## About This Tool

The online Standard Error Calculator is used to calculate the standard error of the mean of a set of numbers.

## Standard Error of the Mean

The standard error of the mean is the standard deviation of the sample mean estimate of a population mean. It is usually calculated by the sample estimate of the population standard deviation (sample standard deviation) divided by the square root of the sample size (assuming statistical independence of the values in the sample):

Where:

SEM = standard error of the mean

s = sample standard deviation (see formula below)

n = size (number of observations) of the sample

The following is the sample standard deviation formula:

Where:

s = sample standard deviation

x_{1}, ..., x_{N} = the sample data set

x̄ = mean value of the sample data set

N = size of the sample data set