Standard Deviation Calculator
Find population or sample standard deviation instantly. Paste in a list of numbers and see the mean, variance, median, mode, and the full deviation breakdown.
Separate values with commas, spaces, or line breaks.
Results
Population statistics for 8 values
Count
8
Mean
21.25
Median
22
Mode
22
Range
18
Min
12
Max
30
Sum
170
Variance
31.6875
Standard Deviation
5.6292
Step-by-Step Breakdown
Standard deviation is based on the squared distance each value is from the mean.
Mean
21.25
Sum of Squares
253.50
Formula
σ² or s² = 253.50 ÷ 8
SD = √31.6875 = 5.6292
| Value | Value - Mean | (Value - Mean)² | Std Devs from Mean |
|---|---|---|---|
| 12 | -9.25 | 85.5625 | -1.6432 |
| 15 | -6.25 | 39.0625 | -1.1103 |
| 18 | -3.25 | 10.5625 | -0.5774 |
| 22 | 0.75 | 0.5625 | 0.1332 |
| 22 | 0.75 | 0.5625 | 0.1332 |
| 24 | 2.75 | 7.5625 | 0.4885 |
| 27 | 5.75 | 33.0625 | 1.0215 |
| 30 | 8.75 | 76.5625 | 1.5544 |
Sorted Data Distribution
See how far each point sits from the mean in standard deviation units.
Negative values are below the mean, positive values are above it, and values near 0 are close to average.
How to Use
- Paste or type your numbers into the input box using commas, spaces, or line breaks.
- Choose whether you want population standard deviation or sample standard deviation.
- Review the summary cards for mean, median, mode, variance, range, and standard deviation.
- Use the breakdown table to see each deviation from the mean and how the variance was calculated.
Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation uses every value in the full dataset and divides by N. Sample standard deviation is used when your data is only a sample of a larger population, so it divides by n - 1 to reduce bias.
What does standard deviation tell you?
Standard deviation measures how spread out your values are around the mean. A small standard deviation means the numbers cluster tightly around the average, while a larger one means the data is more spread out.
How is variance related to standard deviation?
Variance is the average of the squared deviations from the mean. Standard deviation is simply the square root of the variance, which brings the result back to the original unit of the data.
Why do some datasets have no mode?
A mode is the most frequent value. If every number appears only once, there is no mode because no single value occurs more often than the others.
Can I use decimals and negative numbers?
Yes. This calculator accepts whole numbers, decimals, and negative values, as long as they are separated by commas, spaces, or line breaks.