Concepts · 3 min read
Statistics vs Probability: What Is the Difference?
Probability: model → data
Assume a fair coin. How likely are 6 heads in 10 flips? There are C(10,6) = 210 ways out of 2¹⁰ = 1024 equally likely sequences, so the probability is 20.508%.
Ways to choose 6 heads from 10 flips
- 10C6 = 210
Step-by-step working 3 steps
- 1Order does not matter, no repeats
nCr = n! / (r!(n−r)!) = nPr / r!
Use combinations when you only care which items are chosen (committees, lottery picks).
- 2Compute nPr and r!
10P6 = 151,200 6! = 720
- 3Divide
151,200 ÷ 720 = 210
Statistics: data → model
You flip a coin 10 times and see 6 heads. Is the coin fair? The estimate of the heads probability is 6/10 = 60%, but with only 10 flips that is quite compatible with a fair coin.
Side by side
| Probability | Statistics | |
|---|---|---|
| Starts with | a known model | observed data |
| Asks | what data should I expect? | what model produced this? |
| Example | P(6 heads | fair coin) | estimate p from 6/10 heads |
Learn more
Start with probability basics and standard deviation; try the probability calculator.
Frequently asked questions
Which comes first?
Probability, because statistical methods are built on probability models.
Is a sample statistic a probability?
No. It is an estimate computed from data; probability describes a model.
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