A middle school statistics lesson focused on comparing box plots, understanding quartiles, and making proportional predictions using sample data. Includes parallel standard and scaffolded interactive notebook spreads.
B) Compare median travel times. Which route is typically faster?
The median for Route 10 is _______, and Route 12 is _______. Therefore, Route ________ is typically faster.
C) Route 12 has a longer right whisker (skewed). How will mean compare to median?
Since the data is skewed to the right, the mean will be higher / lower than the median.
2 Survey & Prediction Challenges
Scenario A: In a recent school survey, 13 out of 20 students prefer Spring over Fall. If 200 more students were asked, what is a reasonable prediction of how many choose Spring?
1. How do you scale from 20 to 200?
→ Multiply by ________
2. Do the same to the top!
→ 13 × ________ = ________
Scenario B: A sports store surveys customers: 6 out of 15 athletes prefer trail running. If the store plans for 250 additional athletes, how many would you predict prefer trail running?
Hint: 15 doesn't multiply to 250 easily. First, simplify 6/15 to its simplest form by dividing both numbers by 3:
6/15 = 2 / 5
Now, scale from 5 to 250 by multiplying by 50!
💡 INSTRUCTIONS: Glue the back of this page onto the RIGHT PAGE of your notebook spread.
METHOD 2: Percent Route
Find the sample percent:
13 ÷ 20 = 65%
Take 65% of additional:
0.65 × 200 = 130
Lesson Material: Slideshow Component
Slide 4 of 5
Mission Briefing Data Detectives
Your Turn: Detective Field Notebook
Now Open Your Foldable Spreads!
Assemble your spreads, paste them into your composition notebooks, and complete the "Battle of the Bus Routes" cases!
1. CUT & PASTE
Trim along dashed borders and secure into left/right pages.
2. DETECT
Verify the 25% splits and shape skews on Route 10 & 12.
3. FORECAST
Scale up the Spring preference to make predictions.
Lesson Material: Slideshow Component
Slide 5 of 5
Comparing Shapes Rule 1: Symmetric Mean and Median are roughly equal.
Comparing Shapes Rule 2: Skewed Mean is pulled toward the longer tail.
2. Case Study Solutions: Commuter Bus Routes
Question A: Percent under Q3 values
Route 10 (under 42.5 minutes): 42.5 is Q3. Since there are three 25% parts below Q3 (left whisker, left box, right box), 75% of Route 10 trips are under 42.5 minutes. Route 12 (under 50 minutes): 50 is Q3. Three parts of Route 12 also lie below 50, so 75% of Route 12 trips are under 50 minutes.
Question B: Median Comparison
Route 10 Median = 32.5 mins.
Route 12 Median = 40 mins. Route 10 is typically faster because its median travel time is 7.5 minutes shorter.
Question C: Shape & Mean vs Median
Route 12 has a longer right whisker (skewed right). The mean will be higher than the median (Mean > 40 mins) because the outliers pull the average upward.
