Fair point, Smee - and I would have to partially agree with the reservations expressed on the accuracy of any 'sample'.
Where the percentage is significantly small, there are two problems that immediately come to mind:
The first is whether that sample is truly indicative of population it is targeting. For example, if you were surveying supermarket customers about their usage of motor vehicles, you would get two extremely different sets of results if you were to survey a Woolworths at Broken Hill and one downstairs from an inner-city apartment block. However, this is the first skill that market research companies MUST excel at to survive, so it is quite likely they have made a reasonable effort to get this as objective as possible. They also will have an idea of how accurate these results will be - and will have an 'error' figure available so whoever commissioned the survey will have a range of values to look at.
The second is the 'granularity' of a result. If, for example, there are 10,371 people with red hair in a group of 1,000,000 - then sampling 10,000 of that group would (statistically) give you 104 people with red hair. Now if you were to do half a dozen such surveys, you could get results of 103, 107, 100, 110, 99 and 101 - which are all around the "1 in 100" range that would be useful for, say, a hairdresser specialising in working with red hair. ANY ONE of these results would be satisfactory for the "1 in 100" working figure.
If your sample was reduced to 1,000 - then you might get results of 7, 8, 14, 5, 16 and 21 from six different surveys - which would indicate anything from "1 in 50" to "1 in 150". While still giving some idea of the frequency of red headed people, the value to my hypothetical hairdresser could be compromised. Their 'sweet spot' might be at the "1 in 100" mark. At "1 in 50" they might see the market being too great for them to handle on their own and would need to have additional staff - which they may not be ready for. At "1 in 150" they may see the demand would not be enough to support them - and not go into business. Since they will be only commissioning ONE survey, it will depend on which of these results they get as to which way they decide.
If we then reduce the sample to 10, the problem becomes extreme. In six surveys, you could get results of 0, 0, 0, 0, 1 and 0. In five of these surveys, the 'statistical' result will indicate that the number of red headed people in the entire group is so low, that they don't even register. The numbers could back you up if you were to say they just didn't exist - except you know you've seen one or two. However, if you got the result that says that "1 in 10" people had red hair (out of our group of 1,000,000), then our hairdresser would need to set up a salon with ten staff - according to those numbers.
This last example is the only criticism I will make of Smee's example of picking 10 people out of the MCG - since multiple such surveys will give you a zero result most of the time and the odd time you do score a hit, will not be representative.
Sample sizes must be appropriate - as well as the 'evenness' of sampling across the target group.
