Cogito
Grade 7 Math · Chapter 9 · Lesson 2
Samples and What They Tell You
Asking some to learn about all.
10 problems · about 18 minutes · 7.SP.A.1, 7.SP.A.2
What this lesson teaches
The child understands why a sample must be representative and uses samples to draw inferences.
- A sample stands in for a population.
- It must be chosen fairly, or it tells you nothing reliable.
- Scaling a sample up to a population is a ratio.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Probability as a Number: A fair die. Out of 6, how many outcomes are less than 3?
Answer 2
Why 2 out of 6.
Review — When Three Measurements Fix a Triangle: Can sides 4, 4 and 9 make a triangle? 1 for yes, 0 for no.
Answer 0
Why No — 8 is less than 9.
Warm Up
Straightforward practice. Get the method working first.
4 problems9 of 30 sampled. In 300, about how many?
Answer 90
Why About 90.
What makes a sample useful?
Answer It represents the whole population fairly.
Why Representativeness matters more than size.
8 of 40 sampled. In 200, about how many?
Answer 40
Why Scaled by 5.
6 of 25 sampled. In 100, about how many?
Answer 24
Why Scaled by 4.
Build It Up
The same ideas with more to keep track of.
2 problems30 of 60 sampled. In 400, about how many?
Answer 200
Why Half.
Should a sample favour one group?
Answer No.
Why That is what bias means.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Survey: 15 of 50 sampled prefer tea. In 500 people, about how many would prefer tea?
Answer 150 people
Why About 150.
The Bad Sample: Asking only people in a library about reading. Is that representative?
Answer No. Library visitors read more than most.
Why The sample favours readers, so it is biased.