Bound of Error Calculator

Formula

The formula to calculate the bound of error (E) is:

\[ E = \frac{Z \cdot \sigma}{\sqrt{n}} \]

Where:

\( E \) is the bound of error
\( Z \) is the Z-score corresponding to the desired confidence level
\( \sigma \) is the population standard deviation
\( n \) is the sample size

What is a Bound of Error?

The bound of error is a statistic that reflects the amount of random sampling error in a survey's results. It represents the radius of a confidence interval for a particular statistic. The smaller the bound of error, the more confident one can be in the accuracy of the survey's reported percentage.

Example Calculation

Let's assume the following values:

Z-Score (Z): 1.96 (for a 95% confidence level)
Population Standard Deviation (σ): 10
Sample Size (n): 100

Using the formula to calculate the bound of error:

\[ E = \frac{1.96 \cdot 10}{\sqrt{100}} = \frac{19.6}{10} = 1.96 \]

The Bound of Error (E) is 1.96.