Standard Deviation Calculator
Standard deviation answers the question averages hide: how spread out is the data? Two classes can both average 75 while one has everyone at 74-76 and the other ranges from 40 to 100 - the mean is identical, the standard deviations are worlds apart. Paste numbers separated by spaces, commas or new lines and this calculator returns the sample SD (the n-1 figure for data drawn from a bigger population), the population SD (when your data is everyone), the variance both ways, the mean, and the range.
The n-1 versus n choice is where most homework loses marks, so the note line states which divisor produced each number and when to use it: sample data reports n-1, a complete population reports n. Results are rounded to six decimals, datasets are remembered between visits, and it pairs with the average calculator for the rest of the summary statistics.
How to use
- Paste or type your numbers - any mix of spaces, commas and line breaks.
- Read sample SD, population SD, mean, variance and range instantly.
- Check the note for which divisor applies to your data before reporting.
Frequently asked questions
What is standard deviation?
The typical distance of data points from the mean. It is calculated as the square root of variance - the average of squared deviations - which restores the original units. Low SD means values cluster tight; high SD means they spread wide. For the dataset 2, 4, 4, 4, 5, 5, 7, 9 the sample SD is about 2.138.
When do I use sample (n-1) versus population (n)?
Use n-1 when your numbers are a sample estimating a larger population - Bessel's correction compensates for the sample mean underestimating spread. Use n only when you truly have every member: all of a class, a complete production run. When unsure with sampled data, the n-1 sample SD is the defensible default.
What is variance and how does it relate?
Variance is standard deviation squared - the same spread measured in squared units. The calculator shows both: variance feeds other statistics (tests, ANOVA), while SD is the one you quote because its units match the data - centimeters, dollars, points.
Does this handle negative and decimal numbers?
Yes - any finite numbers parse, including negatives and decimals, in any order. Tokens that are not numbers are ignored rather than breaking the run, so a stray label in pasted spreadsheet data will not sabotage the calculation.