When you are using statistics with a large number of values, you may only want a representative sample in your survey. For example if you take 30 pupils as a sample of a school of 500 and ask them what type of music is their favourite, if you choose too many headbangers you'll end up with Heavy Metal showing as the most popular music in the school rather than the true result.

To get a realistic result for the whole school based on your sample of 30 you should take a random sample. In this sample, every value should have an equal chance of being selected. You should make sure there is no bias. One way to do this is to get a list of all pupils names and number them from 1 to 500, then get a computer to spew out a random number between 1 and 500 for each of the 30 pupils in your sample, convert the numbers to names, track down the pupils and do your research.

Stratified Random Sampling
If the school in question consists of 300 boys and 200 girls, then randomly selecting 30 pupils out of 500 will give an unfair bias in favour of the girls (most likely pushing Heavy Metal down the ranks).

To make the sample fair you use the method called stratified random sampling.

For example:

Total Pupils = 500
Boys            = 300
Girls             = 200

To make your sample more balanced with respect to the total population (fancy word for the total you are taking your sample from), you should randomly select more boys than girls to keep things in proportion

3/5 of boys make up the total population and 2/5 of girls make up the total population, so you should make sure that 3/5 of your sample are boys and 2/5 of your sample are girls (i.e. 18 boys and 12 girls).

Selective Sampling
This technique is most often used by manufacturing companies for quality control. The method is to generate a steadily increasing random number and use this to select products to test.

e.g. a ball-point pen company may generate the random numbers ...103,254, 109,965..etc.

So, when pen number 103,254 made that week rolls off the production line someone picks it up and tries to write with it, likewise with pen number 109,965 and so on...