Tar Heel Tallies Slides Math Grade 7-8
Tar Heel Tallies
Sampling Methods & Making Inferences using North Carolina School Data
UNIT: STATISTICS & PROBABILITY
Today's Missions
The "Who" & "How"
Distinguish between populations and samples .
Identify representative (random) vs. biased samples.
The "What" & "Why"
Use samples to predict info about big groups.
Compare two NC districts using center and variability .
STANDARDS: NC.7.SP.1, 2, 3, 4
Population vs. Sample
Population
The entire group you want information about.
Example: Every student in NC!
Sample
A part of the population that is actually surveyed.
Example: 100 students from 5 schools.
Population
Sample
Why not just ask everyone?
The Secret Sauce: Randomness
Simple Random
Every member has an equal chance . Like names in a hat or a computer generator.
Systematic
Pick a starting point and choose every "nth" person (like every 10th student on a roster).
Stratified
Divide the group into subgroups (like grade levels) and pick randomly from each.
Representative Samples = VALID INFERENCES
Spot the Bias!
Scenario A: The Lunch Poll
BIASED?
A researcher wants to know the favorite lunch in NC schools. They survey only students waiting in line for pizza .
WHY: They are only asking people who already like what is being served!
Scenario B: School Start Times
UNBIASED?
A principal wants to know if students want school to start later. She uses a computer to randomly pick 50 ID numbers from the entire student list .
WHY: Every student had an equal chance of being picked.
Tar Heel Math: Making Predictions
Case Study: Career Goals
In a random sample of 200 middle schoolers in Wake County , 30 say they want to be software engineers. There are 12,000 middle schoolers in the district.
The Ratio
\[ \frac{30}{200} = \frac{x}{12000} \]
➔
The Prediction
1,800 students
"Inference" is just an educated guess based on data!
Comparing Districts: The Center
Measure of Center
We use the Mean (Average) or Median (Middle) to find the "typical" value.
North Carolina Context
Imagine comparing the number of library books per student in Durham County vs. Guilford County .
Avg. Daily Attendance (%)
District A (Coastal) 94%
District B (Mountain) 91%
Inference: District A tends to have slightly higher attendance than District B.
Comparing Districts: Variability
MAD & IQR
• MAD: Mean Absolute Deviation
• IQR: Interquartile Range
These numbers tell us how spread out or consistent the data is. Smaller variability = more consistent!
DATA SNAPSHOT: MATH SCORES
District Median IQR Mecklenburg 82 12 Wake 82 5
The Catch: Both have the same median, but Wake is more consistent (smaller IQR).
Overlap & Box Plots
Asheville Schools
Wilmington Schools
Low Overlap
When boxes don't touch, there is a significant difference between the groups.
High Overlap
If boxes are on top of each other, the groups are very similar .
Time to Tally!
Grab your worksheet. We are going to analyze real data from NC districts to find out who's winning the "Data Games."
Check for Bias
Calculate Inferences
Tar Heel Tallies Worksheet Tar Heel Tallies Worksheet
Name: __________________________ Date: __________
MISSION: Use your knowledge of populations, samples, and inferences to analyze data from across North Carolina school districts. Show all your work for full credit!
1
The Data Toolkit
Match the term to its best definition:
Population: A. A portion of a group used to represent the whole.
Sample: B. When a sample does not represent the whole group.
Inference: C. The entire group being studied.
Bias: D. A conclusion reached based on data/evidence.
Pro-Tip: A sample is only "representative" if every member of the population had an equal chance of being chosen!
2
Spot the Bias: NC Scenarios
Scenario A: To find out how many NC families own a boat, a researcher surveys 200 people at a marina in Wilmington .
Is this Biased? (Circle one) YES / NO
Explain why:
Scenario B: To determine the favorite subject of students in Cumberland County , a computer randomly selects 100 student ID numbers from all middle schools in the district.
Is this Biased? (Circle one) YES / NO
Explain why:
3
Tar Heel Predictions
Problem: A random sample of 250 high school students in Charlotte-Mecklenburg Schools (CMS) was asked if they play a varsity sport. 40 students said "Yes." If there are 45,000 high school students in CMS, how many can we infer play a varsity sport?
Set up your proportion:
Final Answer:
________________ students
4
District Duel: Analyzing Data
Compare the box plots below showing the number of science fair projects submitted per school in two NC districts.
District X
District Y
01020304050607080
1. Which district has a higher median?
2. Which district has more variability (IQR)?
3. Is there much overlap between the data?
4. What can you infer about science fairs in District Y?
Tar Heel Tallies Practice Quiz NC Check-In Practice
Tar Heel Tallies Assessment Statistics & Probability • Grade 7
Student Name: __________________________________
The superintendent of Guilford County Schools wants to know how many students plan to attend a community college after graduation. Which method would produce the most representative sample of the student population?
Surveying every 10th student listed in the district's database.
Surveying students at a single high school's football game.
Surveying only students enrolled in Honors English classes.
Surveying students who volunteer to fill out an online form.
A random sample of 80 students at a middle school in Asheville were asked about their favorite outdoor activity. 24 students chose hiking. If there are 600 students in the school, how many would you predict prefer hiking?
120 students
180 students
240 students
320 students
Two random samples of 50 light bulbs were tested from two different NC factories. In Factory A, 2 bulbs were defective. In Factory B, 5 bulbs were defective. Based on this, which inference is most valid ?
Factory A is likely to produce more defective bulbs than Factory B.
Factory B is likely to produce more defective bulbs than Factory A.
Both factories will produce the same number of defective bulbs.
Neither factory will produce any defective bulbs in a larger order.
The median score for District M on a state test is 85 with an IQR of 5. The median score for District N is 75 with an IQR of 5. How many times the IQR is the difference between the two medians?
A 1 time
B 2 times
C 5 times
D 10 times
Compare the box plots showing the daily high temperatures (degrees Fahrenheit) for one week in Boone and Cape Hatteras .
Boone
Hatteras
30405060708090
Which statement is supported by the data in the box plots?
Boone has a higher median temperature than Cape Hatteras.
Cape Hatteras has a higher median temperature than Boone.
The temperatures in Boone are more consistent than Cape Hatteras.
Tar Heel Tallies Teacher Guide Teacher Resource
Tar Heel Tallies Guide
Grade 7-8 Math
Lesson Duration
60-90 Minutes
Focus Standards
NC.7.SP.1, 2, 3, 4
Key Theme
NC School Data
Learning Objectives
Students will identify the difference between a population and a representative sample.
Students will evaluate sampling methods for potential bias.
Students will use proportions to make predictions (inferences) from sample data.
Students will compare two populations visually and numerically using measures of center (mean, median) and variability (MAD, IQR).
Suggested Pacing
10 MIN
Hook & Slide Intro
Use Slide 1-3 to introduce the "Tar Heel Tallies" theme. Discuss why we can't survey all 1.5 million NC students (cost/time).
20 MIN
Direct Instruction (Slides 4-9)
Focus on Slide 5 (Bias) . Have students debate the scenarios before showing the answers. Use Slide 8 to clarify that MAD and IQR measure "consistency" or "spread."
25 MIN
Guided & Independent Practice
Distribute the Tar Heel Tallies Worksheet . Students work through Part 1-3. Circulate during the "District Duel" box plot analysis.
15-20 MIN
Assessment (EOG Quiz)
Administer the 8-question practice quiz to check for mastery. Review the most difficult question as a class.
Watch Out For: Common Misconceptions
Sample Size vs. Randomness
Students often think a larger biased sample is better than a smaller random sample. Reinforce that how you pick is more important than how many you pick.
Measures of Variability
Students often confuse MAD/IQR with "the average." Remind them that a higher MAD means the data is less predictable and more spread out.
Discussion Sparkers
"If we survey every student in our class, is that a representative sample of all middle schoolers in North Carolina?"
"Why might a school district in the mountains (like Boone) have a higher MAD for snowfall than a coastal district (like Wilmington)?"
Tar Heel Tallies Answer Key Answer Key: Tar Heel Tallies
Teacher Copy
Worksheet Answers
Part 1: The Data Toolkit
Population: C | Sample: A | Inference: D | Bias: B
Part 2: Spot the Bias
Scenario A: YES (Biased). People at a marina are more likely to own boats than the general population.
Scenario B: NO (Unbiased). Randomly picking ID numbers from the entire group gives everyone an equal chance.
Part 3: Tar Heel Predictions
Proportion: \[ \frac{40}{250} = \frac{x}{45,000} \]
Steps: 45,000 × 40 = 1,800,000. Divide by 250.
Final Answer: 7,200 students
Part 4: District Duel
Median: District Y (~60) is higher than District X (~40).Variability: District X has more variability (the box is wider, IQR is ~30 vs District Y's ~15).Overlap: There is very little overlap between the boxes.Inference: Schools in District Y typically submit significantly more science fair projects than District X.
EOG Practice Quiz Answers
1
A. Surveying every 10th student. This is systematic random sampling , which is representative.
2
B. 180 students. Set up proportion: \[ \frac{24}{80} = \frac{x}{600} \]. Simplify 24/80 to 3/10. 0.3 × 600 = 180.
3
B. Factory B had 5 defective per 50, which is higher than Factory A's 2 per 50. Inference: Factory B produces more defects.
4
B. 2 times. Difference in medians: 85 - 75 = 10. IQR = 5. Since 10 is 2 × 5, the difference is 2 times the IQR.
5
B. The median for Cape Hatteras (plotted further to the right) is higher than Boone's median.
6
B. Attendees at a pro game (who paid for tickets) may not represent the average income of the whole state.
7
A. District A. A smaller MAD (2.1 vs 8.5) means scores are closer to the mean (more consistent).
8
A. The ratio of supporters to the sample (120/200) should equal the ratio of total supporters to the total population (s/7.5M).
