Algebra 2 / Unit 10: Statistics and Data Analysis
10.6 Margin of Error
Notes
A sample result is only an estimate. The margin of error says how far it might be from the true population value.
- For a sample proportion with sample size $n$, a quick 95% margin of error is about $\displaystyle \frac{1}{\sqrt{n}}$.
- The confidence interval is: sample result $\pm$ margin of error.
- Larger samples give smaller margins of error. To cut the margin in half, use 4 times as many people.
- Example: $n = 2500$ gives $\displaystyle \frac{1}{50} = 0.02$, so $\pm 2\%$.
Practice
A random sample of 400 people is surveyed. What is the approximate margin of error?
$\displaystyle \frac{1}{\sqrt{400}} = \frac{1}{20} = 0.05$.
A poll finds 54% support with a margin of error of 3%. What is the interval for the true support?
$54\% \pm 3\%$.
A pollster wants to cut the margin of error in half. The sample size should be:
The margin depends on $\displaystyle \frac{1}{\sqrt{n}}$, and $\displaystyle \sqrt{4n} = 2\sqrt{n}$.
Ready for more? Take the Unit 10 test.