Standard Deviation Calculator
Calculate population or sample standard deviation, variance and mean of a dataset. Get full statistics for any number list.
Comma-separated numbers, e.g. 2, 4, 4, 4, 5, 5, 7, 9.
Standard deviation
2.1381
Variance
4.5714
Mean
5
Sample divides by n−1; population divides by n. Use sample for a survey, population for a full census.
How it works
σ² = Σ(x − mean)² ÷ n (population) or ÷ (n−1) (sample). σ = √variance.
Example: [2,4,4,4,5,5,7,9] → σ = 2 (population).
Last updated: September 2026
How this calculator is verified
Checked by Rahim Virani on
- Sample (n-1) and population (n) denominators verified on the same dataset
- Variance reported as the square of the standard deviation, not independently computed
- Single-value input returns 0 rather than dividing by n-1 = 0
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Five students scored 62, 68, 74, 80 and 86 in a test. The mean is 74. The population standard deviation is about 8.49, meaning scores typically sit roughly 8.5 marks from the average, while the sample standard deviation is about 9.49. Enter these five marks, choose population if they are the entire class or sample if they are a subset, and the tool returns the mean, variance and standard deviation at once. A smaller standard deviation means the scores are more tightly clustered around the mean.
How to Use This Calculator
- Step 1: Enter your list of numbers, one per line, separated by commas or spaces.
- Step 2: Choose population if the list covers every observation, or sample if it is a subset drawn from a larger group.
- Step 3: Read the count, mean, variance and standard deviation shown together.
- Step 4: Compare the population and sample results by toggling the option, since the sample version divides by n minus 1.
Worked Example
Five students scored 62, 68, 74, 80 and 86 in a test. The mean is 74. The population standard deviation is about 8.49, meaning scores typically sit roughly 8.5 marks from the average, while the sample standard deviation is about 9.49. Enter these five marks, choose population if they are the entire class or sample if they are a subset, and the tool returns the mean, variance and standard deviation at once. A smaller standard deviation means the scores are more tightly clustered around the mean.
Tips and Common Mistakes
- •Tip 1: Use the sample option whenever your data is a subset, like one section of a class, since the n minus 1 adjustment gives a fairer estimate.
- •Tip 2: Check the mean alongside the standard deviation, because the same spread looks very different relative to a small or large average.
- •Tip 3: Watch for one outlier in the list, since a single extreme value inflates the standard deviation more than it shifts the mean.
- ✗Mistake 1: Forgetting to switch between population and sample, which changes the variance and standard deviation noticeably for small lists.
- ✗Mistake 2: Entering values with symbols like the rupee sign or percentage marks, which the parser may reject or misread.
Frequently Asked Questions
What is standard deviation?
It measures how spread out values are around the mean. A small standard deviation means values cluster tightly; a large one means they are widely scattered.
What is the difference between population and sample?
Population divides by n (you have all data). Sample divides by n−1 (you have a subset) to correct for sampling bias. Use sample for survey data.
How is standard deviation used in finance?
It measures investment volatility. A fund with a higher standard deviation has wider swings in returns — more risk.
Why does my result differ from Excel's STDEV?
Excel has two functions: STDEV.P for population and STDEV.S for sample. If your numbers are a subset of data, the sample result with n−1 matches Excel's STDEV.S.
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