Variance & Standard Deviation
Paste a dataset (comma- or newline-separated) and get the full suite of descriptive statistics, a histogram, and a Chebyshev-bound visualization that works for any distribution.
Dataset
Statistics
Histogram + Chebyshev band
Sample vs population std
Use sample standard deviation (n − 1 denominator) when your dataset is a random sample from a larger population — that's almost always the case in real data. Use population std (n denominator) only when your dataset is the entire population (e.g. the scores of every student in one specific class).
Chebyshev's inequality
For any distribution, at least (1 − 1/k²) of values lie within k standard deviations of the mean. So for k = 2, at least 75% of values lie within 2σ — regardless of whether the distribution is normal. This is a worst-case guarantee that always holds, unlike the 68-95-99.7 rule which only applies to normal distributions.
Who uses it
- Students learning descriptive statistics.
- Analysts exploring any new dataset.
- Six Sigma / quality engineers computing process variation.