Mathematics
Error Margin
Quick fact
A poll’s margin of error typically assumes a 95% confidence level, meaning if you repeated the poll 100 times, the result would fall within the margin 95 times.
Why this is interesting
You’ve seen poll results like '45% support Candidate A, with a margin of error of 3%.' But does that mean the true support is between 42% and 48%? Or something else?
Read the full explanation
Understanding Error Margin
Error margin is not a mistake—it's a measure of how much a survey result might vary due to chance. Imagine fishing with a net: you catch a sample of fish, but some might slip through or be overrepresented. The error margin tells you the range where the true average (if you could measure everyone) likely lies. For example, if a poll says 50% with a 3% margin, the real percentage is likely between 47% and 53%. It depends on sample size and how spread out the responses are. Larger samples shrink the margin.
A deeper explanation
The margin of error comes from the concept of a confidence interval. When you take a random sample, the sample proportion is one point from a distribution of possible sample proportions. The standard error measures the spread of that distribution. The margin of error is typically 1.96 times the standard error (for 95% confidence). This works because of the Central Limit Theorem: sample proportions follow a normal distribution for large samples. Therefore, the margin tells you the radius of an interval that captures the true population value 95% of the time. Factors like sample size, population variability, and confidence level directly affect it. Understanding this prevents misreading polls: if two candidates' numbers are within each other's margins, the race is statistically tied.