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Confidence Interval Calculator

Last updated: April 2026

Confidence interval for a mean

Confidence level

Confidence interval

(45.872, 54.128)

50 +/- 4.128

Interval number line

45.8725054.128

Full breakdown

Sample mean
50
Standard error
2
Critical value (t)
2.064
Margin of error
4.128
Lower bound
45.872
Upper bound
54.128
Interval width
8.256
Step-by-step working
  1. SE = s / sqrt(n) = 10 / sqrt(25) = 2.
  2. df = n - 1 = 24; t(24, 95%) ≈ 2.064.
  3. Margin = t x SE = 2.064 x 2 = 4.128.
  4. CI = 50 +/- 4.128 = (45.872, 54.128).

What is a confidence interval?

A confidence interval gives a plausible range for a true population value based on sample data.

The common misconception about CIs

A 95% interval does not mean the true value has a 95% probability of being inside this exact interval.

Z-interval vs t-interval

Use a z-interval when population standard deviation is known. Use a t-interval when you estimate spread from the sample.

How to interpret confidence intervals

Wider intervals mean more uncertainty. Larger samples and lower confidence levels produce narrower intervals.

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.

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