Margin of Error & Confidence Intervals
SAT Math — Statistics & Data Analysis
Essential SAT Topic: Appears on nearly every test!
1. What Is Margin of Error?
The margin of error is a measure of how much a sample result might differ from the true population value. It is written as ± some value after the sample statistic.
Key Idea: When we study a sample instead of the entire population, our result won't be perfect. The margin of error tells us how far off we might be.
Example
A poll shows 48% support with a margin of error of ±3%.
This means the true population support is likely between:
$48\% - 3\% = 45\%$ to $48\% + 3\% = 51\%$
Think of it like a target
Your sample statistic is the arrow you shot. The margin of error is the ring around the bullseye where the true value likely sits.
- The sample statistic is your best estimate
- The margin of error accounts for uncertainty
- The true value is somewhere in the range
2. Confidence Interval
The confidence interval is the range of plausible values for the true population parameter.
$$\text{Confidence Interval} = \text{Sample Statistic} \pm \text{Margin of Error}$$
| Lower Bound | $= \text{Sample Statistic} - \text{Margin of Error}$ |
| Upper Bound | $= \text{Sample Statistic} + \text{Margin of Error}$ |
Example
Sample mean = 72, Margin of error = 4
Lower bound: $72 - 4 = 68$
Upper bound: $72 + 4 = 76$
Confidence Interval: $(68, 76)$