Mean, Median and Standard Deviation Explained
The core statistics everyone should know — mean, median, mode, range and standard deviation — what each tells you, when averages mislead, and how the normal distribution ties them together.
Standard Error Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
Standard error of the mean
2.7386
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Standard Error Calculator
The Standard Error Calculator works out your standard error of the mean in an instant. Enter standard deviation and sample size and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the standard deviation.
- Enter the sample size.
- Read off your standard error of the mean — the calculator updates automatically, with no button to press.
Formula
The Standard Error Calculator uses the formula:
Standard error of the mean = Standard deviation ÷ √(Sample size)
Worked example
For example, with standard deviation of 15 and sample size of 30, the standard error of the mean is 2.7386.
| Standard deviation | 15 |
|---|---|
| Sample size | 30 |
| Standard error of the mean | 2.7386 |
|---|
Results are estimates for educational use, not professional advice.
Key terms explained
- Mean
- The average of a set of numbers — their sum divided by how many there are.
- Standard deviation
- A measure of how spread out a set of values is around their mean.
Frequently asked questions
Divide the standard deviation by the square root of the sample size. An SD of 15 with n = 30 gives a standard error of about 2.74.
It estimates how much the sample mean is likely to vary from the true population mean. A smaller standard error means a more precise estimate.
Standard deviation measures spread of individual values; standard error measures the spread of the sample mean and falls as the sample grows.
Increase the sample size. Because it divides by the square root of n, larger samples steadily shrink the standard error.
Enter the standard deviation. Enter the sample size. Read off your standard error of the mean — the calculator updates automatically, with no button to press.
Related guides
Standard Error Table: Standard error of the mean by Standard deviation
Reference table of standard error of the mean for Standard Error across a range of standard deviation values — exact, engine-computed figures you can read off at a glance.
How to Calculate Standard Error: Formula, Steps & Examples
Learn how to calculate Standard Error — the formula explained step by step, with worked examples and a free calculator to check your answer.