Please provide at least one numeric value. Sample statistics require at least two values. With one value, population variance and standard deviation are zero.
FAQ
Decimal separator
Use a decimal point (1.5). Separate values with commas, spaces, tabs, line breaks or semicolons. Do not use thousands separators. Use a decimal comma (1,5). Separate values with spaces, tabs, line breaks or semicolons, not commas. Example: 1,5; 2,5. Do not use thousands separators.
N / N−1
Use population values for the whole population of interest, and sample values to estimate a larger population from part of it.
Sample (N-1)
Population variance divides by N; sample variance divides by N−1. For independent observations from the same population with finite variance, sample variance is unbiased. Its square root, sample standard deviation, is not generally unbiased.
N = 1
Sample statistics require at least two values. With one value, population variance and standard deviation are zero.
Precision
Results and copies use at most 10 significant digits. Very small and large values use scientific notation. Inputs use JavaScript Number precision, about 15–17 significant digits. Digits lost on input cannot be recovered. Keep units consistent and check the count, minimum and maximum.
Copy result URL
The shared URL contains your input data. For confidential data, copy the results instead. A shared URL is not encrypted storage. This dataset is too large for a shareable URL. Copy the results instead.
Next step: compare with specification limits
If you also have lower and upper specification limits, use the Process Capability Calculator (Cp / Cpk) to compare process spread and centering with Cp, Cpk, Pp, and Ppk.
How to use Mean & Standard Deviation Calculator effectively
What this calculator does
This page summarizes a numeric dataset by count, mean, variance, and standard deviation. It calculates both population and sample formulas so you can match the method to the data you actually have.
Input format
Paste values separated by commas, spaces, or line breaks. Keep units consistent before pasting; the calculator treats every accepted token as one numeric observation in the same dataset.
Sample vs population
Population variance divides by N and describes the exact list you entered. Sample variance divides by N-1 and is usually the better choice when your data is a sample used to estimate a wider population.
Variance and standard deviation
Variance reports the average squared distance from the mean. Standard deviation is the square root of variance, so it returns to the original unit and is usually easier to explain in reports.
Outliers and review
Check the smallest and largest values before interpreting spread. A single unusually high or low value can move variance and standard deviation much more than it moves the mean.
Rounding policy
Calculations use the parsed numeric values and round only for display. If another tool differs slightly, compare whether it used sample or population variance and whether it rounded intermediate values.