Margin of Error Calculator
Calculate the margin of error for a confidence interval given the z-value, standard deviation, and sample size.
Margin of Error
2.3520
Margin of Error vs Z-Value
公式
## How to Calculate Margin of Error ### Formula **E = z * (sigma / sqrt(n))** The margin of error is the half-width of the confidence interval. It depends on three factors: the confidence level (via z), the variability of the data (sigma), and the sample size (n). A smaller margin of error means a more precise estimate.
计算示例
z = 1.96, SD = 12, n = 100. What is the margin of error?
- 01Standard Error = 12 / sqrt(100) = 12 / 10 = 1.2
- 02Margin of Error = 1.96 * 1.2 = 2.352
- 03The sample mean will be within +/- 2.352 of the population mean with 95% confidence.
常见问题
What is a good margin of error?
It depends on the context. Political polls often aim for +/-3%. Medical studies may require smaller margins. Generally, smaller is better, but achieving it requires larger samples.
How do I reduce the margin of error?
Increase the sample size (most practical), accept a lower confidence level (reduces z), or reduce variability (better measurement techniques). Quadrupling n halves the margin.
Is margin of error the same as standard error?
No. Standard error = sigma/sqrt(n). Margin of error = z * standard error. The margin of error multiplies the standard error by the critical value to account for the desired confidence level.
学习