Confidence Interval Calculator
A confidence interval gives a range where the true average probably sits, based on your sample. It is wider when the numbers vary more, and narrower when the sample is larger.
- Free
- Works offline after your first visit
- Saves on this device
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- Updated
How it works
Divide the spread by the square root of the sample size, then multiply by a z value for your chosen level: 1.645 for 90 percent, 1.96 for 95 percent, or 2.576 for 99 percent. That product is the margin of error.
Subtract the margin from the average for the low end, and add it for the high end.
Worked example
With an average of 72 from a sample of 36, the margin of error is 2.61 either side, so the range runs from 69.39 to 74.61.
Questions
Which level should I pick?
Ninety-five percent is the most common choice in published work. Higher levels give a wider range, so you can be more sure the true average falls inside it.
Why does a bigger sample make the range narrower?
More numbers give a steadier average. The spread is divided by the square root of the sample size, so the margin shrinks as the sample grows.
Is this right for a small sample?
For small samples a t value is more accurate than a z value, so this estimate is rough. Check with someone who works with statistics before relying on it.
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