How a poll of 1,000 people can speak for millions
Sample size depends on the precision you want, not the size of the population. Why 1,000 responses is enough, and what a margin of error really means.
Every election season someone asks the same reasonable question: how can asking a thousand people tell you anything about a country of a hundred million? It sounds like it cannot possibly work. The mathematics says otherwise, and the reason is genuinely surprising — population size barely enters the calculation at all.
The population is almost irrelevant
To reach a 3% margin of error at 95% confidence you need 1,068 responses. That is the answer for a city of 100,000, a country of 100 million, or the entire planet. Only when the population becomes comparable to the sample does it start to matter:
| Population | Sample needed for ±3% at 95% |
|---|---|
| 1,000 | 517 |
| 100,000 | 1,056 |
| 100,000,000 | 1,068 |
| Effectively infinite | 1,068 |
The intuition that trips people up is thinking of a sample as a *fraction* of the population. It is not. What matters is the absolute number of independent observations, because precision comes from how much random noise averages out — and noise cancels at the same rate regardless of how many people you did not ask.
Precision is expensive, and it gets worse fast
Here is the real constraint. Halving your margin of error does not double the sample — it quadruples it, because error falls with the square root of the sample size.
| Margin of error (95% confidence) | Responses needed |
|---|---|
| ±5% | 385 |
| ±3% | 1,068 |
| ±2% | 2,401 |
| ±1% | 9,604 |
This is why almost every published poll lands between 800 and 1,200 responses. It is the point where cost and precision meet: going from ±3% to ±1% means calling nine times as many people for an improvement most readers would not notice.
What "margin of error" actually claims
A poll reporting 52% with a ±3% margin is not saying the true figure is 52%. It is saying the plausible range is roughly 49% to 55%. If a rival is polling at 48% with the same margin, their range is 45% to 51% — and those ranges overlap. The honest description is "too close to call", not "a four-point lead".
The "95% confidence" part describes the method rather than any single poll: if you ran the same survey many times, about 95% of the intervals produced would contain the true value. One poll in twenty is expected to fall outside its own stated range purely by chance, which is worth remembering before treating any single surprising result as a turning point.
What the margin of error does not cover
This is the part that matters most, and it is almost always omitted. The margin of error measures only the randomness of sampling. It assumes everything else was done perfectly. In practice the larger errors usually come from elsewhere:
- Who you can reach. If a method systematically misses certain groups — people without landlines, people who never answer unknown numbers — no sample size fixes the gap.
- Who chooses to respond. People with strong opinions answer surveys more readily than the indifferent.
- How the question is worded. "Do you support the measure?" and "Do you oppose the measure?" reliably produce different numbers from the same people.
- Who actually turns up. Election polls must guess which respondents will really vote — often the single largest source of error.
Reading a poll sensibly
Check the sample size and the margin of error, then treat the headline number as the centre of a range rather than a fact. Compare ranges instead of point estimates. And be most sceptical of a single poll that breaks sharply from the others — the mathematics predicts that roughly one in twenty will do exactly that without anything having changed.
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