Sampling from a mystery population

The task is to determine the identity of 10 elements in a finite population by sampling. This activity considers how the reliability improves as the sample size increases.

Make a mystery bag with a population of 10 cubes of different colours.

Set this question to the class:

How does sample size affect the information gained about a 'mystery population'?

Data collection

Remove one cube and record its colour. Replace the cube. Repeat this 10 times. Guess the colours of the bag's contents. Repeat the process several times. Keep track of how the guesses change each time.

Repeat the above instructions with a sample size of 2.

Repeat again with a sample size of 4.

Representing data

Record the data for different sample sizes and the associated guesses about the make up of the population.

Summarising data

Discuss the logical conclusions that can be drawn about the minimum numbers of each colour based on the sample sizes and the likely relative frequencies of the colours.

Degree of certainty

What part does chance play in the sampling process? What assumptions are made?

Why is replacement necessary after each draw?

Why does sample size make a difference?

Drawing a conclusion

What is the probable number of cubes of each colour in the bag? Write a report on how this conclusion was reached.

Was the conclusion correct?

Discuss what circumstances might have affected the conclusion.

There is further discussion on data collection in Sample size and variation.