# Point estimate and bias

A point estimate is a single number guessing a parameter, such as the sample mean for the population mean. An estimator is unbiased if its average over many samples equals the true parameter.

Statistics (university) · Part 05: Sampling and estimation · Card 5 of 8 · Last updated 2026-10-19

## Analogy

A dart thrower whose throws centre on the bullseye is unbiased, even if single throws miss.

## Example

**Estimating spread**

Sample: 12, 15, 9, 14, 10
Mean = 60 / 5 = 12
Gaps squared: 0,9,9,4,4 = 26
s squared = 26 / 4 = 6.5
s = 2.55

## In practice

The sample mean and the sample variance with n minus 1 are unbiased estimators.

## Practice

### Flashcards

- **What makes an estimator unbiased?** Its average over many samples equals the true parameter.

## Questions people ask

### Is an unbiased estimator always the best?

Not always. It means the estimate is right on average, but any one estimate can still be far off. A slightly biased estimator with much smaller spread can have lower total error. Statisticians also look at variance, not only bias.

### Why is a point estimate not enough?

A single number gives no sense of how far off it might be. A poll saying 54 percent backs a law is far less useful than 54 percent plus or minus 3. A confidence interval adds the missing information about precision.

## Related concepts

- [Confidence interval for a mean](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-5/statistics-university-part-5-concept-6)
- [t distribution](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-5/statistics-university-part-5-concept-7)
- [Confidence interval for a proportion](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-5/statistics-university-part-5-concept-8)

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