A mean is defined as the average of a numerical set. It is found by dividing the sum of a set of numbers by the number of members in the group A sample mean is defined as a mean of a numerical set that includes an average of only a portion of the numbers within a group.
A sample for a poll contains no sets, nothing is averaged and there are no sample means.
But thanks for the condescension.
I guess I shouldn't expect much from victims of the American public school system.
And speaking of condescension... and this coming from a person who apparently doesn't realize that some of the most advanced tools in mathematical Analysis are used in statistics, and who apparently is confused about where statistics even enters this discussion at all.
But for the benefit of FReepers who can be educated:
In polling, we are not aware of the value of a desired number, say the number of people voting for Mitt Romney. It isn't practical to ask every person doing so, so consequently we call a random sample of people. The tools of statistics that can be brought to bear on this question is 1) How many people do we need to ask for our sample to be representative and 2) is there a practical bound on the error?
This question is answered by the Central Limit Theorem. Roughly this says: the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will, in the limit of large numbers be normally distributed.
So, each time a poll is conducted, we come up with a percentage of Romney voters. Each measurement will be slightly different. However, if we take the average -- or mean -- of these measurements, that average percentage is subject to our theorem, provided we meet its conditions, one of which, is that the variable (number of Romney voters, etc.) is truly random.
And, what the Central Limit Theorem tells us is that ALL of those measurements, with unknown mean, will converge to the true result if we take enough of them. And that result WHICH IS THE MEAN OF ALL OF THE SAMPLES is the mean of a normal or Gaussian distribution. And furthermore, those measurements will also have the SAME STANDARD DEVIATION AS NORMAL DISTRIBUTION.[aside: "variance" is referred to in the theorem. This is mathematically interchangeable with the standard deviation, because the standard deviation is just the positive square root of the variance.]
The variance of a normal distribution is well known, and from it we can calculate a practical bound on a range in which the TRUE MEAN of all these measurements must lie. About 2/3 of all the measurements we take will lie within one standard deviation from the true mean. About 95% will lie within 2 standard deviations, and about 99.7% will lie within three standard deviations. Since we can say that 95% of a random sample lies within two standard deviations of the mean of our samples, this is called a 95% confidence interval, and it can be easily calculated because the variance of a Gaussian Distribution is well known.
So you see folks, there IS a mean involved in this discussion, and there is a standard deviation in this discussion, and now you know it, although FReeper jwalsh07 is unaware of it. And simply understanding this fact, allows you to understand how "margins of error" are calculated.
The WIKIPEDIA entry on "Margin of Error" is actually not too bad (WIKI is generally pretty good on matters mathematical and statistical.) Have a look. In just a few minutes, you will know a great deal more about statistics than the poseur posting so condescendingly here.