Number Set Standard Deviation Calculator

Calculate population or sample standard deviation for a list of numbers.

How to use Number Set Standard Deviation Calculator

1. Enter Number Set Values as matching lists where weights are used; separate numbers with commas, spaces, semicolons or new lines. 2. Choose Population or Sample mode. 3. Select Calculate or press Enter, then read standard deviation. 4. Copy result copies the answer; Reset clears the form. Do not use thousands separators inside lists.

Why use this tool?

Check a descriptive-statistics exercise while distinguishing population and sample denominators.

How the calculation works

Find the arithmetic mean, add the squared deviations from that mean, divide by count for Population or count − 1 for Sample, then take the square root. Sample requires at least two observations. Entries are ordinary numbers. The result describes only the supplied list and makes no claim about a wider population. Results use up to six decimal places, or six significant digits in scientific notation for nonzero magnitudes below 0.000001. Calculations use browser floating-point arithmetic. Each list supports up to 20,000 numbers. Entry and result magnitudes must not exceed 9,007,199,254,740,991; unrepresentable variance or weighted products are rejected. General descriptive-statistics reference: https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm. Weighted conventions are defined explicitly on this page.

Example

For number set 1,2,3,10 in Population mode, the standard deviation is 3.535534.

Practical tip

Use Population when describing the complete set of interest, or Sample when using observations to estimate a wider population’s variability.