# S5-3: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.

Elaboration on this Achievement Objective

Students at Level Five understand that elements of chance have an effect on the certainty of results from surveys or experiments. Through examples from real life they should understand that statistics usually involves situations where the actual probabilities are not known, for example, probability of catching a disease. They should recognise situations where deterministic theoretical models are not possible, for example chance of a bus being early, and distinguish them from situations where probabilities can be reasoned from all the possibilities.
This means that students will identify the theoretical probabilities for situations involving chance by using proportions of possible outcomes.  For example, they will recognise that the probability of rolling an even number on a standard die is 1/2 because there are 6 possible outcomes and 3 of them are even, 3/6 = 1/2.

They will carry out experiments to test the probability of events and compare their results with theoretical probabilities. They will understand that some variation between experimental estimates of probability and theoretical probabilities is normal, for example, when rolling a die 10 times they will not usually roll an even number 5 of the times.  They will understand that a larger sample is likely to provide a more accurate theoretical probability, proportionally speaking, than a small one.

Students will also understand that the results of past trials in probability experiments do not impact on future events, for example the fact that an even number has been rolled three times in a row does not make it more likely that the fourth roll will be an odd number.