Mean & Standard Deviation Calculator
Enter your data points below (comma, space, semicolon, or new line separated). Then click Calculate.
Accepted formats: 1,2,3 or 1 2 3 or one number per line.
What this calculator does
If you work with numbers, you often need two quick answers: the average and how much the values vary around that average. This calculator gives you both:
- Mean (arithmetic average)
- Population standard deviation (uses
n) - Sample standard deviation (uses
n - 1) - Helpful extras like count, sum, min, max, range, and median
That makes it useful for students, researchers, analysts, and anyone doing quick descriptive statistics.
Mean vs. standard deviation (plain English)
Mean
The mean tells you the center of your data. Add all values, then divide by the number of values.
Formula: Mean = (x₁ + x₂ + ... + xₙ) / n
Standard deviation
Standard deviation tells you how spread out your data is.
- Small standard deviation = values are close to the mean
- Large standard deviation = values are more spread out
This matters because two datasets can have the same mean but very different consistency.
Population or sample: which one should you use?
You’ll see two standard deviations in the result because each serves a different purpose:
- Population standard deviation (σ): Use when your data includes every value in the entire group of interest.
- Sample standard deviation (s): Use when your data is only a sample from a larger population.
In most practical data analysis situations, if you are estimating from a sample, use the sample standard deviation.
How to use this calculator
- Paste or type your numbers into the input box.
- Separate values with commas, spaces, semicolons, or line breaks.
- Click Calculate.
- Read the output metrics and choose population or sample standard deviation as needed.
Worked example
Suppose your values are: 10, 12, 14, 16, 18.
- Count: 5
- Mean: 14
- Population SD: about 2.828
- Sample SD: about 3.162
The values are symmetric around 14, and the standard deviation gives you a quick sense of the typical distance from the center.
Common mistakes to avoid
- Mixing text with numbers: Remove labels like “N/A”, “missing”, or units in the same cell.
- Using the wrong SD type: Population and sample standard deviation are not interchangeable.
- Ignoring outliers: Extreme values can pull the mean and inflate the standard deviation.
- Comparing different units: Always compare values measured on the same scale.
Why this matters in real life
Mean and standard deviation appear everywhere: exam scores, investment returns, quality control, health metrics, A/B testing, and machine learning feature analysis. If you can compute and interpret these two values, you already have a strong base in statistics.
Quick FAQ
Can I use decimals and negative numbers?
Yes. The parser accepts decimals (like 3.75), negatives (like -2), and scientific notation (like 1e3).
What if I only enter one value?
You will still get the mean and population standard deviation (which will be 0), but sample standard deviation is undefined for fewer than two values.
Does order matter?
No. Mean and standard deviation are order-independent statistics.
Bottom line
This calculator of mean and standard deviation is a fast, practical tool for descriptive statistics. Paste your data, compute instantly, and use the results to make better decisions backed by numbers.