Calculator Inputs
Example Data Table
This sample shows how ten observations can produce a prediction interval for the next single outcome.
| Observation | Value |
|---|---|
| 1 | 41.20 |
| 2 | 44.70 |
| 3 | 43.80 |
| 4 | 46.10 |
| 5 | 45.50 |
| 6 | 42.90 |
| 7 | 47.30 |
| 8 | 44.10 |
| 9 | 45.80 |
| 10 | 43.60 |
| Sample Mean | 44.50 |
| Sample Standard Deviation | 1.77 |
| 95% Lower Bound | 40.31 |
| 95% Upper Bound | 48.69 |
Formula Used
Prediction Interval: PI = x̄ ± t × s × √(1 + 1/n) Sample Mean: x̄ = Σx / n Sample Standard Deviation: s = √[Σ(x - x̄)² / (n - 1)] Prediction Standard Error: SEpred = s × √(1 + 1/n) Margin of Error: Margin = t × SEpredWhere:
- x̄ is the sample mean.
- s is the sample standard deviation.
- n is the sample size.
- t is the critical value from the Student t distribution.
This calculator estimates the range for one future observation. It assumes the sample is independent and reasonably representative.
How to Use This Calculator
- Select Summary statistics or Raw sample values.
- Enter a scenario name and optional units.
- Add mean, standard deviation, and sample size, or paste raw sample values.
- Choose a confidence level or enter a custom one.
- Optionally add a future value to test against the interval.
- Pick the number of decimal places.
- Press Calculate Interval to view the interval, table, and graph.
- Use the CSV or PDF buttons to export the current result.
Frequently Asked Questions
1) What does a prediction interval show?
A prediction interval estimates where one future observation is likely to fall. It is wider than a confidence interval because it includes both parameter uncertainty and natural observation-to-observation variation.
2) How is this different from a confidence interval?
A confidence interval estimates the range for the population mean. A prediction interval estimates the range for a single future value, so it is usually wider.
3) Why does the interval widen with smaller samples?
Smaller samples provide less stable estimates of spread and center. That raises the critical value effect and increases uncertainty, which makes the interval broader.
4) Why does a larger standard deviation matter?
A larger standard deviation means the data are more dispersed. Greater spread increases the prediction standard error, so the final interval becomes wider.
5) Can I paste raw observations instead of summary values?
Yes. Choose raw data mode, then paste values separated by commas, spaces, or line breaks. The page will compute the mean and standard deviation automatically.
6) What happens when I enter a future value?
The calculator compares that value with the lower and upper prediction bounds. It then marks the value as inside or outside the interval.
7) Does this calculator assume normal data?
It works best when the sample comes from a roughly normal process or when the sample is large enough for the approximation to behave well. Strong skew or outliers can reduce reliability.
8) When should I use a higher confidence level?
Use a higher confidence level when missing a future value would be costly. Higher confidence gives a safer but wider interval.