Margin of Error
The margin of error measures the uncertainty associated with a statistical estimate.
What is margin of error?
The margin of error represents the maximum expected difference between a sample estimate and the true population value. It is commonly reported in surveys, polls, and statistical studies.
Margin of error formula
For a population mean using the normal distribution, the margin of error is calculated as:
Margin of Error = Z × (σ / √n)
Example
Standard deviation (σ) = 12
Sample size (n) = 400
Confidence level = 95% (Z = 1.96)
→ Margin of Error = ±1.18
Sample size (n) = 400
Confidence level = 95% (Z = 1.96)
→ Margin of Error = ±1.18
How to interpret the margin of error
A margin of error of ±1.18 means that the true population value is expected to lie within 1.18 units above or below the sample estimate, with the specified level of confidence.
What affects the margin of error?
- Larger sample sizes reduce the margin of error
- Higher confidence levels increase the margin of error
- Greater variability leads to larger uncertainty
Why is margin of error important?
Margin of error helps quantify reliability in statistical results, allowing more informed interpretation and decision-making.