Algebra
Data and statistics
Populations and samples
20 practice questions
2 video lessons
Theory + worked examples
Theory
When gathering data:
- The population is the entire group of interest.
- A sample is the subset actually studied.
- A random sample avoids bias and represents the population.
A biased sample misrepresents the population.
A sample is a subset of the population.
Populations and samples.
The idea:
\[\text{sample}\ \subset\ \text{population}\]
Random selection is what makes a sample fair.
How to sample well
- Define the population.
- Select a random subset.
- Avoid bias in how you choose.
- Use the sample to estimate the population.
Example 1 — Identify each
A survey asks \(200\) of a school's \(1500\) students. Name each group.
Solution
Whole group vs those asked.
| \(\text{population}\) | \(=\) | \(1500\) |
| \(\text{sample}\) | \(=\) | \(200\) |
Example 2 — Why random?
Why survey a random sample?
Solution
To avoid bias and represent the population fairly.
Example 3 — Biased sample
Is surveying only the math club about favorite subjects biased?
Solution
Yes — it over-represents math fans, so it is biased.
Example 4 — Sample size
Does a larger random sample help?
Solution
Yes — it usually gives a more reliable estimate.
Common pitfalls
A non-random sample is biased.
The sample must represent the whole population.
Bigger samples reduce variability, not bias.
Frequently asked questions
What is a population?
The entire group of interest.
What is a sample?
A subset of the population that is studied.
Why use a random sample?
To avoid bias.
What is a biased sample?
One that misrepresents the population.
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