08 / 12 · Learn from a sample
Why does a small sample jump around?
Understand why larger random samples usually give steadier proportions, not guaranteed exact answers.
Builds on Who actually answered?
Go to practice ↓A question to keep in mind
Does 7 heads in 10 fair tosses mean the coin's true chance is 70%?
A sample proportion is a result from this run. Change the run and the result can change, even when the underlying chance stays the same. This is sampling variation, not necessarily a calculation error.
With independent draws from the same process, larger samples usually make proportions less variable. They do not guarantee an exact answer, and do not repair a biased way of choosing people.
Work through an example
| Run | Out of 10 | Out of 100 |
|---|---|---|
| 1 | 3 (30%) | 45 (45%) |
| 2 | 7 (70%) | 55 (55%) |
| 3 | 4 (40%) | 48 (48%) |
| 4 | 6 (60%) | 52 (52%) |
- Seven heads out of ten gives a sample result of 70%.
- The fair-coin assumption still says the chance of each independent toss is 50%.
- The gap is 20 percentage points. A short run can differ from the underlying chance.
Your turn
0 / 3Over many repeated runs of independent fair-coin tosses, which sample proportion usually varies less?
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The proportion from 100 tosses.
This is a statement about repeated sampling, not a claim that every 100-toss run is closer than every 10-toss run.
One run has 4 heads out of 10; another has 52 out of 100. How far is each percentage from 50%, in percentage points?
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- Gap for 4 out of 10: 10 points
- Gap for 52 out of 100: 2 points
The gaps are 10 and 2 percentage points. In this particular example the larger sample is closer; no single example proves the general pattern.
A website surveys only its most active readers. Would collecting ten times as many of those readers automatically represent all readers?
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No. The same selection can still miss less-active readers.
A larger sample can reduce random variation while leaving selection bias in place.
Bring it back to your own work
Explain to a friend why 'more responses' and 'a better survey' are not always the same thing. Use one concrete example.
Statistical literacy: directory, audit and transfer assessment
How do I retain independent judgment when using AI here?
Keep your own answer before consulting an AI candidate. Check sources, calculations, inference and conditions; explain adoption or rejection. Then solve a new-context task independently and apply the checks to this lesson.
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