Find Upper Bound and Lower Bound Calculator
Find upper bound and lower bound calculation is a crucial statistical technique used to estimate the range within which a population parameter lies with a certain degree of confidence. This calculator helps you perform these calculations with ease.
- Enter your data values, separated by commas.
- Select your desired confidence level.
- Click ‘Calculate’ to find the upper and lower bounds.
The calculation uses the following formula for the margin of error (E):
E = t * (s / √n)
Where:
- t is the critical value of the t-distribution with n-1 degrees of freedom at the desired confidence level.
- s is the standard deviation of the sample.
- n is the sample size.
The upper bound is calculated as:
Upper Bound = Sample Mean + E
The lower bound is calculated as:
Lower Bound = Sample Mean – E
| Confidence Level | Critical Value (t) |
|---|---|
| 95% | 2.064 |
| 99% | 2.898 |
| 99.9% | 4.604 |
- Ensure your sample size is representative of the population.
- Consider using a larger sample size for a more accurate estimate.
- Be aware that the confidence level and margin of error are inversely related.
What is the difference between confidence interval and confidence level?
The confidence level is the probability that the calculated confidence interval contains the true population parameter. The confidence interval, on the other hand, is the range of values within which the true population parameter is likely to fall.
For more information, see the Statistics How To guide on confidence intervals.