Algebra 2
Statistics and probability
Sampling and inference
20 practice questions
0 video lessons
Theory + worked examples
Theory
Statistical inference uses a sample to draw conclusions about a population:
- Population: the entire group of interest.
- Sample: the subset actually studied.
- A statistic (from the sample) estimates a parameter (of the population).
Random sampling makes the sample representative and avoids bias.
A sample is a subset chosen from the population.
Population, sample, and inference.
The idea:
\[\text{sample statistic}\ \longrightarrow\ \text{estimate of population parameter}\]
Bigger random samples give more reliable estimates.
How to sample well
- Define the population.
- Select a random sample.
- Compute the sample statistic.
- Infer the population parameter, noting uncertainty.
Example 1 — Population vs sample
A poll asks \(500\) of a city's \(200{,}000\) voters. Identify each.
Solution
The whole group is the population; those asked are the sample.
| \(\text{population}\) | \(=\) | \(200{,}000\ \text{voters}\) |
| \(\text{sample}\) | \(=\) | \(500\ \text{polled}\) |
Example 2 — Why random?
Why choose a random sample?
Solution
Random selection avoids bias, so the sample represents the population fairly.
Example 3 — Statistic vs parameter
The sample mean is \(52\%\). What does it estimate?
Solution
A sample statistic estimates the population parameter.
| \(52\%\) | \(\text{estimates}\) | \(\text{the true } \%\) |
Example 4 — Sample size
How does a larger sample affect the estimate?
Solution
A larger random sample generally gives a more reliable estimate (less variability).
Common pitfalls
Non-random samples are biased and may not represent the population.
A statistic is an estimate, not the exact parameter.
Bigger samples reduce variability, not bias.
Frequently asked questions
What is the difference between a population and a sample?
The population is the whole group; the sample is the subset studied.
Why use random sampling?
To avoid bias and represent the population fairly.
What is a parameter?
A numerical fact about the population, estimated by a sample statistic.
Does a bigger sample remove bias?
No — it reduces variability, but only random selection removes bias.
← Previous subtopic
Normal distribution and fitting data with mean & SD
Next subtopic →
Random processes and statistical experiments
More in Statistics and probability