The law of large numbers tells us that experiments with a large number of observations or participants, tend to have results that are close to the expected values: the statistical mean.
This law is important to understand public opinion, because it can explain why, after surveying a large number of people (remember, this law only applies when a large number of subjects are part of the experiment), the result: the public opinion, is close to the values that were expected at first.
The Declaration of Independence was signed on July 4, 1776. The document declared independence for the American colonies from England, their former tyrannical ruler- and now Independence Day is national holiday celebrated every July 4th.