Why this matters for FAST: Data analysis is a key component of the FAST assessment. Students must critically evaluate sampling methods and use sample data to make reasonable predictions about larger populations.
Students think that as long as the sample is large, it will be representative. A large biased sample is still biased!
"A sample of 10,000 people who all live in one city won't represent the whole country! How we SELECT the sample matters more than the size. A random sample of 100 people from across the country is better than 10,000 from one city."
Students think asking "whoever wants to answer" creates a random sample.
"Random means everyone has an equal chance of being selected - like drawing names from a hat. If you only survey people who volunteer, you might only get opinions from people who feel strongly about the topic!"
Students think if 40% of a sample prefers pizza, exactly 40% of the population prefers pizza.
"Sample results give us an ESTIMATE of the population. If our random sample shows 40% prefer pizza, the true percentage is CLOSE to 40% but might not be exactly 40%. That's why we say 'about' or 'approximately.'"
Ask: "If I want to know what all 7th graders in Florida think about homework, can I ask everyone?" Introduce why we use samples.
"The POPULATION is the whole group we want to learn about. A SAMPLE is a smaller part of the population we actually study. We use sample data to make INFERENCES - educated guesses - about the population."
Population vs Sample
Population: All 7th graders in Florida (millions!)
Sample: 200 randomly selected 7th graders from different schools
Inference: Using the sample to predict what ALL 7th graders think
Random Sample: Every member has an equal chance of being selected
Examples: Drawing names from a hat, using a random number generator, selecting every 10th person on a list
Biased Sample: Some members are more likely to be selected than others
Examples: Only surveying people at a mall, asking friends, voluntary online surveys
"If a random sample of 100 students shows 60% prefer pizza, we can predict that ABOUT 60% of ALL students prefer pizza. To find how many, multiply: 0.60 x total population."
Example: Making a Prediction
Sample: 50 of 200 students surveyed prefer vanilla ice cream (25%)
School population: 800 students
Prediction: About 25% of 800 = 0.25 x 800 = 200 students prefer vanilla
Work through these together:
"A researcher wants to know what teenagers think about social media. She surveys 100 teenagers at a technology convention. Is this a valid sample?"
A) Yes, 100 is a good sample size B) Yes, they are all teenagers C) No, this is a biased sample D) No, the sample is too small
Correct answer: C) No, this is a biased sample. Teenagers at a tech convention likely use technology more than average teenagers, so their opinions aren't representative.
For struggling students: Use hands-on activities with colored candies to demonstrate sampling. Draw samples multiple times to show variation. Focus on the concept of "fair" vs "unfair" selection.
For advanced students: Discuss sample size and margin of error. Have students design their own surveys and analyze potential biases. Compare multiple samples from the same population.
For home: Send Parent Activity sheet. Families can discuss sampling in news reports, product reviews, and election polls.