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Paste values
Add test scores, measurements, or data points in any common separated format.
Free Standard Deviation Calculator
A standard deviation calculator shows how spread out a data set is from the mean. Paste scores, measurements, or classroom data to calculate sample or population standard deviation with variance and step-by-step work.
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Statistics calculator
Enter your data set
Sample result
Standard deviation: 7.13
8 values | denominator 7
Mean 84
Variance
50.86
Range
22
Minimum
72
Maximum
94
Sum
672
Sorted values
72, 78, 81, 83, 85, 88, 91, 94
Formula steps
- 1. Add all values and divide by count: mean = 84.
- 2. Subtract the mean from each value, then square each difference.
- 3. Add squared differences and divide by n - 1.
- 4. Take the square root: 7.13.
ValueDifferenceSquared
72-12144
78-636
81-39
83-11
8511
88416
91749
9410100
How to Use This Standard Deviation Calculator
2
Choose the formula
Use sample mode for a subset or population mode for the complete group.
3
Review the work
Check mean, variance, sorted values, squared differences, and final standard deviation.
Standard Deviation Calculator FAQ
What is a standard deviation calculator?
A standard deviation calculator measures how spread out a set of numbers is from the mean and shows the variance and square-root steps.
Should I use sample or population standard deviation?
Use sample standard deviation when your numbers are part of a larger group. Use population standard deviation when your numbers are the whole group.
What numbers can I paste into the calculator?
You can paste whole numbers, decimals, percentages, or currency-style values separated by commas, spaces, tabs, semicolons, or new lines.
Why does sample standard deviation divide by n minus 1?
Sample standard deviation divides by n minus 1 to correct for estimating spread from a subset instead of measuring every value in the population.
How can standard deviation support instruction?
Teachers can use standard deviation to discuss variability, compare data sets, and show students how one score differs from a group pattern.