Statistics
Confidence Interval Calculator
Compute 90%, 95%, or 99% confidence intervals. Enter sample mean, standard deviation, and sample size to get the confidence interval for any significance level.
Dataset Input
Valid formats: 12, 15.5, 20 or newline separated lists. Non-numeric values are automatically excluded.
Summary Metrics
Sample Size (n)10
Min / Max Range[12, 30]
Summation (Σx)212
Arithmetic Mean
21.2
Median Value
21.5
Modal Value
22
Std. Deviation
5.2688
Population Variance
27.76
Total Range Spread
18
Frequency Distribution
Dataset visualization across unique values
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Solution Methodology
01
Enter Sample Statistics
Provide sample mean x̄, standard deviation (σ or s), and sample size n.
02
Select Confidence Level
Choose 90%, 95%, or 99% to determine the critical value z* or t*.
03
Compute Interval
Calculate margin of error E = critical value × (SD/√n), then output [x̄−E, x̄+E].
Common Questions
What is a 95% confidence interval?
A 95% confidence interval means that if you repeated the sampling process 100 times, approximately 95 of the resulting intervals would contain the true population parameter. It does NOT mean there is a 95% probability the parameter falls in this specific interval.
When should I use a t-distribution instead of z?
Use the t-distribution when the population standard deviation σ is unknown and you are estimating it from the sample (using s). The t-distribution has heavier tails, producing wider intervals that account for the additional uncertainty from estimating σ.