MSV 8: Sampling

You are given 100 natural numbers, all less than 100. Your task is to estimate the mean by taking a sample.

Select what you consider to be a representative sample of 20 numbers, using nothing but intuition (you can pick the same one twice or more if you wish). Calculate the mean for your sample. Now the sample means from the whole class will be collected together so that the mean of the sample means can be calculated.

Now you need to select a sample once more, this time using random numbers. Pick 20 integers from 0 to 99 at random (think hard about how you do this!) – repeats are allowed – find your sample from the table below.

Find the sample mean for this sample, and once again contribute this result to those of the rest of the class, so that the mean of the randomly-chosen sample means can be calculated. How do the means for the randomly-chosen samples compare with the means for the samples chosen by people?

The true mean of these 100 numbers is (They are in fact a random sample of size 100 from a geometric distribution where p =1/12. This is the distribution of X, where X is the number of goes to throw a 12 on a twelve-sided dice. Here E(X) = 1/(1/12) = 12.) In terms of estimating the mean of the 100 numbers, which kind of sampling gives the best results?

With thanks to Mary Rouncefield and Peter Holmes for publishing the activity that inspired this one in Practical Statistics, Macmillan is written by Jonny Griffiths