Curriculum placement
Precalculus. This describes the skill, not a learner estimate.
A distribution built from frequencies
Estimate distributions from observed frequencies and compute expectations
Problem types
- Empirical distributions and expected value
Builds on
- Defining a random variable
- Using expected value to compare choices
- Comparing uncertain strategies · Useful idea
When expected value is hard to compute, a decision strategy is evaluated by simulating it and averaging the simulated results.
- A margin of error from simulated samples · Earlier idea
Repeating a sample many times builds an empirical distribution of sample estimates, whose spread is the margin of error.
- The addition rule for probability · Useful idea
Relative frequencies of disjoint results add to 1, as the addition rule requires for probabilities.
Leads to
- Margin of error and what a sample supports · Extend the idea
The distribution of many simulated sample statistics estimates the sampling variability used in statistical inference.
Related skills
- Checking a model against evidence · Related idea
An empirical distribution of results is compared with the model's theoretical distribution to check the model.
- Testing a difference by randomization · Related idea
The results of reshuffled data form an empirical distribution against which the observed result is compared.
- Checking a chance model by simulation · Related idea
Simulated results form an empirical distribution, and its relative frequencies estimate how often a result as extreme as the observed one arises.
- Association is not causation · Related idea
Reshuffling treatment labels many times builds an empirical distribution of differences, against which an observed difference supporting a causal claim is judged.
- A distribution from a sample space · Shared foundations
Open the interactive map to explore lessons and skill connections.