Confidence Interval Formula

The confidence interval formula in statistics is used to describe the amount of uncertainty associated with a sample estimate of a population parameter. It describes the uncertainty associated with a sampling method.

To recall, the confidence interval is a range within which most plausible values would occur. To calculate the confidence interval, one needs to set the confidence level as 90%, 95%, or 99%, etc. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter; 95% of the intervals would include the parameter and so on.

Formula for Confidence Interval

The formula for the confidence interval is given below:

Confidence Interval Formulas
If n ≥ 30 Confidence Interval = x̄ ± zα/2(σ/√n)
If n<30 Confidence Interval = x̄ ± tα/2(S/√n)


  • n = Number of terms
  • x̄ = Sample Mean
  • σ = Standard Deviation
  • zα/2 = Value corresponding to α2 in z table
  • tα/2 = Value corresponding to α2 in t table
  • α = (1 – Confidence Level /100)

Also Try: Confidence Interval Calculator


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