Enter the sample size, population standard deviation, and confidence level into the calculator to determine the bound of error for a given set of data.
Bound of Error Formula
The following formula is used to calculate the bound of error (E).
E = (Z * σ) / √n
Variables:
- E is the bound of error
- Z is the Z-score corresponding to the desired confidence level
- σ is the population standard deviation
- n is the sample size
To calculate the bound of error, multiply the Z-score by the population standard deviation and then divide by the square root of 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.
How to Calculate Bound of Error?
The following steps outline how to calculate the Bound of Error.
- First, determine the sample size (n).
- Next, determine the population standard deviation (σ).
- Next, determine the Z-score corresponding to the desired confidence level (Z).
- Next, gather the formula from above = E = (Z * σ) / √n.
- Finally, calculate the Bound of Error (E).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
sample size (n) = 100
population standard deviation (σ) = 50
confidence level (Z) = 1.96 (for 95% confidence)
