos / Mission 2 Chase Durations (min) Records: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 8, 10 7. Create a Dot Plot for the durations: 012345678910 Nap Frequency (min) Data: 15, 22, 45, 50, 55, 62, 65, 70, 75, 80, 85, 90, 110, 115, 120 8. Frequency Table: RangeFreq0 - 3031 - 6061 - 9091 - 120 9. Sketch Histogram: 86420 0-3031-6061-9091-120 10. Describe the shape of the histogram. What does it suggest about Tom's typical nap length? Cartoon Chaos / Mission 3 Trap Outcome Data (n=50) Trap TypeSuccessFailureTotalMouse Trap81220Box & String51015Anvil Drop21315Total153550 11. P(Success)? (as fraction) 12. P(Anvil Drop)? 13. P(Box & String | Failure)? 14. Best Trap? (Show math for highest success rate) The Ultimate Gamble Jerry has 20 marbles: 8 Red, 5 Blue, and 7 Green. He picks one at random. 15. What is P(Not Red)? 16. What is P(Blue or Green)?
Chaos Key Answer KeyChaos Key Answer Guide Part 1 & 2 1. MEAN Cheese 15.7g 2. MODE Cheese 12g 3. MEDIAN Cheese 13.5g Order: 8,10,12,12,12,15,15,18,20,28 4. RANGE Cheese 20g (28-8) 5. Tom's Traps Center Measures Mean: 6.375 Median: 5.5 Mode: 5 The Median (5.5) or Mode (5) are better than the mean (6.375) because the outlier "10" pulls the mean upward, making Tom look more aggressive than he actually is in most rooms. 6. The 50g Outlier Effect The Mean is most sensitive. It uses the sum of all values, so a massive 50g increase spikes the average significantly. The Median only moves one position in the list, making it "robust." 7-9. Visualization Guide 7. Dot Plot Stack dots above 1(1), 2(2), 3(3), 4(4), 5(2), 6(1), 8(1), 10(1). 8. Frequencies 0-30: 2 | 31-60: 3 | 61-90: 7 | 91-120: 3 9. Histogram Bars Bars should reach heights of 2, 3, 7, and 3 respectively on the frequency axis. 10. Shape & Habit Analysis The histogram is Symmetrical / Bell-shaped. This suggests Tom has a very consistent routine, usually napping between 61-90 minutes. He rarely takes power naps or 2-hour marathons. Chaos Key Answer Guide Part 3 11. P(Success) 15 / 50 = 3/10 12. P(Anvil Drop) 15 / 50 = 3/10 13. P(Box | Failure) 10 / 35 = 2/7 14. Best Trap Analysis Mouse Trap: 8/20 = 40% Box: 33%, Anvil: 13%. Mouse Trap is most effective. 15-16. MARBLE PROBABILITY 15. P(Not Red) 12 / 20 = 3/5 Complement rule: 1 - P(Red) = 1 - 8/20 16. P(Blue or Green) 12 / 20 = 3/5 Addition: (5/20) + (7/20) = 12/20 End of Assessment All student responses should be provided in simplified fraction form unless otherwise specified.
Plotting the Chase SlidesUnit: Cartoon Chaos Plotting the Chase Mastering Dot Plots and Histograms with Tom and Jerry Why Visualize Data? Raw data like chase times (2, 5, 2, 8, 2, 10...) can be messy and hard to read at a glance. "A graph tells a story. Is Jerry getting faster? Is Tom getting closer? Visualization reveals the pattern." See clusters and gaps Identify outliers (extreme events) Understand the "shape" of the chase Anatomy of a Dot Plot Best for small datasets where every individual value matters. The Axis A horizontal number line covering the full range of your data. The Dots One dot (or X) for every time a value appears. Stack them vertically! Labels Always title your graph and label what the numbers represent (e.g., "Minutes"). Building The Cheese Log The Data: 2, 2 3 4, 4 4, 4 5, 8 Step 1: Draw axis 2-10. Step 2: Stack dots for each value. 2345678910 Cheese Holes per Slice The Histogram Best for large datasets grouped into intervals (bins). What's different? • No space between bars. • Values are grouped (e.g., 0-10 minutes). • Focuses on frequency distribution. If Tom naps for 15, 22, and 28 minutes, we would stack them into the 11-20 and 21-30 bins respectively. 0-1011-2021-3031-40 Example: Tom's Nap Durations Reading the Shape Symmetrical Data is evenly spread around the center. Looks like a hill. Skewed Right The "tail" goes to the right. Most data is on the low end (like Tom's rare successes). Skewed Left The "tail" goes to the left. Most data is on the high end (like Jerry's escape rates). Quick Check! If we have 500 data points for Tom's speed, should we use a Dot Plot or a Histogram? Histogram! (Too many dots!)
Plotting the Chase WorksheetData Detectives Part 1: The Dot Plot Mission NAME: _________________________ DATE: _________________________ Detective's Notebook A Dot Plot uses a number line to show frequency. Every time a value appears, place a dot above that number. If it repeats, stack them! This helps us see clusters and gaps at a glance. The Great Cheese Count Jerry counted the holes in 12 different slices of cheese: 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 9, 10. 1. Construct a Dot Plot for the cheese holes: 3 4 5 6 7 8 9 10 2. What is the MODE? 3. Is there a gap? Where? Data Detectives Part 2: Pursuit Histograms Detective's Notebook A Histogram groups data into "bins". Bars touch because the data is continuous. Height shows frequency—how many values fall into that range. Pursuit Pace Tom recorded his top speeds (mph) during 20 chases: 8, 12, 14, 15, 18, 19, 21, 22, 22, 24, 25, 26, 28, 29, 31, 32, 33, 35, 38, 42. 4. Complete the Table: Speed (mph)Freq0 - 1011 - 2021 - 3031 - 4041 - 50 5. Sketch Histogram: 86420 0-1011-2021-3031-4041-50 6. Describe the shape. What does it suggest? Data Detectives Part 3: Advanced Analysis The Extreme Outlier Imagine Tom drinks an ACME Rocket Potion and has one "Extreme Chase" where he reaches 85 mph. 7. Shape Shift How would this affect your histogram's shape? Mention "tail" or "skew". 8. Mean vs. Median Which measure is hit harder by this extreme 85 mph outlier? Why?
Trap Tactics SlidesMission: Probability Trap Tactics Mastering Frequency Tables and Predicted Outcomes What is Frequency? Frequency is simply how often something happens. Tom's Saturday: Tripped over rug: 4 times Hit with pan: 7 times Caught Jerry: 0 times Total Sample Space The sum of all frequencies is your Total (n). In the example above, the total events recorded are 4 + 7 + 0 = 11. The Two-Way Table Comparing two different categories at the same time. Weapon UsedSuccessFailureTOTALMouse Trap121830Iron Drop52530TOTAL174360 The Probability Formula General Rule: P(Event) = Wanted Outcomes Total Outcomes Always simplify your fractions or convert to a percentage! Example Case: Using the table on Slide 3, what is the probability of a Success? 17 / 60 ≈ 28.3% Reality vs. Theory Theoretical "What SHOULD happen." Example: If Jerry has 4 escape holes, the theoretical probability of him picking the kitchen hole is 1 out of 4 (25%). Experimental "What ACTUALLY happened." Example: Jerry escaped 10 times today. He used the kitchen hole 8 times. The experimental probability is 8 out of 10 (80%). "Theoretical probability is the plan. Experimental probability is the cartoon chaos." Pro Tip: "OR" vs "AND" The "OR" Rule Probability of A OR B? ADD THEM! *Works when events are separate (mutually exclusive). The "AND" Rule Probability of A AND B? MULTIPLY! *Multiply the independent probabilities.
Trap Tactics WorksheetTrap Tactics Part 1: The Weekly Tally NAME: _________________________ DATE: _________________________ Tactical Briefing A Frequency Table organizes raw data by counting how often each result occurs. Relative Frequency is that count divided by the total, shown as a percentage. Object Observations Tom recorded the type of object he was hit by over 15 chases: Pan, Pan, Iron, Pan, Anvil, Iron, Pan, Anvil, Pan, Pan, Pan, Iron, Anvil, Pan, Anvil. 1. Construct a Frequency Table: ObjectFreqFrying PanHeavy IronFalling AnvilTOTAL (n)15 2. Rel. Freq (Pan) %: 3. Experimental P(Anvil): Trap Tactics Part 2: Room Results Outcome Data Table A Two-Way Table shows frequency for two categorical variables. LocationCaughtMissedTotalKitchen41620Living Room62430Total104050 4. P(Caught AND Living Room)? 5. Given Kitchen, P(Caught)? Trap Tactics Part 3: Theoretical Chaos The Marble Bag Jerry has 100 marbles: 40 Red (Left), 35 Blue (Right), 25 Green (Up). 6. Theoretical Probability of GREEN? 7. Prediction: 500 picks, how many BLUE? 8. Frequency Plot Review Using the Weekly Tally counts from Page 1 (Pan=9, Iron=3, Anvil=3), create a dot plot of these frequencies on the line below. Anvil Iron Pan Mastering the Chaos
Unit Expansion Answer KeyAnswer Keys Unit Phase 2 & 3 Quick Guide Plotting the Chase 1. Dot Plot Stack dots: 4(1), 5(2), 6(4), 7(2), 8(1), 9(1), 10(1). 2. Mode 6 holes 3. Gaps Gaps at 0, 1, 2, 3 holes. 4. Frequencies 0-10: 1 | 11-20: 5 | 21-30: 8 | 31-40: 5 | 41-50: 1 6. Shape Analysis Symmetrical. Tom's speeds are consistent around 25 mph. 7-8. Outlier (85 mph) Yes, it's an outlier. Effect: Skews right. Mean is pulled significantly; Median stays stable. Trap Tactics 1. Weekly Tally Pan: 9 | Iron: 3 | Anvil: 3 | Total: 15 2. Rel. Freq (Pan) 60% (9/15) 3. P(Anvil) 1/5 or 20% 4. P(Caught AND Living Room) 6 / 50 = 3/25 (12%) 5. P(Caught | Kitchen) 4 / 20 = 1/5 (20%) 6-7. Theoretical Twist 6. 25/100 = 25% 7. 0.35 * 500 = 175 BLUE 8. Review Dot Plot Height of stacks match frequencies (9, 3, 3).
