A parameter describes a population and is usually unknown. A statistic describes a sample and is what you compute.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Randomness is the safeguard
A random sample gives every individual an equal chance of selection, which is what makes it representative.
Bias is systematic
Convenience and voluntary response samples miss whole groups. A larger sample repeats that error more precisely.
Sampling variability
Two random samples give two different statistics. That variation is expected, not an error.
Larger samples vary less
As the sample grows, statistics cluster more tightly around the true value.
Why this matters
Knowing how much a statistic naturally varies is what lets you say how close your estimate probably is.
Two samples never quite agree
Different random samples from the same population give different statistics. That variation is expected and quantifiable, and it is what all statistical inference is built to handle.
Randomness makes it calculable
A random sample has a known selection mechanism, which is what allows the sampling distribution to be worked out. Without randomness there is no basis for any inference at all.
Bias comes from the method
Voluntary response, convenience sampling and undercoverage all produce systematic error. No sample size fixes bias — a large biased sample is a precise wrong answer.
Larger samples vary less
Variability shrinks with the square root of the sample size, so quadrupling the sample halves it. That square-root relationship is why precision improves slowly and expensively.
Step 2: Try It Yourself
Tap and try it out.
- Minimum9
- Lower quartile9.50
- Median10
- Upper quartile11.50
- Maximum12
- Interquartile range2
Each of the four sections holds a quarter of the values, however wide it looks. A narrow box means the middle half of the data is packed close together.
Step 3: Watch an Example
One step at a time.
Watch Rosa Compare Two Sample Sizes
A population is 50% in favour. Rosa takes samples of size 10 and of size 1000.
- Step 1
With 10 people, 7 in favour is entirely ordinary, giving 70%.
Step 4: Your Turn
Practice makes it stick.
The Name
Problem 1 of 2
A value describing a whole population. 1 parameter, 2 statistic.
The Size
Problem 2 of 2
Does a larger sample fix bias? 1 yes, 0 no.
Samples and Populations
1 of 8
A value describing a sample. 1 parameter, 2 statistic.
2 of 8
Do two random samples usually give identical statistics? 1 yes, 0 no.
3 of 8
Which sample varies less? 1 for size 25, 2 for size 2500.
4 of 8
An online poll where readers choose to respond. Biased? 1 yes, 0 no.
5 of 8
Which is usually unknown? 1 parameter, 2 statistic.
6 of 8
Which matters more for accuracy? 1 method, 2 size.
7 of 8
Sort each term by what it describes.
Tap something to move it.
- Empty
- Empty
8 of 8
Population 50% in favour. Is 70% from a sample of 10 surprising? 1 yes, 0 no.
Step 5: Quick Check
Show what you know.
Question 1 of 2
Which sample gives a more reliable estimate? 1 for size 30, 2 for size 3000.
Question 2 of 2
Why does a larger sample not fix bias?
What You Learned
- A parameter describes a population; a statistic describes a sample.
- Random sampling protects against bias; a larger sample does not.
- Statistics vary from sample to sample, and larger samples vary less.