Free Online Standard Deviation Calculator
Calculate mean, variance, and standard deviation
Calculate mean, variance, and standard deviation from any data set.
8 numbers parsed
Mean
18
Pop. Std Dev (σ)
4.899
Sample Std Dev (s)
5.2372
Pop. Variance (σ²)
24
Sample Variance (s²)
27.4286
Count (n)
8
Sum
144
Min
10
Max
23
Range
13
Step-by-Step Calculation
Step 1: Find the mean
Mean = (10 + 12 + 23 + 23 + 16 + 23 + 21 + 16) / 8 = 18
Step 2: Find squared differences from the mean
(10 − 18)² = 64
(12 − 18)² = 36
(23 − 18)² = 25
(23 − 18)² = 25
(16 − 18)² = 4
(23 − 18)² = 25
(21 − 18)² = 9
(16 − 18)² = 4
Step 3: Find variance
Population variance (σ²) = 192 / 8 = 24
Sample variance (s²) = 192 / 7 = 27.4286
Step 4: Take the square root
Population std dev (σ) = √24 = 4.899
Sample std dev (s) = √27.4286 = 5.2372
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About this tool
Calculate the standard deviation, mean, variance, and other statistics from any data set with this free calculator. Paste or type your numbers — separated by commas, spaces, or line breaks — and get instant results including population and sample standard deviation, variance, sum, min, max, and range. The calculator parses flexible input formats and shows a count of detected values so you can verify your data was read correctly. Includes a worked example with step-by-step calculations showing how standard deviation is derived from the mean. Built for students, researchers, and anyone who needs quick descriptive statistics without opening a spreadsheet.
How to use Standard Deviation Calculator
- Enter data. Paste or type your numbers, separated by commas, spaces, or line breaks.
- Verify count. Check that the parsed number count matches your data set.
- View statistics. See mean, standard deviation, variance, and other descriptive statistics.
Frequently Asked Questions
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means values cluster near the mean; a high one means they are spread out. It is the square root of variance.
Population standard deviation (σ) divides by N (total count). Sample standard deviation (s) divides by N−1 to correct for the bias of estimating a population from a sample. Use sample SD when your data is a subset of a larger population.
1) Find the mean. 2) Subtract the mean from each value and square the result. 3) Find the average of those squared differences (variance). 4) Take the square root. That's your standard deviation.
It depends entirely on context. A standard deviation of 5 is tiny for stock prices but huge for exam scores out of 10. Compare it to the mean — a coefficient of variation (SD ÷ mean × 100) below 15% is generally considered low variability.
Variance is the average of the squared differences from the mean. It is standard deviation squared. While variance is useful in many statistical formulas, standard deviation is more intuitive because it is in the same units as the data.
Enter numbers separated by commas, spaces, line breaks, or any combination. The calculator parses your input and shows how many values it detected so you can verify.
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