How to use this mean and standard deviation calculator
This calculator helps you quickly compute the average (mean) and spread (standard deviation) of a dataset. Just paste your values, choose whether you want sample or population standard deviation, and click Calculate.
- Works with integers and decimals
- Accepts negative numbers
- Supports input separated by commas, spaces, semicolons, or line breaks
What mean and standard deviation tell you
Mean (average)
The mean is the center of your data. You compute it by adding all values and dividing by the number of values. It gives a fast summary of the “typical” value in your dataset.
Standard deviation
Standard deviation tells you how spread out values are around the mean. A small standard deviation means values are tightly clustered; a large one means values are more dispersed.
Sample vs population standard deviation
Choose the right mode based on your data source:
- Population standard deviation (σ): use when your data includes every value in the full group you care about.
- Sample standard deviation (s): use when your data is only a subset and you want to estimate variation of the full population.
Formulas:
- Population variance:
Σ(x - mean)² / n - Sample variance:
Σ(x - mean)² / (n - 1) - Standard deviation:
sqrt(variance)
Example
Suppose your values are 10, 12, 8, 11, 9.
- Mean = 10
- If treated as a population, standard deviation is lower
- If treated as a sample, standard deviation is slightly higher because of the
n - 1correction
This difference matters in analytics, quality control, A/B testing, finance, and scientific research.
Common use cases
- Comparing exam score consistency across classes
- Measuring volatility of monthly returns
- Evaluating process stability in manufacturing
- Summarizing experiment outcomes
Tips for accurate results
- Make sure all values are in the same unit (e.g., all in dollars or all in centimeters)
- Remove accidental text labels before calculating
- Use sample mode unless you truly have the full population
Quick FAQ
Can I include decimals?
Yes. Values like 3.14, 0.5, and -12.7 are fully supported.
Why is my sample standard deviation larger than population?
Because sample variance divides by n - 1, which adjusts for the uncertainty of estimating a full population from a sample.
Does this calculator store my data?
No. Everything is calculated directly in your browser.