Studio Aletheia · The Center for Quantitative Studies
6.DPSR.1.1SC 6th Grade Math
Sizing Up the Sample
Lesson 03 · Guided Practice, Identify Sample Size
Yesterday you named a sample size and a population one scenario at a time. Today you'll size up several real scenarios back-to-back, deciding quickly whether each sample is big enough, and fair enough, to trust.
Learning Targets and Success Criteria
A quick recap, then a harder question: how a sample is chosen matters as much as how big it is.
What I will learn
- I can identify the sample size and population in a variety of scenarios.
- I can compare a sample size to its population to judge fairness.
- I can explain how the way a sample is chosen, not just its size, can bias results.
- I can revise a weak sampling plan to make it more representative.
What success looks like
- I quickly and accurately name sample size and population across multiple scenarios.
- I explain my fairness judgment using both size and how the sample was chosen.
- I identify at least one source of bias in a flawed sampling scenario.
- I propose a specific fix that would improve a weak sample.
Judge whether a variety of sample sizes fairly represent their populations.
The words we'll use in today's lesson.
These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.
Sample Size
The number of data values collected from a population to represent it in a data set.
Population
The entire group being studied, from which a smaller sample may be collected.
Where this shows up in the real world.
Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.
Spotting a Shaky Sample From a Mile Away
Data analysts get pitched shaky samples all the time, a survey of 12 loyal customers presented as "what everyone thinks." Learning to catch the mismatch between sample size, or sampling method, and population is a skill you'll lean on constantly once you're the one reading someone else's numbers.
Size Isn't the Only Question
A quick recap, then a harder question: how a sample is chosen matters as much as how big it is.
Remember, the populationThe entire group being studied, from which a smaller sample may be collected. is the whole group you care about, and the sample sizeThe number of data values collected from a population to represent it in a data set. is how many values you actually collected from it. A bigger sample size is usually more trustworthy, but size alone doesn't guarantee fairness. If you want to know what the whole school thinks about lunch, but you only ask kids sitting at one table, a sample size of 20 still won't represent the population well, because everyone you asked is alike in a way the rest of the school isn't.
So when you check a sample today, ask two things at once: is the sample size big enough, and was it chosen in a way that gives every part of the population a fair chance to be included? A small, carefully chosen sample can sometimes beat a large, lopsided one. Today's scenarios will test both instincts.
Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.
Materials for the Data Lab.
- A. Sample Size Scenario Cards (Set B)
- B. Bias Detective Checklist
- C. Sticky notes
- D. Your Data Journal
- E. A calculator (optional)
Every time a data set shows up, name the population, then check both the size and the selection method before judging fairness.
Sample Size Sort
We'll sort today's scenarios by whether their sample size, their selection method, or both, cause a problem.
Fix a Flawed Sample
You'll take a biased sampling plan and redesign it so it actually represents its population.
Data Journal Entry
Accountability Checklist
Big Enough Isn't Always Fair Enough
A company wants to know what all of its 2,000 customers think, so it surveys 500 customers, but only ones who left a 5-star review. Is this sample size appropriate for the population? Explain.
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