Statistics
Standard deviation calculator
Paste your numbers to get the standard deviation and variance — both sample and population — alongside the mean, so you can see not just the average but how much the data varies.
- Sample std. deviation (s)
- 13.4907
- Population std. deviation (σ)
- 12.3153
- Sample variance (s²)
- 182
- Population variance (σ²)
- 151.6667
- Mean
- 18
- Count (n)
- 6
Use the sample figures when your numbers are a sample drawn from a larger group; use population when they are the whole group.
What standard deviation tells you
Two data sets can share the same average yet feel completely different. Test scores of 70, 70, 70 and 40, 70, 100 both average 70, but the second is far more variable. Standard deviation puts a single number on that variability — how far, on average, the values sit from the mean.
Sample or population?
If your numbers are the whole group, use the population figure (σ). If they’re a sample you’re using to estimate a larger group, use the sample figure (s), which divides by n − 1 to avoid understating the spread. When in doubt with real-world data, the sample version is usually the safer choice.
Related
Start with the center of your data using the mean, median & mode calculator, then build real fluency in the Statistics subject.
Frequently asked questions
- What is standard deviation?
- Standard deviation measures how spread out a set of numbers is around their mean. A small standard deviation means the values cluster tightly near the average; a large one means they’re widely scattered.
- What’s the difference between population and sample standard deviation?
- Population standard deviation (σ) divides by n and is used when your numbers are the entire group. Sample standard deviation (s) divides by n − 1 and is used when your numbers are a sample from a larger group — the smaller divisor corrects a bias that would otherwise underestimate the spread.
- How is standard deviation related to variance?
- Variance is the average of the squared distances from the mean; standard deviation is its square root. Standard deviation is usually easier to interpret because it’s in the same units as the original data.
- What counts as a “high” standard deviation?
- There’s no universal cutoff — it depends on the scale of your data. Comparing the standard deviation to the mean (the coefficient of variation) is one way to judge whether the spread is large relative to the typical value.