A parameter describes a population and is usually unknown. A statistic describes a sample and is what you actually compute.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Statistics vary
Two different samples from the same population give two different statistics. That variation is expected, not an error.
The sampling distribution
Collecting the statistic from every possible sample gives its own distribution, centred on the true parameter.
Bigger samples vary less
As the sample size grows, the sampling distribution narrows. Large samples give estimates that cluster tightly around the truth.
Centred, if unbiased
Random sampling centres the distribution on the true value. Bias shifts that centre, and no sample size will shift it back.
Why this matters
Knowing how much a statistic naturally varies is what lets you say how close your estimate probably is. That is inference.
Two samples never quite agree
Different random samples from the same population give different statistics. That variation is sampling variability, and it is expected rather than a sign that something went wrong.
Larger samples vary less
The variability of a sample statistic shrinks with the square root of the sample size. Quadrupling the sample halves the variability, which is why precision improves slowly and expensively.
Margin of error quantifies it
A poll reporting 52% with a margin of error of 3 points is saying the true value is plausibly between 49% and 55%. Reporting the estimate without the margin conceals exactly what matters.
Reading poll coverage
A shift from 50% to 52% between two polls with 3-point margins is not a change worth reporting. Most reported movement in tracking polls is sampling variability being narrated as news.
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 Marcus Compare Two Sample Sizes
A population is 50% in favour. Marcus takes samples of size 10 and of size 1000.
- Step 1
With 10 people, getting 7 in favour is entirely ordinary, giving 70%.
Step 4: Your Turn
Practice makes it stick.
The Names
Problem 1 of 2
A value describing a whole population is called what? 1 parameter, 2 statistic.
The Size
Problem 2 of 2
Which sample varies less? 1 for size 25, 2 for size 2500.
How Much Does It Vary?
1 of 8
A value describing a sample is called what? 1 parameter, 2 statistic.
2 of 8
Do two random samples usually give identical statistics? 1 yes, 0 no.
3 of 8
Does a larger sample narrow the sampling distribution? 1 yes, 0 no.
4 of 8
A sampling distribution from random samples centres on what? 1 the true parameter, 2 zero.
5 of 8
Does increasing sample size remove bias? 1 yes, 0 no.
6 of 8
Which is usually unknown? 1 parameter, 2 statistic.
7 of 8
Sort each term by what it describes.
Tap something to move it.
- Empty
- Empty
8 of 8
Population is 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
What is a sampling distribution?
What You Learned
- A parameter describes a population; a statistic describes a sample.
- Statistics vary from sample to sample, and that variation is predictable.
- Larger samples vary less, but no sample size removes bias.