Standard Deviation & Variance

Up to 20,000 unweighted observations. Decimal dot only; list commas, whitespace and semicolons separate numbers. CSV settings select one column; nonnumeric cells reject rather than being silently discarded. Quartiles use linear interpolation at (n−1)p (type 7). Statistics use approximate floating-point arithmetic; variance underflow requires rescaling. Sample variance is undefined with fewer than two values.

Integer, fraction, combinatorial and supported rational algebra operations use exact BigInt rational arithmetic, within explicit resource limits. Scientific functions, descriptive statistics and labeled irrational-root approximations use finite IEEE-754 numbers. Display precision never changes exact inputs, rational decisions or stored data.

Invalid input, incompatible dimensions, division by zero, unsupported domains or resource limits produce a clear message and clear prior outputs. Undefined sample variance with one observation is labeled explicitly. Reports are available only after a successful complete calculation.

No. Optional Statistics file selection reads UTF-8 locally and shows filename, size and loading/ready/error status. Failed imports preserve previous working text. Manual replacement, sample and clear remove obsolete file selections. Downloads and clipboard copies exist outside the application only when you request them.