Standard Deviation of Sample Mean Calculator
Enter sample data to compute the sample standard deviation and the standard deviation of the sample mean (standard error of the mean).
Sample mean
19.5000
Sample SD
5.6125
SD of sample mean
2.2913
How to Use This Calculator
- Enter your sample observations.
- Review the sample mean and sample standard deviation.
- The standard deviation of the sample mean equals sample SD divided by √n.
- Use this value as the standard error when constructing confidence intervals for the mean.
Formula
Sample SD (s) = √[Σ(xi − μ)² / (n − 1)]
Standard deviation of sample mean = s / √n
The standard deviation of the sample mean is also known as the standard error of the mean (SEM).
Full Description
The standard deviation of the sample mean quantifies the variability of sample means around the population mean. As sample size increases, SEM decreases, reflecting improved precision.
Frequently Asked Questions
Is this the same as standard error?
Yes. The standard deviation of the sample mean is commonly called the standard error of the mean.
Why does SEM shrink with larger samples?
Because sample means average out noise; variability decreases with √n.
Can I use population SD instead?
If the population standard deviation is known, divide it by √n directly. Here we estimate it from samples.
What if all values are equal?
Sample SD and SEM are zero, indicating no variability within the sample.