Sample Showdown Slides Sample Showdown
Comparing Populations with Data
The Big Question
"How can we use small samples to tell us about entire populations?"
Center (Mean)
The "typical" or "average" value in our data set.
Variability (MAD)
How "spread out" or "consistent" the data is.
Mystery Word Lengths
Book A: Picture Book
Word lengths (number of letters):
3 2 4 5 1
Book B: Science Journal
Word lengths (number of letters):
10 8 12 7 13
Which book has longer words?
Just looking at the numbers is okay, but we need statistical evidence to make an inference about the whole book.
Discussion Tip:
Do you think every word in the Science Journal is 10 letters? Why or why not?
Step 1: Finding the Center
Mean Calculation
1
Add all values
2
Divide by the count (\(n\))
Book A (Picture Book)
\(3+2+4+5+1 = 15\)
\(15 \div 5 = 3\text{ letters}\)
Book B (Science Journal)
\(10+8+12+7+13 = 50\)
\(50 \div 5 = 10\text{ letters}\)
Step 2: How Spread Out? (MAD)
Mean Absolute Deviation (MAD)
The average distance of each data point from the mean.
Find distances from mean
Add distances up
Divide by count (\(n\))
The Verdict
If the means are far apart and the MAD is small, the populations are likely very different!
Our Inference
"Based on our samples, the Science Journal likely has significantly longer words than the Picture Book because its mean is \(7\text{ letters}\) higher and the data sets don't overlap much."
Book A (Center at 3)
Book B (Center at 10)
Look at that gap! No overlap = Strong Inference.
Inference Insider Teacher Guide Inference Insider Teacher Guide
Lesson: Sample Showdown (Grade 7 Tier 2 Intervention)
Teacher Resource
Objective
Students will use measures of center (mean) and variability (MAD) from random samples to draw informal comparative inferences about two populations. They will justify their inferences using the degree of overlap between data sets.
Standards Alignment
Colorado 7.SP.B.4
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.
Quick Prep
Print Sample Showdown Worksheets
Calculator for each student
Two colored highlighters
Instructional Sequence
1
Introduction & Warm-Up (5 min)
Show Slide 2 . Activate prior knowledge about "Mean" (the balance point) and "Spread" (how different the data points are). Use the analogy of two basketball players: one averages 20 points every single game (low variability), one averages 20 points but scores 2 one night and 38 the next (high variability).
2
Guided Case Study (15 min)
Use Slides 3-5 alongside the student worksheet. Guide students through the word length calculation.
Prompt: "If Book B's mean is higher, but its MAD is HUGE (like 8), would we still be certain that Book B always has longer words? Why or why not?"
3
Comparative Paragraph Writing (10 min)
Use Slide 6 . Students transition to the back of the worksheet or the Exit Ticket. They must use the "Inference Formula":
Common Misconceptions
Confusing Mean with MAD
Students often try to use the MAD as the "center." Remind them that MAD is like a "wiggle room" measurement, while Mean is the "anchor."
Sample vs. Population
Students might think the mean of 5 words is the mean of the *whole book*. Stress the word "Inference"—we are making an educated guess about the rest of the book based on our small window.
Sample Data Key
Metric Book A (Picture) Book B (Science) Sum 15 50 Mean 3 letters 10 letters MAD 1.2 2.0
Sample Showdown Worksheet Sample Showdown Lab Report
Data Detective Agency • Investigation #042
Agent:
Date:
Mission: Compare two sets of "Mystery Book" word lengths. Calculate the average (Mean) and consistency (MAD) to decide which book likely has longer words overall.
1
Find the Mean (The Center)
Book A: Picture Book
Sample # Letters Word 1 3 Word 2 2 Word 3 4 Word 4 5 Word 5 1
Sum calculation:
Mean (Sum ÷ 5):
Book B: Science Journal
Sample # Letters Word 1 10 Word 2 8 Word 3 12 Word 4 7 Word 5 13
Sum calculation:
Mean (Sum ÷ 5):
2
Find the MAD (The Variability)
Directions: For each word, find how far it is from the Mean you just calculated. (Distance is always positive!) Then find the average of those distances.
Book A: Distances from Mean
Add distances and divide by 5:
Book B: Distances from Mean
Add distances and divide by 5:
3
The Inference
Final Conclusion
Based on my calculations, I infer that Book _______ has longer words overall.
I know this because the mean of Book A is and the mean of Book B is .
The difference between the means is . This difference is (circle one) Large / Small compared to the MAD.
Show your visual evidence: Plot the means and MAD range below.
0
4
8
12
16
Plot Twists Exit Ticket Progress Monitor: Comparative Inference
Student:
Date:
The Case of the Rival Teams
Coach Quinn measured a random sample of players from two rival basketball teams. You are the league statistician. Use the data below to make an inference about which team is taller overall.
The Bluebirds (Heights in inches)
60, 62, 64, 58, 61
Mean
61
MAD
1.6
The Hawks (Heights in inches)
68, 72, 70, 75, 65
Mean
70
MAD
2.8
The Comparative Inference
Write a paragraph answering the question: Which team is likely taller overall, and how much evidence do you have?
Include: The Means, the MAD, and a comment on the overlap.
Self-Check Checklist:
Mentioned Means
Mentioned MAD
Made an Inference
