Identify Sample Size | The Center for Quantitative Studies | Studio Aletheia
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Identify Sample Size

Lesson 02 · New Content, Identify Sample Size

Every survey, poll, and experiment starts with a choice: how many people or things do you actually measure? Today you'll learn to name that number, the sample size, and decide whether it's big enough and fair enough to stand in for the whole group it came from.

Focus Sample size vs. population
Accountability Data Journal + Exit Ticket
Indicator Identify the sample size of a data set and determine ...
The Center for Quantitative Studies Color Palette Aletheian Green · Aletheian Gold
Learning Targets

Learning Targets and Success Criteria

Every data set comes from somewhere; today you'll learn to ask where.

Targets

What I will learn

  • I can find the sample size of a data set by counting its values.
  • I can explain the difference between a sample and the population it comes from.
  • I can decide whether a sample size is large enough to represent its population fairly.
  • I can explain why a sample that is too small or too biased can mislead a conclusion.
Success Criteria

What success looks like

  • I correctly state the sample size for a data set without miscounting.
  • I name both the sample and the population in a given scenario.
  • I judge a sample as appropriate or not, and give a reason based on size.
  • I use the terms sample size and population correctly in my own sentences.
Standard 6.DPSR.1.1

Decide whether a data set's sample size fairly represents its population.

6.DPSR.1.1 — Identify the sample size of a data set and determine if it is an appropriate representation of the population from which it was taken.
Vocabulary

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.

01 · Collect

Sample Size

The number of data values collected from a population to represent it in a data set.

02 · Describe

Population

The entire group being studied, from which a smaller sample may be collected.

College & Career Connections

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.

Data Analyst / Data Scientist

Why Size Matters Before the Math Even Starts

Before a data analyst calculates anything, they check how the data was collected. A sample that's too small or handpicked can produce numbers that look official but tell the wrong story, so this is one of the very first questions a professional asks.

Mini-Lesson

Sample vs. Population

Every data set comes from somewhere; today you'll learn to ask where.

Imagine you want to know the favorite lunch of every sixth grader in your school, all 400 of them. Asking all 400 would take forever, so instead you might ask 20 students and use their answers to make a guess about everyone. The entire group you actually care about, all 400 sixth graders, is called the populationThe entire group being studied, from which a smaller sample may be collected.. The smaller group you actually asked, the 20 students, is your data set, and the number of values in it has its own name.

That number, how many values you actually collected, is called the sample sizeThe number of data values collected from a population to represent it in a data set.. A sample size of 20 out of 400 might work well, but a sample size of 2 almost never will, because two opinions can't speak for a whole school. When you check a data set, always ask two questions: how many values are here, and does that number seem big enough and fair enough to stand in for the whole population?

Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.

Check for Understanding · CFU 1
A researcher asks 5 out of the 600 students in a school what time they go to bed. What is the sample size, and is it an appropriate representation of the population? Explain your thinking.
Toolkit

Materials for the Data Lab.

  • A. Today's Sample Size Cards
  • B. Population Scenario Sheet
  • C. Colored pencils (2 colors)
  • D. Your Data Journal
  • E. A calculator (optional)
Non-negotiable routine

Every time a data set shows up, name the population it came from before you touch a single number.

Guided Practice

Sample Size Lab

We practice on today's scenario cards before you tackle sample size on your own.

Data Lab
Each scenario below names a population and describes how a sample was collected from it.
1 · Identify
Identify the sample size and the population in your chosen scenario.
2 · Compare
Compare the sample size to the population size. Does it seem like a fair-sized slice?
3 · Describe
Describe one reason this sample might, or might not, fairly represent the population.
4 · Question
Write one question you'd still want to ask about how this sample was collected.
Hands-On

Build a Sample Size Case

You'll design your own quick survey and defend whether your sample size is solid.

1
Choose: Choose a population you could realistically ask about today, such as your class, your grade, or your bus.
2
Collect: Collect a sample size of at least 5 responses to a yes/no or short-answer question.
3
Record: Record your sample size and your population size side-by-side in your Data Journal.
4
Judge: Judge whether your sample size is large enough to represent the population, and write one sentence defending your answer.
Required

Data Journal Entry

Which Mathematical Process Standard did you rely on most today — Problem Solving, Connections, Representation & Communication, Analyze & Justify, or Structure & Patterns? Give one specific example from your Data Lab or hands-on work.
Checklist

Accountability Checklist

Required · Exit Challenge

Is 5 Enough?

A student wants to know the favorite streaming show among all 6th graders (about 150 students) and asks only their 4 closest friends. Is this an appropriate sample size for the population? Explain why or why not.

Lesson 02 · New Content, Identify Sample Size

The Center for Quantitative Studies · Course Navigation

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