What this mean and SD calculator does
This tool calculates the mean (average) and standard deviation (SD) from a list of numeric values. It reports both:
- Population SD (divide by n)
- Sample SD (divide by n - 1)
You also get useful supporting stats including count, sum, minimum, and maximum. That makes this calculator useful for statistics homework, lab summaries, and quick quality checks.
How to use it
Step 1: Paste your data
Enter numbers in the box. You can separate values with commas, spaces, semicolons, or new lines. Decimals and negative values are accepted.
Step 2: Choose decimal precision
Set how many decimal places you want in the output. For most reporting, 2 to 4 decimals is common.
Step 3: Click calculate
The tool instantly computes the results and displays them in a highlighted result panel.
Formulas used
Mean
Mean \( \bar{x} = \frac{\sum x_i}{n} \) where \(n\) is the number of observations.
Population standard deviation
Population SD \( \sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n}} \)
Sample standard deviation
Sample SD \( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} \)
Use sample SD when your data is a subset from a larger population. Use population SD when your dataset includes every value in the full population of interest.
Quick example
For data: 10, 12, 14, 16, 18
- Mean = 14
- Population SD ≈ 2.8284
- Sample SD ≈ 3.1623
Notice sample SD is slightly larger because of the \(n-1\) adjustment.
Common mistakes to avoid
- Mixing text with numbers (e.g., "12kg" instead of "12").
- Using population SD when the dataset is only a sample.
- Rounding too early before final interpretation.
- Comparing SDs across groups with very different units.
When mean and SD are most useful
Mean and SD are especially useful for roughly symmetric numeric data. If your data is heavily skewed or contains extreme outliers, consider adding median and IQR to your analysis. Still, mean and SD remain the most common summary pair in science, business, and education.