For Educators

As of the 23rd May 2022 this website is archived and will receive no further updates.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Submitted by gmp26 on Tue, 08/04/2008 - 12:54pm

We hope this site may be useful to people teaching about uncertainty, whether it's the mathematics of probability and statistics, or the responses of individuals or society to risk.

For a related schools-based enrichment activity, see the Risk Roadshow offered by the Millennium Mathematics Project.

The mathematics of uncertainty

The 'stories' on this site are structured at multiple levels corresponding to difficulty. For pages with mathematical content, these levels correspond roughly to

No maths, just pictures and text for general readership
Basic arithmetic and probability theory, at a high GCSE level (say up to aged 16). For example:
- What are the chances shows probability calculations requiring multiplication of probabilities of independent and dependent events, as well as introducing ideas of expectation.
- Lottery expectations and Luck or skill? compare observed and expected distributions: Binomial, normal and geometric expected distributions are provided but not derived.
- Maternal death coincidence features quite a complex piece of probabilistic reasoning concerning the chance of two deaths occurring close in time and space.
Some algebra, probability distributions, basic statistical concepts at a high A level standard (ages 16 to 18). For example:
- Maths of coincidence provides a general algebraic form for the probability of at least one event occurring, both for dependent and independent events. This uses the exponential $e$ and mentions the Poisson distribution.
- Is the lottery biased? features chi-squared tests for goodness-of-fit, the derivation of the geometric distribution, and ideas of testing hypotheses by simulating distributions of test statistics under the null hypothesis.
- May the best team win derives the mean and variance of a test statistic under a null hypothesis and uses a normal approximation to the sampling distribution to derive confidence intervals. Uncertainty about ranks is explored using Monte Carlo methods.
Full mathematical exposition, at university level. No level 4 pages written yet!