The important rule in sampling is not how many poll respondents are selected but how they are selected. A reliable sample selects poll respondents randomly to insure that everyone in the area being surveyed has an equal chance of being selected. The sample of phone numbers chosen was drawn by recognized probability sampling methods to insure that each region of the country was represented in proportion to its population and by a method that gave all residential telephone numbers, both listed and unlisted, an equal chance of being included in the poll. Another step is to dial numbers again and again when no one answers to insure that people often away from home are included in the sample. Sampling methods and measures of sample reliability or precision are derived from the mathematical science of statistics.
Heads is one of only two possible outcomes.
As the number of coin tosses increases, it becomes increasingly more likely to get outcomes that are either very close to half heads or exactly half because, as with two coins, there are more ways to get such outcomes. As in coin tosses, the most likely sample outcome is the true percentage of whatever it is we are measuring across the total population. Next most likely are outcomes very close to this true percentage. A statement of potential margin of error or sample precision reflects this. A wide spread of opinions means there is less consensus in people's answers.