Ever wondered how sure you can be about survey results or average values? Thatโs where confidence intervals come in!
Confidence intervals give you a range around a number (like an average) that shows how confident you are the true value falls within it. Think of it like a margin of error, but with math behind it.
Table of Contents
๐โโ๏ธ What is a Confidence Interval?
A confidence interval gives an estimated range thatโs likely to include the true population value, based on your sample data.
For example:
If the average test score is 75, a 95% confidence interval might say:
“Weโre 95% confident the true average lies between 72.5 and 77.5.”
๐งฎ The Basic Formula
Hereโs the standard formula for a confidence interval:
CI = xฬ ยฑ Z ร (ฯ / โn)
Where:
- xฬ = sample mean
- Z = Z-score (based on confidence level, e.g., 1.96 for 95%)
- ฯ = population standard deviation
- n = sample size
โ You can also use the sample standard deviation (s) if the population SD is unknown.
๐ฏ Common Z-Scores
| Confidence Level | Z-Score |
|---|---|
| 90% | 1.645 |
| 95% | 1.96 |
| 99% | 2.576 |
โ๏ธ Example
Say you have:
- Sample Mean: 70
- Standard Deviation: 10
- Sample Size: 100
- Confidence Level: 95%
Using the calculator, youโll get something like:
“Weโre 95% confident the true average is between 68.04 and 71.96.”
๐ Final Thoughts
Confidence intervals arenโt just for scientists or statisticians. Theyโre used in marketing, medicine, finance, and anywhere youโre working with data and want to make smart guesses.
Instead of just saying โthe average is 70,โ with a confidence interval, you say:
โIโm 95% confident itโs between 68 and 72.โ โ Much more trustworthy!