Cogito
Integrated Math 3 · Chapter 7 · Lesson 1
Sampling and Sampling Variability
Why two samples never agree.
12 problems · about 21 minutes · S-IC.A.1, S-IC.B.4
What this lesson teaches
The student distinguishes parameters from statistics and describes sampling variability.
- A parameter describes a population; a statistic describes a sample.
- Random sampling protects against bias; a larger sample does not.
- Statistics vary from sample to sample, and larger samples vary less.
Warm Up
Straightforward practice. Get the method working first.
5 problemsWhich sample gives a more reliable estimate? 1 for size 30, 2 for size 3000.
Answer 2
Why The larger one.
Why does a larger sample not fix bias?
Answer Bias is systematic, so more data repeats the same error.
Why It makes a wrong answer more precise.
A value describing a sample. 1 parameter, 2 statistic.
Answer 2
Why S for sample.
Do two random samples usually give identical statistics? 1 yes, 0 no.
Answer 0
Why Variation is expected.
Which sample varies less? 1 for size 25, 2 for size 2500.
Answer 2
Why Bigger settles down.
Build It Up
The same ideas with more to keep track of.
3 problemsAn online poll where readers choose to respond. Biased? 1 yes, 0 no.
Answer 1
Why Voluntary response.
Which is usually unknown? 1 parameter, 2 statistic.
Answer 1
Why You estimate it.
Which matters more for accuracy? 1 method, 2 size.
Answer 1
Why Size cannot repair bias.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each term by what it describes.
Answer Describes a population: Parameter, The true proportion in favour · Describes a sample: Statistic, The proportion among 200 people asked
Why Only one of the two can actually be measured.
Population 50% in favour. Is 70% from a sample of 10 surprising? 1 yes, 0 no.
Answer 0
Why Small samples swing widely.
The Name: A value describing a whole population. 1 parameter, 2 statistic.
Answer 1
Why A parameter.
The Size: Does a larger sample fix bias? 1 yes, 0 no.
Answer 0
Why No.