Let’s say you picked a specific number of people in the United States at random. What then is the chance that the people you picked do not accurately represent the U.S. population as a whole? For example, what is the chance that the percentage of those people you picked who said their favorite color was blue does not match the percentage of people in the entire U.S. who like blue best?
(Of course, our little mental exercise here assumes you didn’t do anything sneaky like phrase your question in a way to make people more or less likely to pick blue as their favorite color. Like, say, telling people “You know, the color blue has been linked to cancer. Now that I’ve told you that, what is your favorite color?” That’s called a leading question, and it’s a big no-no in surveying.)
Common sense will tell you (if you listen…) that the chance that your sample is off the mark will decrease as you add more people to your sample. —Robert Niles —How Poll Sampling Works (Journalism.org)
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"Common sense will tell you (if you listen...)" Unfortunately, when it comes to mathematical thinking, the words "common" and "sense" rarely go together... Of course you get a more accurate result when you survey more people! This is why even though we take polls about elections, we still HAVE elections! That's the one chance we have to ask EVERYONE our survey question...
:)