Confidence interval calculator

Calculate the confidence interval of the mean and the standard deviation using Normal distribution or T distribution for the mean and Chi-Square distribution for the standard deviation.

p-value video
example digits=2: (0.001234 => 0.0012)
The probability that the true value of the estimated parameter will be in the confidence interval.
The population's standard deviation, if you don't know leave empty
Enter raw data directly
Enter summarized data
It is not recommended to exclude outliers unless you know the reasons

Enter sample data

When entering data, press Enter or comma , after each value, or paste data from excel.

The tool will not count empty cells or non-numeric cells.

The sample standard deviation.
Sample size.
Shapiro Wilk test
count: ,based on the Tukey's fences method, k=1.5

Confidence interval
When using the sample data we know the sample's statistics but we don't know the true value of the population's measures. Instead, we may treat the population's measures as random variables and calculate the confidence interval.
First, we need to define the confidence level which is the required certainty level that the true value will be in the confidence interval Researchers commonly use a confidence level of 0.95.

Mean confidence interval
When we know the population's standard deviation (σ), we will use the normal distribution. The average's (X) distribution is Normal (Mean, SD/√n) Otherwise, we will use the sample size standard deviation with the t distribution with n-1 degrees of freedom. The (X-Mean)/(S/√n) distribution is T.

Standard deviation confidence interval
(n-1)S22 distributed Chi-square with n-1 degrees of freedom.

n - sample size.
S - sample standard deviation.
SD - population standard deviation.