Head to Head Slides Small Group Intervention
HEAD-TO-HEAD
DATA
Comparing populations using measures of center and variability.
Measures of Center
Variability
The Big Question
01
"How can we use samples to tell the difference between two large populations?"
Center
Where is the middle of the data?
MEAN MEDIAN
Variability
How spread out is the data?
MAD IQR
The Case: Game Time
02
Two middle schools are having a competition to see which school spends more time practicing sports.
Population A: Oak Academy
500 Students
Population B: Pine Prep
480 Students
Should we survey all 980 students?
Why or why not?
Calculator Squad
03
1
Input Data
Enter your values into a list or table.
2
Stats Mode
Select "1-Var Stats" to get your measurements.
3
Read Results
Identify &xbar; (mean) and Med (median).
Pro Tip: MAD vs. IQR
Use MAD when the data is symmetric. Use IQR when there are outliers!
The Comparison
04
Comparing Centers
Difference in Means = Mean A - Mean B
How many variations (MADs) fit between the centers?
High Overlap
The groups are very similar.
Low Overlap
The groups are distinct and different.
Collaborative Project
05
THE DATA DUEL
In your teams, you will investigate two snack brands. You will calculate the stats, compare the spread, and declare a "Statistical Winner"!
1. Calculate
2. Compare
3. Conclude
Stat Squad Teacher Guide Teacher Resource
REF: 7.SP.B.4 | TIER 2 INTERVENTION
STAT SQUAD TEACHER GUIDE
Head-to-Head Data: Comparing Populations
Objective
Students will use measures of center (mean, median) and variability (MAD, IQR) from random samples to make informal comparative inferences about two populations. They will identify the degree of overlap and quantify the difference between centers.
Target Skills
Calculating mean/median using digital tools (calculators/Desmos).
Understanding MAD as a "standard" unit of distance between centers.
Expressing the difference between centers as a multiple of a measure of variability.
Materials Needed
• Scientific Calculators (TI-30XS or similar)
• Student Worksheets & Project Packs
• Chromebooks (optional for Desmos)
• Highlighters (2 colors per student)
Phase 1: Launch (5-7 mins)
Prompting Question:
"If I tell you the average height of a basketball player is 6'7" and the average height of a gymnast is 5'2", do you need to see every single athlete to know which group is taller?"
Key Point: Samples give us a snapshot. We use center and spread to see if that snapshot represents the whole group or if it's just a coincidence.
Phase 2: Scaffolding Calculation (15 mins)
Focus on efficiency over manual arithmetic. Intervention students often get lost in the addition/division steps of calculating the mean.
Misconception Alert
Students often think a larger range means a higher mean. Explicitly show two sets with the same mean but different ranges to break this link.
The "MAD" Distance
Help students see MAD as a "ruler." If the distance between means is 10 and the MAD is 2, the means are "5 MADs apart." This is a huge distance!
Phase 3: Collaborative Data Duel (20 mins)
Group students in pairs. Give them the "Data Duel" sheet. They must choose two populations (Brand A vs Brand B) and use their calculators to "duel" the data.
Facilitation Prompts:
"Look at the box plots—do the boxes overlap or are they completely separate?"
"If you picked a random data point from Brand A, is there a high chance it's higher than a point from Brand B?"
"Which brand is more 'predictable' (lower variability)?"
Monitoring for Success
Use the Statistical Reasoning Rubric during the Data Duel. Don't just look for correct numbers—look for students using comparative language like "significantly higher," "more consistent," or "higher degree of overlap."
Population Showdown Worksheet Population Showdown
Stat Squad Field Mission 01
Agent Name:
Mission Date:
The Mission
The "Daily Fuel" cafeteria wants to know if 7th Graders or 8th Graders eat more apples per week. They took a random sample of 10 students from each grade.
7th Grade Sample
2 3 2 5 4 3 3 1 2 3
8th Grade Sample
5 6 4 5 7 5 4 6 5 3
1
Crunch the Numbers
(Use your Stat Squad Calculator)
7th Grade Stats
Mean (\(\bar{x}\)):
MAD:
8th Grade Stats
Mean (\(\bar{x}\)):
MAD:
2
Measure the Distance
A. Difference in Means
8th Mean
−
7th Mean
=
Distance
B. How many MADs fit in that distance?
Pick the MAD from either grade (use the larger one if they are different).
Distance
÷
MAD
=
Scale
3
Draw the Inference
Based on your results, do 8th graders really eat more apples, or is the data too similar?
High Overlap (Difference is less than 1 MAD)
Large Difference (Difference is 2+ MADs)
Data Duel Project The Data Duel
Collaborative investigation: Which granola bar brand is the "hidden sugar" champion?
The Briefing
Your team has been hired by a health magazine to compare two popular brands of granola bars. We want to know: "Is there a significant difference in the sugar content between Brand A and Brand B?"
Brand A: Berry Blast
9g, 12g, 10g, 11g, 9g, 13g, 10g, 11g, 10g, 12g
Brand B: Nutty Nature
15g, 14g, 18g, 16g, 15g, 17g, 15g, 16g, 14g, 19g
Team Goal
Create a "Duel Report" comparing the two brands. You must use Mean, MAD, and the "Distance Scale" to justify your conclusion.
Analyze Data
Draw Box Plot
Declare Winner
Team Duel Report
Team: ____________________
1. Visual Comparison
Sketch a simple double dot plot or box plot to show the sugar grams of both brands.
2. Statistical Proof
Metric Brand A Brand B Mean (\(\bar{x}\)) MAD
3. The MAD Distance
Difference in Means:
Distance Score (Diff ÷ MAD):
4. The Verdict
Write 2-3 sentences explaining if Brand B has "significantly" more sugar. Use your numbers to prove it!
