The way that Nielsen Media Research finds out about who is watching is to measure what a sample of television viewers are watching. For our national ratings estimates, we use a sample of more than 5,000 households, containing over 13,000 people who have agreed to participate. Since there are over 99 million households with TVs in the U.S., it might seem that a sample of 5,000 is just not big enough to represent the nation.

Actually, a representative sample doesn't have to be very large to represent the population it is drawn from. For example, you don't need to eat an entire pot of vegetable soup to know what kind of soup it is. A cup of soup is more than adequate to represent what is in the pot. If, however, you don't stir the soup to make sure that all of the various ingredients have a good chance of ending up in the cup, you might just pour a cup of vegetable broth. Stirring the soup is a way to make sure that the sample you draw represents all the different parts of what is in the pot.

While a sample doesn't have to be very large to represent the population, the sample does need to be selected in a way which gives all members of the population the same chance of being chosen.

If 50% of the vegetable pieces in a huge pot are carrot cubes, the only way to know it for sure would be to examine and count the contents of the entire pot. Let's say we stir well and pour a cup of soup with 10 vegetable pieces in the cup. If sampling were a perfect process, we would get five carrot cubes out of ten pieces. What actually happens is that we usually get close to five carrot cubes-sometimes a little more and sometimes a little less and sometimes exactly five. It is possible, but really unlikely, to stir well and get no carrot pieces-or to get all carrot pieces. So we could get a rough estimate of the proportion of carrots in the pot from counting what is in the cup.

If we wanted a closer estimate, we would take a larger sample. Imagine if we stirred well and then poured out enough soup to contain 5,000 vegetable pieces. We probably wouldn't get exactly 2,500 carrot pieces, but the chance of getting no carrots at all is very remote. In fact, according to sampling theory and a very tasty laboratory test, 19 out of 20 times we take a well-stirred sample of soup containing 5,000 vegetable pieces, we get between 48% and 52% carrots. There is no guarantee that the percentage of carrots in a sample of this size will be between 48% and 52% (one time in 20 it will be outside this range, but usually not far outside this range). The same sampling errors apply to a representative sample of television viewers.